Search

• This paper proposes a novel geometrically nonlinear topology and fiber orientation optimization method of composite structures using membrane-embedded model. • The fiber layers are volumetrically equivalent into membrane structure and then embed into matrix to realize the modeling of fiber-reinforced composites. • An optimized interpolation scheme for the membrane-embedded model is constructed for geometrical nonlinearity. • The proposed method is applied to the optimized design of cylindrical tube. The membrane-embedded model can be efficiently used in the finite element analysis of composite structures considering geometrical nonlinearity because of its practicability. This paper extends this model to the topology and fiber orientation optimization considering geometrical nonlinearity. The discrete design variables of topology and fiber orientation are continuous by the solid isotropic material with penalization method and bi-value coding parameterization method. An optimized interpolation scheme for the membrane-embedded model is constructed for geometrical nonlinearity. The filtering function is added to improve the convergence of the fiber orientation. To reduce the computational complexity, topology and fiber orientation are independently updated at each iteration during the optimization process. Numerical examples demonstrate the effectiveness of the proposed method for membrane-embedded composite considering geometrical nonlinearity. [ABSTRACT FROM AUTHOR]

This paper presents an efficient approach for modeling beams with crack propagation and discontinuities. The proposed approach relies on a globally enriched element within the framework of eXtended/Generalized Finite Element method (XFEM/GFEM), utilizing the principle of partition of unity to incorporate analytical global equations that mimic the beam's deformation in the longitudinal direction. This enables a substantial reduction in the number of elements required along the beam's length, resulting in a decreased computational burden of the model. A typical Euler–Bernoulli beam free-vibration problem is utilized to derive enrichment functions that enhance the approximation space in each strip of a complex cross-section beam. This problem provides an infinite number of vibration modes of the beam, depending on its end boundary conditions. Thus, one can also employ high-order modes to enhance the approximation of the solution. Previous works have demonstrated the method's effectiveness for homogeneous uncracked thin-walled beams. In this paper, the method is extended to address crack propagation problems. A convergence study is presented, assessing the effectiveness of the enrichment functions for various crack lengths and orientations where the cracks are modeled using the double nodes approach. Additionally, the crack propagation is modeled using cohesive zone elements for two and three-dimensional beams. The results demonstrate that our approach produces accurate results even with a small number of elements in the longitudinal direction. Furthermore, it is shown that including the higher deformation modes significantly improves the convergence when evaluating these problems. • A new approach for modeling cracked extruded beams is proposed. • The method relies on enhancing the approximation field with global enrichment functions derived from beams' free vibration. • The results show that the high vibration modes significantly improve the approximation of cracked elements. • The convergence of the method is investigated for various crack lengths and orientations. • The method is implemented for crack propagation utilizing cohesive zone elements. [ABSTRACT FROM AUTHOR]

• The thermal-mechanical behavior of the CHS T-joints with a welded collar plate under load, including the evolution laws of temperature field, strain, and displacement, is elucidated. • The welding residual effects on the CHS T-joints reinforced with a collar plate under load are revealed, where the thermal expansion and contraction deformation induced by high temperature dominates. • The applicability of existing specifications' strength reduction factors for the CHS T-joints reinforced with collar plate under load is discussed. • Size recommendations for the compressive strength of the CHS T-joints reinforced with collar plate under the chord preload are presented. The paper presents a comprehensive test program on collar plate reinforced CHS T-joints under different preload conditions, in order to investigate the effect of preload and welding thermal on reinforced joints. A total of four specimens, including specimens with and without preload when the collar plates were welded, were tested under brace axial loading. The test results, including welding temperature field, development of strain as well as welding residual deformation during the welding process are measured and presented in this paper. Furthermore, the failure model and compressive strength of the collar plate reinforced T-joints were determined. The test results demonstrated that the localized high temperature and rapid attenuation are the characteristics of the welding temperature field, which instantaneous peak temperature rose to 1808 °C at the local area and attenuated to 600 °C in an elliptic range of about 3.1 cm × 1.7 cm. The failure modes of collar plate reinforced CHS T-joints do not change with preload on the chord and welding thermal. Furthermore, preload on the chord reduces the compressive strength of reinforced joints. The strain distribution and residual deformation are affected by the thermal expansion and cold shrinkage, while the development of the welding temperature field is not affected by the preload. Finally, for compressive strength of CHS T-joints reinforced with collar plate by welding, the applicability of the reduction coefficient due to preload calculated by existing codes was assessed by comparing design values with experimental results. A finite element model by ANSYS, considering the welding heat, was established. Key parameters affecting the strength of the T-joint at the reinforced collar plate under load were identified through parametric study with finite element models. Construction recommendations of welded CHS T-joints are proposed. [ABSTRACT FROM AUTHOR]

• Novel insights into bolted connections to I-section webs and tubular column chords under out-of-plane loads via experimental testing. • Calibration of numerical models with experimental results for improved accuracy. • Extensive analysis of single and double bolt row connections in a parametric study to identify key parameters affecting face plate behavior. • Comparative analysis of existing methods for initial stiffness estimation using parametric analysis data, revealing their limitations. • Proposal of a refined analytical method for initial stiffness prediction, validated by experimental data. This paper presents a comprehensive investigation into the behavior of column webs/faces under out-of-plane loading within steel joints. The experimental component of the study involves testing five profiles, encompassing both open and closed sections with varying web slenderness and steel grade, subjected to direct out-of-plane tensile loads through bolted connections, utilizing both single and double rows of bolts. Concurrently, numerical simulations are conducted using finite element models, thoroughly calibrated with the experimental results. Drawing upon the calibrated numerical models, the paper systematically explores the influence of key parameters, including web slenderness, bolt arrangement, and analysis methods, through a parametric study involving 167 cases. A careful comparison of the observed behavior of the component from experimental tests, numerical models, and analytical models for initial stiffness is presented. Finally, the initial stiffness formulation derived from a recent model developed by the authors is improved to align with the observations from the experimental and numerical results. [ABSTRACT FROM AUTHOR]

• Experimental tests of CFDSST columns is presented in detail in this paper. • Using ABAQUS, 3D finite element CFFSST column models under axial compression are developed. • The fundamental behaviour of the CFDSST columns is discussed in detail. • The feasibility of current design codes to design the CFDSST columns is evaluated. • The proposed design model is shown to predict well the strengths of CFDSST columns. This paper explores the performance of concrete-filled double-skin (square stiffened hollow sections (SHS) outer and circular hollow sections (CHS) inner) steel tubular (CFDSST) stub columns under axial compression through experimental research and finite element analysis. The static axial compression experiments of six concrete-filled stiffened steel tubular (CFST) stub columns and fifteen CFDSST stub columns were conducted. The test method, process, phenomena and results are introduced in detail. The results indicated that compared with conventional CFST stub columns, CFDSST stub columns with reasonable hollow ratio can maintain load-carrying capacity, increase ductility and reduce self-weight. Increasing the strength of concrete is the most effective way to increase the load-carrying capacities of specimens when other variables remain constant. Finite element (FE) software was then utilised to generate the models of current specimens. The simulation results showed reasonableness and accuracy compared to the experimental results. Based on the validated models, parameter analysis was performed to reveal the influence of concrete strength, width-to-thickness ratio of the outer steel tube, stiffener depth, hollow ratio and yield strength of the outer steel tube on the ultimate strengths of the specimens. In addition, compared with test and FE strengths, the ultimate strengths predicted by available international codes were found to be quite conservative. Consequently, a formula was proposed to predict the load-carrying capacity of CFDSST stub columns considering the effective cross-sectional areas of the outer steel tubes and the strength of the confined concrete. The formula has been shown to provide the best prediction with acceptable reliability. [ABSTRACT FROM AUTHOR]

• A vertically oriented double corrugated steel plate shear wall is proposed. • The elastic buckling behavior of the wall is affected by the bolt spacing. • The compressive and shear stability coefficients are established. • The stability of the wall affects the correlation curve of N/N u - V / V u. As a novel structural component, the Double Corrugated Steel Plate Shear Wall (DCSPSW) is formed by interlocking two corrugated steel plates using high-strength bolts. This paper investigates the global stability design methods for DCSPSWs under combined shear and compression loads. Firstly, this paper examines the elastic buckling performance of DCSPSWs under horizontal shear loads and vertical compression loads separately. A bolt spacing factor (η) is introduced to reflect the influence of bolt spacing on the elastic buckling stress of DCSPSWs. Then, based on extensive finite element analysis (FEA), this paper investigates the elastoplastic buckling behavior of DCSPSWs under shear loads and compression loads and establishes the corresponding stability curves to predict ultimate load-bearing capacity. It is found that the stability coefficients (φ s and φ c) are closely related to the normalized slenderness ratios (λ ns and λ nc). A smaller bolt spacing allows the DCSPSWs to exhibit improved elastic and elastoplastic stability. Finally, this study investigates the load-bearing performance of DCSPSWs under combined shear and compression loads and proposes the design formulas. The results show that the correlation curve of N / N u - V / V u can provide a conservative and accurate design. The research findings of this paper are advantageous for promoting the application of the innovative DCSPSWs. [Display omitted] [ABSTRACT FROM AUTHOR]

• The paper presents a novel approach for calculating the elastic critical moment of corrugated web girders. • The results obtained with the new proposal significantly enhance the outcomes of previous methods. • The new proposal is based on closed-form formulas to determine equivalent section properties. Using corrugated web girders offers several advantages, including increased resistance to lateral-torsional buckling. Researchers have proposed various methods for determining the critical moment value as a function of the cross-sectional geometry. Previous studies have suggested that the enhanced critical moment is attributable to a larger warping constant. In this paper, we present the results of a systematic numerical study using finite element analysis on girders with various corrugated web shapes. Bending along the weak axis demonstrates that corrugated web girders possess a higher moment of inertia. Furthermore, our torsion linear analysis indicates that the increase in the critical moment is primarily due to a larger torsional constant. We compare the elastic critical moment values obtained using finite element linear buckling analysis to those derived from theoretical expressions that introduce equivalent section properties. Our results illustrate that the equivalent section properties method provides values that closely resemble those obtained using finite elements. Finally, we provide closed-form expressions that can be used to estimate equivalent section properties for any girder with a corrugated web. Our findings suggest that employing these expressions to calculate the critical moment yields results that are satisfactory when compared to those obtained through finite element linear buckling analysis. [ABSTRACT FROM AUTHOR]

• Inclined stiffened panels of the fuselage tail were tested under shear load. • The simulation model was established to predict the buckling, post-buckling, and failure modes of inclined stiffened composite panels. • The non-linear relationship between the debonding of the stiffeners and the skin was quantitatively analyzed. • The concept of equivalent skin thickness was introduced to analyze the influence of stringer configuration on panel buckling and post-buckling. The purpose of this paper is to investigate the buckling and post-buckling behavior of inclined stiffened composite panels under shear load. Two types of stiffened composite panels were manufactured and tested. The buckling load, ultimate load and other required structural properties of the inclined stiffened composite panels were obtained. The test results show that the failure load of the two types of panels are 5.79 times and 11.2 times of the buckling load, respectively, indicating that such inclined stiffened panels have a large post-buckling capacity. The damage modes of the panel are tearing around the skin near the clamps and debonding of the stringers from the skin. The combination of Hashin failure criterion, Cohesive model and nonlinear connection of clamp was used to conduct finite element modeling, which effectively predicts the buckling, post-buckling and damage modes of the structure. The buckling and post-buckling behavior of stiffened panels with different stinger configurations were discussed based on finite element analysis. The results show that when the initial buckling occurs between the stringers, the buckling and failure load of the stiffened panel become larger as the equivalent skin thickness between the stringers become larger. The research in this paper can provide reference for aircraft structural design. [ABSTRACT FROM AUTHOR]

• A modified force density method utilizing the concept of relation matrix was proposed in this paper. The modified method realized the establishment of a clear correspondence between members and nodes of cable net structures. • The modified force density method was used in the single-layer spoke cable net structures, and the effect of pretension on form-finding was analyzed. • The surface equation of circular single-layer crossed cable net structure without inner ring was derived. Combined with the modified force density method, the form-finding process of this type of structure is achieved. Form-finding is crucial for the design of typical cable net structures. Based on the original basic force density method, a modified force density method utilizing the concept of relation matrix is proposed in this paper. The modified method realizes the establishment of a clear correspondence between members and nodes of cable net structures. On the basis of the relation matrix, the find function is introduced, and the calculation formula of the modified branch-node matrix is derived. Meanwhile, the corresponding analysis steps and calculation process are given. The modified method is verified by the analysis of representative structural forms. The results show that for the saddle-shaped orthogonal cable net structure, the outcomes obtained from the modified force density method highly agree with the theoretical values, providing preliminary verification of the method's effectiveness. For single-layer spoke cable net structures, the relative error between the results calculated by the modified force density method and the numerical solution is approximately 5 %. The results of both methods are relatively consistent, and the relative error varies in relation to the ratio of inner ring cable force density to radial cable force density. For circular single-layer crossed cable net structure without inner ring, the results of the modified force density method are very close to the numerical solution. The maximum relative error between the two is 6.95 %, and the accuracy is higher than that of the nonlinear finite element method. The outcome of this research demonstrates the accuracy of the modified force density method and its effective application in the form-finding of actual cable net structures. [ABSTRACT FROM AUTHOR]

• Residual stress in steel column repaired by LC is measured using blind-hole method. • RS values in both the LC sheet and substrate are less than their respective yield strength values. • RS in LC sheet is much greater than that in substrate located far away from LC sheet. • A simplified RS model was developed by introducing the linear-exponential two-stage cooling curve. • RS results predicted by simplified RS model are in good agreement with experimental results. This paper presents a study that investigates the magnitude and distribution of residual stress (RS) in laser cladding (LC) repaired circular steel tubular columns. The study involves experimental tests and numerical simulation. The familiar blind-hole method is employed in the experimental investigation for two RS measurement tests, while the finite element method is used for numerical thermal-mechanical analysis to obtain the temperature field and RS field. The results indicate the presence of residual tensile stress in the LC sheet and its surrounding area. The RS in the LC sheet area and in the vicinity of the LC sheet-substrate boundary is much greater than that in the substrate area located far away from the LC sheet. Additionally, the RS in the LC sheet along the scanning direction is larger than that perpendicular to the scanning direction. Nevertheless, the RS values in both the LC sheet and substrate are less than their respective yield strength values. The temperature-time cooling curves obtained from the finite element analysis, which simulate the laser cladding process for repairing the circular steel tubular column, are used to develop a theoretical model for predicting the RS in the LC sheet. A simplified RS model is proposed based on the thermal-mechanical theory, utilising the linear-exponential two-stage cooling curve. Comparisons between the experimental results and the theoretical results that are predicted using the proposed simplified RS model show both results to be in good agreement. Therefore, the simplified RS model proposed in this paper is suitable for efficiently and accurately predicting the RS in LC sheet for circular steel tubular columns repaired by LC. [ABSTRACT FROM AUTHOR]

This paper is focused on the interaction of local modes in pin-jointed structures, with the aim to present an algorithm for the appraisal of the lowest critical load characterizing the structure under the effect of small imperfections. This interaction phenomenon is framed within Koiter's theory of elastic instability as a quartic system. First of all, the paper discusses the theoretical results of Koiter's theorem about the determination of the worst imperfection with respect to the critical load. In doing this, the characterization of the fold lines in the modal space is recalled and used for the purposes of the reformulation of the theorem. Then, a FEM code aimed at the determination of the most dangerous shape of the imperfection, and at performing the related sensitivity analysis, is presented. The basis of the code is a nonlinear model of a 3D rod equipped with a planar flexural deformation, within the context of Eulerian instability. Some numerical results having a practical interest are discussed. • Optimization is generator of structural instability. • Multimode buckling and erosion of structural ultimate load are associated. • Search for the worst imperfection to verify whether the optimization is not harmful. • Finite element analysis should be driven by mechanical awareness. [ABSTRACT FROM AUTHOR]

• The response of expansion tube structure (ETS) under the coupled loading of blast wave and detonation products is investigated. • The deformation mode of ETS transitions from expansion to one-end buckling, and then to both-ends simultaneous buckling as the scaled distance decreases. • The energy absorption (EA) of ETS exhibits distinct trends for different explosive masses in the scaled distance range of 0.4–0.5 m/kg1/3. • Under oblique impact, the percentage decrease in EA within the near-field range is higher than that at mid-to-far range. Expansion tube structures (ETSs) are extensively employed as energy-absorbing components in protective structures, yet their dynamic response under near-filed explosion remains inadequately understood, which limits their applications in anti-explosion devices. This paper investigates the response of ETS through explosion experiments, testing both the overpressure history of blast loading and the propagation process of detonation products. Following experimental verification, finite element models are established to obtain the characteristics of explosive loading and the response of ETS. The findings demonstrate that as the velocity of slider increases, the embedding displacement of ETS exceeding its limit induces a local buckling transformation in thin-wall tubes from one end buckling to simultaneous buckling at both ends. In the scaled distance range of 0.4–0.5 m/kg1/3, the energy absorption (EA) of ETS under different explosive masses exhibits distinct trends as the scaled distance increases, despite the decrease in peak pressure of blast loading. This is due to the coupling effect between blast shock waves and detonation products, resulting in diverse alterations in specific impulse with increasing scaled distance for varying explosive masses. In the case of oblique impact of blast loading, the percentage decrease in EA within the near-field range (Z < 0.8 m/kg1/3) is higher than that at mid-to-far range due to the uneven and random ejection of detonation products. The study elucidates the dynamic response of ETS under the coupled loading of blast wave and blast products, and provides valuable insights for optimizing designs of ETS utilized in near-field blast-resistant structures. [ABSTRACT FROM AUTHOR]

• The geometrically nonlinear free vibration analysis of multi-directional functionally graded porous sandwich plates is addressed for the first time. • A finite element model for nonlinear free vibration analysis based on shi's higher-order shear deformation refined theory with the von kármán assumption is developed and solved by an iterative algorithm with displacement control strategy. • New parametric studies regarding the influence of key input parameters such as material gradient indexes, pore coefficients, aspect ratios, thickness ratios, and boundary conditions on the nonlinear free vibration characteristics of the multi-directional functionally graded porous sandwich plates are conducted and discussed. Multi-directional functionally graded materials (MFGMs) have attracted significant research attention due to their advantages over one-directional FGMs. In MFGM structures, material properties can be tailored to grade in the required direction, overcoming practical problems like excessive temperature gradients or extreme deflections. This paper aims to investigate the nonlinear free vibration of MFG porous sandwich plates to improve their application in sandwich structures. The two outer layers of the plates are composed of three-directional functionally graded material (3D-FGM), with a bi-directional functionally graded material (2D-FGM) core layer. Additionally, the porosity distribution within the material matrix is assumed to be either even or uneven across the plate thickness. A higher-order finite element model based on Shi's plate theory and the von Kármán assumption is developed. The nonlinear free vibration frequencies are determined through the maximum vibrational amplitude using an iterative algorithm with a displacement control strategy. The accuracy and effectiveness of the proposed model are demonstrated through a comparison with published data. The results show that the vibration response is significantly influenced by various parameters. Specifically, increasing the material gradient indexes in the thickness direction enhances the frequency ratio, while increasing the gradient indexes in the length and width directions reduces it. Higher porosity coefficients in the core layer decrease the frequency ratio, whereas higher pore coefficients in the outer layers increase it. The additional knowledge gained from this study can help with future analysis and design procedures related to the nonlinear responses of these complex structures. [Display omitted] [ABSTRACT FROM AUTHOR]

This paper presents a new and general first-order Generalized Beam Theory (GBT) formulation for thin truncated conical shells with circular cross-section. With respect to the previous formulations (Nedelcu, 2011; Mureşan et al., 2019), which were developed for the linear stability analysis case and therefore only required the consideration of rather simple load cases, the present one keeps all membrane strain terms and therefore is able to enforce the standard GBT membrane strain assumptions exactly. Even if the resulting expressions and the boundary conditions are more involved, it is shown that it is possible to define the so-called GBT "Vlasov warping deformation modes" also in the conical case, which are essential for the overall performance of the formulation. For instance, these deformation modes allow finding the shell inextensible deformation shapes. Several numerical tests are presented to show the excellent performance of the resulting finite element, through comparison with refined shell finite element models, and the advantages offered by the GBT modal decomposition features. • A new and general first-order GBT formulation for conical shells is presented. • Vlasov warping deformation modes are consistently defined. • Inextensible deformation is readily identified. • The examples show that the proposed formulation is very accurate and efficient. [ABSTRACT FROM AUTHOR]

• The compressive behaviour of S690 high strength steel welded π-shaped and cruciform sections is studied. • Twenty stub column tests on S690 high strength steel welded π-shaped and cruciform sections are conducted. • FE models are developed to validate against the test results, and then used to conduct parametric studies. • Current design codes are assessed against test and numerical results. This paper reports experimental and numerical investigations into the cross-sectional behaviour and resistances of S690 high strength steel welded π-shaped and cruciform section stub columns under compression. An experimental investigation was firstly carried out on five S690 high strength steel welded π-shaped sections and five S690 high strength steel welded cruciform sections (covering both non-slender and slender sections) and included material tensile coupon tests, initial local geometric imperfection measurements and twenty stub column tests. The experimental investigation was supplemented by a numerical modelling investigation, where finite element models were firstly developed to simulate test structural responses and subsequently adopted to conduct parametric studies to generate further numerical data. On the basis of the obtained experimental and numerical data, the relevant design rules for high strength steel welded sections under compression, as set out in the European code, American specification and Australian standard, were assessed. The assessment results indicated that (i) the European code and American specification led to overall accurate and consistent cross-section compression resistance predictions for S690 high strength steel welded π-shaped sections, but provided slightly conservative and scattered resistance predictions for their cruciform section counterparts, and (ii) the Australian standard was accurate and consistent when used for non-slender S690 high strength steel welded π-shaped sections, but the design resistances were conservative and scattered for slender S690 high strength steel welded π-shaped sections as well as non-slender and slender S690 high strength steel welded cruciform sections. [ABSTRACT FROM AUTHOR]

• A free and random vibration model for double-layer lattice truss sandwich plates is proposed. • Good accuracy of the natural frequency and random response of double-layer lattice truss sandwich plates is achieved. • The effects of material properties and geometric parameters on free and random vibrations are illustrated. In this paper, Legendre–Ritz solutions for vibration characteristics of double-layer lattice truss sandwich plates are proposed based on three-dimensional (3-D) elasticity theory. Double-layer lattice truss sandwich plates consist of three face sheets and two cores. The face sheets are composed of fiber-reinforced composites and the cores are composed of pyramidal lattice trusses made of isotropic materials. The pyramidal lattice core is equated to a homogeneous plate according to equivalence principle. Based on 3-D elasticity theory and pseudo excitation method (PEM), each layer's energy expressions of double-layer lattice truss sandwich plates are constructed. After that, Legendre polynomials are adopted to describe displacement components in length, width and thickness directions. On this basis, the Rayleigh-Ritz method is used to solve energy functions to obtain motion equations of double-layer lattice truss sandwich plates. The accuracy and validity of the present method are corroborated by comparisons with references and finite element method (FEM). Additionally, in order to find out effects of relevant parameters on dynamical characteristics of double-layer lattice truss sandwich plates, parametric studies are carried out by means of some numerical examples. [ABSTRACT FROM AUTHOR]

• The inherent strain method significantly reduces running time. • Deposition along crack is more effective than along loading directions. • Optimal in-plane dimensions and maximum thickness of deposited WAAM were achieved. • Maximum stresses notably decrease by using a suitable deposition strategy. Wire and arc additive manufacturing (WAAM), also known as wire arc directed energy deposition (WA-DED), offers valuable capabilities not only for manufacturing but also for strengthening and repairing aging components. This paper employs the finite element (FE) method to investigate the influence of deposition parameters on the strengthening efficiency of damaged steel plates strengthened by WAAM material. The study calibrates the inherent strain method (ISM) with thermo-mechanical analysis to accurately predict residual stresses (RS) in manufactured samples, demonstrating that the ISM enhances computational efficiency while effectively predicting RS. It thoroughly examines key parameters such as the deposition direction, maximum thickness, and the geometric configuration of the WAAM material, including shapes and in-plane dimensions. The results indicate that deposition perpendicular to the loading direction provides better performance compared to deposition along the loading direction as it induces less normal and through-thickness stresses. Furthermore, this research determines the optimal maximum thickness for the WAAM material, showing that an increase in thickness can lead to higher maximum tensile stresses at the interface between the newly WAAM material and the underlying base plate. The study also establishes the optimal in-plane dimensions for the WAAM material. The results suggest placing the maximum thickness of WAAM material near the damaged area and gradually decreasing it in two directions to ensure sufficient stiffness around the cracked area, while avoiding an abrupt change in stiffness. This approach generates appropriate compressive stresses around the crack tip and decreases maximum tensile stresses in the plate. The study further illustrates that employing a proper printing strategy without a subsequent machining process can effectively reduce the maximum tensile stress in the steel plate while minimizing material usage. [ABSTRACT FROM AUTHOR]

• An adaptive modeling methodology which allows a local and optimal choice of theory is proposed. • The methodology proposed, based on a 3D geometry discretized with solid elements, avoids the difficulties of connecting different types of finite elements. • Beam or shell displacement fields are directly applied on the solid finite element model. • The methodology proposed leads to a significant reduction of the number of degrees of freedom and especially the number of floating-point operations. • The methodology proposed is particularly relevant for variability calculation or optimization techniques, which generally require a large number of finite element analyses. In the standard finite element procedure, the user chooses himself which mechanical theory will be used for a given application. To this end, he relies on some rules acquired through experience or some theoretical consideration. But choosing an appropriate theory may be a difficult task when geometry, boundary conditions, loadings, and materials are complex. This paper aims to define an adaptive methodology to identify, in the context of linear static analysis, optimal finite element models from a theory choice point of view. A criterion is defined to choose, in each part of the structure, the relevant mechanical theory: solid, shell or beam. A solid mesh is defined for the whole structure while specific solid-shell or solid-beam approaches are used in shell or beam areas respectively. This avoids the construction of mid-surface or mid-axis geometries from solid ones, which is a complicated task, in particular for industrial applications. Kinematic relations between nodes are imposed to apply the displacement fields of shell or beam theories. This leads to a set of linear equations which are used for eliminating slave degrees of freedom. The methodology proposed can also be interpreted as a model size reduction method, compared to a complete solid approach. The effectiveness of this approach is demonstrated through two numerical examples, including academic cantilever structures and an industrial multilayered composite structure. [ABSTRACT FROM AUTHOR]

• Developed a comprehensive approach that integrates theoretical analysis, finite element modeling, and experimental validation to achieve uniform deformation of forged rings and minimize defects. • Introduced the isothermal field method for designing ring preforms of irregular cross-section rings. • Employed a combination of isothermal field method, finite element simulation, and intelligent optimization algorithms to determine the reasonable size range of preforms. • Through comprehensive consideration of various forming preforms, rational ring preforms were obtained through redesign. One of the main challenges faced by the profiled ring rolling (PRR) process is to ensure the deformation uniformity of the ring, which is closely related to the design of the ring preform. The paper explores the application of the isothermal field method (IFM) in designing preforms for PRR processes, targeting the aerospace sector's high-end equipment manufacturing. Through the integration of advanced computational models and practical design principles, a comprehensive approach involving IFM, finite element simulation, support vector machine modeling, and genetic algorithm optimization is employed to determine the geometric dimensions of rational preforms. The material flow behavior during the PRR process is analyzed, and the effects of different isotherms combinations on strain, stress and temperature distribution are discussed. The findings demonstrate that adjusting the preform's shape during the section forming stage can optimize the uniformity of strain, stress, and temperature within the forging. The stable ring rolling process revealed no macroscopic or microscopic defects, validating the design method of ring preform based on IFM is reasonable. The research contributes to advancing near-net shape forming technologies, offering a novel approach to preform design that marries theoretical analysis with practical manufacturability considerations. [ABSTRACT FROM AUTHOR]

• Buckling and vibration of AFG-nanobeam is studied with nonlocal integral models. • Finite element model with Lagrangian multiplier method is developed to obtain the numerical solution. • GDQM is developed to validate the efficiency and accuracy of finite element method. • The effect of AFG index on buckling and vibration of nonlocal nanobeam is studied. This paper presented an efficient finite element formulation for analysis of the buckling and free vibration of the axial functionally graded (AFG) Euler-Bernoulli nanobeam based on minimum total potential energy principle with linear constraints. The stress- and strain-driven two-phase local/nonlocal integral models are utilized to address small scale effects. The material properties of the AFG nanobeam vary exponentially along the axial direction. The nonlocal integral constitutive equation can be equivalently transformed into a differential equation with two constitutive boundary conditions. The governing equation and standard boundary conditions are derived via Hamilton's principle. The weak form associated with total potential energy is derived and the constitutive boundary conditions can be converted to external forces at the boundaries. By employing a numerical solution methodology on the basis of the finite element method (FEM) together with Lagrangian multiplier method (LMM), a unified finite element formulation based on stress- and strain-driven two-phase local/nonlocal elasticity is constructed to obtain the critical buckling load and vibration frequency. Meanwhile, the numerical results obtained through generalized differential quadrature method (GDQM) validate the efficiency and accuracy of the present results. The influence of gradient index, nonlocal parameter and local phase parameter on buckling and free vibration of AFG Euler-Bernoulli nanobeam is investigated in detail under different nonlocal models and boundary conditions. It is demonstrated that the gradient index has more effect on mode shapes than the buckling load and vibration frequency between the local stress- and strain-driven two-phase local/nonlocal models. [ABSTRACT FROM AUTHOR]

• A frame reinforced cell with superior and consistent bi-stable property is proposed and fabricated. • The proposed cell increases flexibility in designing geometric parameters that enable bi-stability. • The proposed metamaterial exhibits programmability with its mechanical response linearly correlating with the number of cells. • The cushioning performance is investigated through the analysis of peak force and energy trapping mechanism. Curved beams are a class of elements capable of bi-stability and can be used to construct multi-stable metamaterials. These materials leverage elastic snap-through in curved beams to transition between multiple stable states, effectively achieving energy absorption and trapping. The elastic deformation allows the structure to be used repetitively. However, the conventional curved beam unit cells design process omits the influence of supporting frames, resulting in inadequate constrains of the beam in the fabricated metamaterials. Its mechanical properties and number of stable states can be significantly diverged from theoretical predictions. This paper presents a novel multi-stable metamaterial with improved and consistent energy trapping ability based on frame reinforced curved beams. Comparative finite element analysis of three unit-cell types demonstrates the superior bi-stability of the proposed cell. Moreover, parametric analysis reveals the proposed cell has a wider range of parameters that can achieve bi-stability. The mechanical properties of the single cell and the 2 × 2 metamaterial are obtained by compression tests. The results validate the linear mechanical response that correlates with the number of unit cells which allows optimal programming of multi-stable metamaterials. Finally, plate impact test is conducted to investigate and analyze the cushioning performance of the multi-stable metamaterial. [ABSTRACT FROM AUTHOR]

• The mechanical behavior is studied on the FGM pipeline in geohazard area. • An S-shape profile is introduced to describe the deformation of the FGM pipeline. • Explicit expressions are obtained to predict the yield displacements and strains. • The present derivations are verified validly by the numerical results. • Material and geometric parameters are examined to evaluate the mechanics of the FGM pipeline. This paper focuses on the mechanical performances of the buried pipelines with functionally graded materials (FGM) subjected to strike-slip faults. A refined displacement function is introduced to derive the fault displacement and the strain distributions. The yield fault displacement is obtained by using the classical beam theory and the first yielding scheme. A finite element model is developed to verify the present derivations, and the verification indicates that the numerical results are in close agreement with the present analytical predictions characterized by the yield displacement and the strains, respectively. Finally, a parametric analysis is carried out to assess the factors that impact the performances of FGM pipelines, such as the diameter-to-thickness ratio of the pipeline, volume fraction exponent, fault inclination angles, the properties of the soil, and so on. [ABSTRACT FROM AUTHOR]

• A pseudo-static test research of special-shaped concrete-filled steel tube specimens was carried out under combined compression and torsion. • The finite element model for SCFSTs was developed and parametric analysis was conducted. • Calculation method for the T / T u - N / N u bearing capacity correlation curve were proposed. This paper discussed the combined compressive and torsional performance of special-shaped concrete-filled steel tubes (SCFST) columns. A pseudo-static test research of eight specimens including two kinds of stiffening forms was carried out under compression and torsion. The investigated factors include section shape, stiffening form, stiffening position and axial compression ratio. From the test, specimens presented the characteristics of compression-torsion failure. The steel tube experienced buckling deformation and separated from the concrete at the middle and bottom of the column. The welds of some specimens cracked from the top to the bottom at the concave corner during the stage of decreasing load capacity. This resulted in localized crushing and the generation of torsional oblique cracks in the concrete. The hysteresis curves of the SCFST columns were relatively full in spindle shape without obvious pinching phenomenon, representing a good energy dissipation capacity. The ductility of the multi-cell CFST (MCFST) column is slightly better than that of the tensile-bar stiffened CFST (BCFST) column. There is a positive correlation between the torsion bearing capacity and parameters, such as the column limb width-thickness ratio, steel tube thickness and yield strength. When the axial compression ratio is less than 0.5, the axial compression can improve the torsion bearing capacity; when the axial compression ratio exceeds 0.5, the existence of axial compression will weaken the torsional capacity. The finite element model was established for parameters analysis, and calculation method for the T / T u - N / N u bearing capacity correlation curve was proposed, and the calculation results are more conservative and have certain safety reserve. [ABSTRACT FROM AUTHOR]

• A lightweight metamaterial plate for low-frequency and broadband vibration attenuation. • An ideal attenuation band generated based on the effect of acoustic black hole coupling with local resonance. • Extended applications on vibration reduction and isolation. • Experimental validation for practical applications. Acoustic metamaterials with bandgap properties can lead to effective vibration attenuation in a targeted frequency range. In this paper, a novel locally resonant metamaterial plate is proposed, connected with acoustic black hole (ABH) resonators. The structure is shown to achieve low-frequency and broadband vibration absorption. The proposed microunit design consists of three parts: the ABH resonator, supporting beams as the connector, and the frame (FC-ABH). The modal characteristics of the microunit and the dispersion relation of the infinite periodic FC-ABH structure are calculated by both Gaussian expansion method and finite element method. By the effects of flexural wave absorption of ABH coupled with the local resonance mechanism, a low-frequency and broad vibration attenuation band can be generated. When the damping of materials is included, the attenuation band can be further widened, with relative bandwidth measured by the experiment up to 0.93. The results of numerical simulations and experimental tests demonstrate that the finite periodic FC-ABH can act as an effective vibration absorber and isolator. The proposed structure may provide new ideas for the design and application of broadband vibration mitigation metadevices. [ABSTRACT FROM AUTHOR]

• A DE-GDQ algorithm in free vibration analysis of shells of revolution with free-form meridian and their combined structures is proposed. • A complete solution procedure for free vibration analysis based on 3D inverse modeling, FSDT and DE-GDQ is established. • Validated numerically the reliability and accuracy of the DE-GDQ algorithm on multiple models, different boundary conditions and types of materials. In this paper, a data-driven enhanced generalized differential quadrature (DE-GDQ) algorithm in free vibration analysis is proposed, which can be applied to shells of revolution with free-form meridian and their combined structures. According to first order shear deformation theory (FSDT) and Hamilton's principle, the governing equation for doubly-curved shells is obtained. The general boundary conditions are considered through artificial springs. Then the GDQ is introduced to solve the governing equations and the DE-GDQ is proposed on the basis of GDQ. After a detailed solution procedure of DE-GDQ is introduced and the convergence analysis is finished, multiple models and boundary conditions are validated including shells of revolution with conic section meridian, Haack series meridian, rational Bézier curve meridian. Isotropic materials and anisotropic materials including functionally graded (FG) materials are both verified. The free vibration analysis of combined structures is also finished and compared with finite element method (FEM). The comparison among DE-GDQ, GDQ and FEM shows that the DE-GDQ has greater advantages in terms of calculation efficiency, accuracy, and scope of application. [Display omitted] [ABSTRACT FROM AUTHOR]

• 2D and 3D multi-material lattices were designed and manufactured. • Analytical models were modified to be applicable to the multi-material lattices. • Homogenization-based models were applied to the designed lattices. • A comparison was conducted between the developed models, FEA, and experiment. • Anisotropy of the 3D lattice was studied with different material arrangements. Advances in multi-material additive manufacturing have opened unprecedented new opportunities for the design and manufacture of lightweight multifunctional structures. The ability to create complex topologies, at a relatively fine resolution, in addition to controlling the material composition on a voxel basis have significantly expanded the design space. To explore this large design space efficiently, accurate and cost-effective modeling tools are essential. In this paper, mechanics-based models for predicting the elastic properties of multi-material 2D and 3D lattice structures are developed or extended. The outcomes are compared with the predictions obtained from finite element models and experimental data. The results reveal that the adapted analytical models demonstrate good accuracy in predicting the elastic modulus of multi-material lattices for relative densities up to approximately 25 % while have considerably less computational cost compared to finite element using solid elements (providing the most accurate results in comparison with experiment). Careful consideration of the accuracy of the predictions is necessary for the use of these models for lattices with high relative density values. Besides, several homogenization-based models were studied to investigate their applicability to multi-material lattice structures when the assumption of scale-separation is considered valid. The capability of these models in predicting the whole elasticity tensor and the potential of multi-material lattices in manipulating the anisotropy are demonstrated. Finally, the introduced prediction frameworks are compared in order to provide an overview of their respective advantages and disadvantages in the case of multi-material lattice structures. [Display omitted] [ABSTRACT FROM AUTHOR]

• Repair of CFRP with asymmetric damage through double-sided adhesive patch. • Investigation on the mechanical performance of the repaired CFRP with different bondline thicknesses. • A numerical damage model was constructed using FEM, aiding the analysis of damage evolution and failure mode in the repaired CFRP with different bondline thicknesses. As a common CFRP repair method, double-sided adhesive patch has been widely used in the automotive and aeronautic industry. More specific research is thus needed to help better understanding the effect of repairing parameters on the mechanical performance of CFRP structures after patch bonding. In this paper, experimental and Finite Element Modelling (FEM) efforts were made on the adhesive repaired CFRP laminate with different bondline thicknesses. Artificial damage was prefabricated in the centre of the CFRP laminate, which was then repaired through double-sided adhesive patch. Quasi-static tensile tests were conducted on the repaired specimen up to failure, to obtain the load-displacement curves. With a bondline thickness of 0.5 mm, the repaired CFRP structure reached its maximum peak load, increased by 25.3% and 26.4% compared to 0.2 mm and 1.0 mm bondline thicknesses, respectively. SEM observations were used to analyse the influence of adhesive thickness on the fracture modes. Combined with Cohesive Zone Model (CZM) for the adhesive layer and Hashin damage criterion for the CFRP, the FE model of the CFRP laminate repaired with double-sided adhesive patch subjected to tensile loading was established. Finally, the damage evolution as well as the failure modes in the parent laminate and adhesive layer with different bondline thicknesses were compared and analysed. It was revealed that bondline thickness can effectively affect the mechanical performance of CFRP laminate after adhesive patch repair. [ABSTRACT FROM AUTHOR]

In this paper, a bionic bamboo beam composed of bionic bamboo tubes and bionic bamboo diaphragms is first presented, which is inspired by the macro structures of bamboo due to lightweight characteristics of bamboo in nature. Then, the bending model of bionic bamboo beam is established on the basis of the Euler-Bernoulli beam theory. The correctness of the model is verified by comparing the results by its own compiled code with those by the finite element method (FEM). The effects of wall thickness of bionic bamboo tube, number of bionic bamboo diaphragms and wall thickness of bionic bamboo diaphragm on the bending characteristics of bionic bamboo beams are also analyzed. On the basis of that, the lightweight design of bionic bamboo beam is established by using the response surface method (RSM). The results show that the P10N2 is 3.9% lighter than hollow beam C10T7, and 45.1% lighter than solid beam S10B. Further, the three point bending test is used to verify the correctness of the optimization results. Test models of P10N2, C10T7 and S10B are obtained by using the SLA 3D printing technology. Experimental results show that the relative bending resistance of P10N2 is 234% of hollow beam C10T7 and 271% of solid beam S10B, respectively. It is verified that P10N2 is the optimized lightweight bionic bamboo beam. The research in this paper provides new ideas and methods for the design of beams and rotors. • A bionic bamboo beam was designed. • The bending model of bionic bamboo beam is established. • The bending characteristics of bionic bamboo beams are analyzed. • Lightweight design of bionic bamboo beam has been carried out. • The research provides a new idea for the design of beams and rotors. [ABSTRACT FROM AUTHOR]

The concept of local buckling of compressed isotropic cylindrical shells is developed in this paper. Buckling of axially compressed cylindrical shells under different types of local perturbations has been studied in many theoretical and experimental researches. Different methodologies, based on these studies, were suggested for design buckling load estimation. However, in most calculations and experiments only two classical boundary conditions were considered: fixed displacement of the shell edges in the axial direction or fixed and uniformly distributed compressive load. Both of them are hard or even impossible to realize in practical applications. In the present paper we studied the shell behaviour with 6 different types of boundary conditions, which included the above mentioned two types. We considered shell loading through rigid plates with different types of possible displacements (degrees of freedom) and through stiffening ribs at the edges of the shell. Two theoretical methods were applied: numerical (finite element method) and analytical (Pogorelov's geometrical method). Lateral force was applied as a perturbation and stability of the shell under load combination was studied. The results of calculations were compared with obtained experimental data for validation of numerical solutions. Then metastability and post-buckling behaviour of the structure was studied using theoretical and experimental methods. In particular the interval of existence and stability of post-buckling equilibrium states of the shells with one or several buckles was studied systematically. The post-buckling equilibrium paths and corresponding energy barriers for all mentioned types of boundary conditions were analyzed. Parametric analysis of boundary value problem allowed to establish the main (Batdorf) structure parameter. Formula for design buckling load was suggested and discussed. • The effect of boundary conditions on stability of compressed cylindrical shells under local perturbations is studied. • Results obtained by numerical method are validated by comparison with experimental data. • Post-buckling behaviour and metastability of the structure was studied using analytical, experimental and numerical methods. • Analysis of boundary value problem allowed to establish the main (Batdorf) structure parameter. • Formula for design buckling load is suggested and discussed. [ABSTRACT FROM AUTHOR]

In the current study, deflections, buckling loads, natural frequencies and the corresponding mode shapes and forms for BDFG thin-walled tapered beams of generic open/closed/open-closed sections are examined using the finite element method. A tapered thin-walled beam finite element with the seven degrees of freedom at each node is investigated. A rigorous expression for strains based on the membrane theory of shells is considered. The flexural stiffness matrix, geometric stiffness matrix and the consistent mass matrices are developed in a companion paper. Using the present theory, one is able to investigate various torsional, flexural static and dynamic systems. Examples are presented and comparisons are made with the existing available literature. With the modifications of axial, coupled and bending rigidities one will be able to investigate composite beams with fibre reinforced composite laminates. • Static, buckling and vibration behavior for BDFG tapered beams of thin-walled sections is investigated. • Different material and geometric variations are considered in this paper. • Considering any reference point and axes passing through it, BDFG tapered Euler thin-walled beam analysis becomes simpler. • Different types of thin-walled both open/closed cross sections are considered. • The validity and the adequacy of the theory are verified by many examples through comparisons made by other investigators. [ABSTRACT FROM AUTHOR]

This paper presents a detailed treatment of the formulation for buckling and free vibration analysis of Bi-Directional Functionally Graded (BDFG) Thin-Walled non-prismatic beams of generic open/closed cross section. The theory developed is limited to small strains, moderate deflections and small rotations. It is based on the assumption that the shear strain on the mid-surface contour of the cross section of the member is neglected. Using the membrane theory of shells rigorous expressions for strains are obtained by which the effect of nonlinear tapering is considered. The material properties are assumed to be graded both in the longitudinal and depth-wise directions of the plate segment of the thin-walled beams. The governing equations are developed defining the displacements with reference to any arbitrary point (say geometric centre) and get away with the usual shear centre and centroid. For computer solutions for classical buckling and vibration analyses, the Finite Element Method is used. Simpson's rule of numerical integration is adopted for the computation of axial, coupled and bending rigidities as well as inertial properties of the plate segment and the Gaussian Quadrature of numerical integration is used for the computation of flexural stiffness, geometric stiffness and mass matrices of an element over the length of the beam. Critical buckling loads and the natural frequencies and their corresponding buckled and mode shapes for various examples are obtained by solving as an eigen-value problem and compared with the published results in the companion paper. • Using Membrane theory of shells, rigorous expressions for strains have been developed. • The governing equations for BDFG thin-walled beams are arrived at defining displacements with respect to any arbitrary point. • Different material and geometric variations are considered in this paper. • Property constants are determined using Simpson's rule and elements of Stiffness, Mass matrix using Gaussian quadrature. • Static, Stability and Free vibration of BDFG tapered beam of generic open/closed sections can be investigated. [ABSTRACT FROM AUTHOR]

Thin-walled structural members have complex behavior. It is usual to interpret the complex behavior as the superposition of simpler behavior components, like global, distortional, local, in-plane shear and transverse extension. When the standard shell finite element method is employed for the analysis, the behavior components are not separated, and the results can be difficult to interpret due to the complexity of the deformations. The results are more meaningful if identified, i.e., if the participations of the behavior components are quantified. Methods for the formal identification of the deformations have already been proposed, by using either the modes of generalized beam theory, or the basis functions of the constrained finite strip method. In this paper a newer and more general method, the constrained finite element method is used. Since this method can handle a wide range of thin-walled members, including members with holes, or members with varying cross-sections, or even stiffened plates, the identification can readily be applied to various thin-walled members. In the paper some particularities of the identification method are highlighted, as well as several sample examples are presented and discussed. • The constrained finite element method is applied to modal identification. • Participation of global, distortional and local deformations are objectively calculated. • In the case of simple problems the results are similar to those from other identification methods. • The new method can handle a wide range of thin-walled members. • Examples are shown: channel members with holes, channel members with non-uniform cross-section, and stiffened plates. [ABSTRACT FROM AUTHOR]

The shear stability of steel webs near the support section for long-span composite girders with corrugated steel webs is one of the main control factors for structural safety, which should be paid special attention to. Generally, concrete is poured on the inner side of corrugated steel webs to improve its shear stability, but encased concrete increases the weight of the girder, raises the difficulty of the construction process, and reduces the efficiency of the prestressing application. This paper proposes a new type of stiffened corrugated steel webs at the support area by adopting vertical or/and horizontal stiffeners instead of encased concrete. In order to explore the shear performance of proposed stiffened corrugated steel webs, experimental and numerical investigations were carried out in the present paper and the companion paper [1] , respectively. Four steel I-girders with corrugated webs considering different stiffener arrangements were designed and tested under shear loading. The failure modes, shear strength and stiffness, strain distributions were obtained and analyzed in detail. The test results show that all specimens failed due to interactive shear buckling of corrugated steel web; shear buckling occurred between horizontal stiffeners and bottom flange for horizontal stiffened corrugated steel webs, but extended to the entire height for vertical stiffened corrugated steel webs, the stiffeners distorted associated with the deformation of corrugated steel web. Shear strength of corrugated steel webs can be improved by vertical and horizontal stiffeners. The vertical stiffeners do not affect the "accordion effect" of corrugated steel webs, but the horizontal stiffeners increase the axial stiffness of corrugated steel web in local area and resist bending moment together with top and bottom flanges. The shear strain of stiffened corrugated steel web still distributes uniformly along the height of the web. All the experimental results are then employed in the companion paper for the validation of finite element method and the evaluation of existing analytical models for predicting shear strength of un-stiffened and stiffened corrugated steel webs. • We proposed a new type of stiffened corrugated steel web. • Shear behavior of steel I-girder with stiffened corrugated webs has been experimentally investigated. • Shear strength of corrugated steel web can be improved by vertical and lateral stiffeners. • Lateral stiffeners increase the axial stiffness of corrugated steel webs in local area. [ABSTRACT FROM AUTHOR]

Abstract This paper presents the generalisation of an energy-based method for the modal decomposition of buckled shapes of thin-walled members. This comprehensive method is derived and validated for fully decomposing the elastic buckling solution of a thin-walled member into the pure buckling mode classes of global, distortional, local, shear and transverse extension. The first three modes are de-facto prerequisites for buckling capacity predictions found in current design standards for thin-walled structures. In the literature, two main methods, namely the generalised beam theory (GBT) and the constrained finite strip method (cFSM), are widely employed for modal decomposition. Recently, an alternative energy-based approach has been presented for the decomposition of buckling modes into the classical local, distortional and global modes. This method is generalised in the present study to achieve a complete decomposition that also accounts for shear and transverse extensional modes in addition to global, distortional and local modes. In this method, each of the buckling classes is separated by imposing constraints that are defined by enforcing specific criteria on the total strain energy of the member. The adopted criteria are based on the fundamental mechanical assumptions of the GBT which were also implemented in the conventional cFSM and later were further detailed for modal classification in the generalised cFSM. This paper is accompanied by a paper in which derivation of a modified global torsion mode for sections with closed loops is presented and the applicability of the proposed method is demonstrated using a series of numerical examples. Highlights • Modal finite strip method (mFSM) is proposed for analysis of thin-walled structural members. • The particularity of the method due to the use of strain energy for the derivation of modal spaces is discussed. • The constraint matrices defining the global, distortional, local, shear and transverse extension modes are derived. • The proposed method can be applied to modal decomposition of members with arbitrary cross-sections. [ABSTRACT FROM AUTHOR]

Abstract This paper describes a step improvement in the numerical modelling of the structural response of axially and rotationally restrained stainless steel columns at elevated temperatures. The developed finite element models form a sequentially coupled thermal stress analysis that comprises a heat transfer model, a buckling analysis, and a geometrically and materially non-linear stress analysis. The proposed finite element methodology is more sophisticated than any other reported attempts to model the fire response of structural stainless steel that take into account influence of adjoining members. A high degree of predictive accuracy is achieved, with the developed models on average predicting the failure temperatures and times of test specimens reported in the literature within 2% and 6%, respectively. A parametric study is performed that investigates the influence of axial restraint stiffness, rotational restraint stiffness, column slenderness and load level. It is shown that while increasing axial restraint stiffness reduces the failure temperature of stainless steel columns in fire, increasing rotational restraint stiffness has the opposite effect. The methodology and results of this paper will provide both a tool for practice and a suite of results that can be extended to develop the existing and currently limited codified approaches to structural stainless steel design. Highlights • Finite element modelling of axially and rotationally restrained stainless steel columns in fire. • Validation of developed finite element models against fire tests reported in the literature. • Parametric studies examining the effect of varying degrees axial and rotational stiffness. • Investigation of the structural fire response and discussion of design implications. [ABSTRACT FROM AUTHOR]

Abstract This paper presents a numerical investigation on the fire resistance of pultruded GFRP columns with tubular cross-section, both unprotected and protected with a passive fire protection. Three-dimensional finite element models were developed and they considered the thermo-mechanical behaviour of GFRP material (temperature-dependent mechanical properties) and the temperature distributions previously obtained through heat transfer analyses and fluid dynamics inside the tube cavity. The numerical results presented include the time evolution of axial and flexural deformations of the GFRP columns, as well as the stress distributions in both longitudinal and transversal directions of the unprotected column under one-side fire exposure and axially compressed (designated as reference column). In comparison with this reference column, the paper focuses on the evaluation of the several effects, such as the use of fire protection system, the imposition of different fire exposure conditions and the application of distinct load levels. The Tsai-Hill criterion is used to identify the initial failure of GFRP columns and assess the evolution of failure index with fire exposure time, while the Hashin criterion is used to obtain an estimate of column strength and collapse mode. It is concluded that the proposed models are able to qualitatively capture the general trend of the experimental results, despite the quantitative differences not yet overcome. With the consideration of creep, delamination effects and fracture, the authors are confident that these models will soon correctly predict the complex mechanical behaviour and the fire resistance of GFRP columns. Highlights • 3D-FEM of pultruded GFRP columns exposed to fire. • Effects of fire protection, type of fire exposure and load level. • Evolution of axial and flexural deformations and stress distributions. • Failure analysis with Tsai-Hill and Hashin criteria. [ABSTRACT FROM AUTHOR]

Abstract This paper describes a numerical study on the section moment capacity of a doubly symmetric hollow flange steel plate girder (HFSPG) for use in long span applications. The HFSPG is manufactured by welding industrially available cold-formed rectangular hollow sections to a steel web plate. Suitable finite element models were developed first to simulate the section moment capacity tests conducted on the proposed HFSPGs using a four-point bending test arrangement. The experimental conditions in terms of boundary conditions, lateral restraints, mechanical properties, initial geometric imperfections and residual stresses were modelled carefully. The comparison of ultimate moment capacities, moment versus deflection plots and failure modes proved the validity of the developed finite element models to investigate the section moment capacities of HFSPGs. However, the slenderness of the tested HFSPGs was limited to the inelastic region. Hence the validated finite element models were used in a detailed parametric study to extend the results to a wider slenderness range. The parametric study results of the section moment capacities were compared with the predictions of the relevant Australian, American and European hot-rolled and cold-formed steel design standards and suitable recommendations were made in relation to their accuracy in predicting the capacities of compact, non-compact and slender HFSPGs. Finally this paper proposes a new Direct Strength Method based design for HFSPGs. Highlights • Developed and validated finite element models of hollow flange steel plate girders (HFSPG). • Investigated the effects of strain hardening and imperfections on the section moment capacities of HFSPGs. • Ideal finite element models were developed and used in a detailed parametric study. • Parametric study results showed that current design rules underestimate the section moment capacities. • Proposed new Direct Strength Method based equations to predict the section moment capacities of HFSPGs. [ABSTRACT FROM AUTHOR]

Abstract Influence of the ultimate strength of stee This study presents a new fiber reinforced polymer tube/filling strengthening method (i.e., FRP tube/filling strengthening) that creates a new composite compression member with a novel mechanical behavior, "bilinear behavior." Previous experimental and theoretical studies have been conducted based on the ultimate state of the section. To thoroughly study the stiffness and entire loading process of this novel member, finite element analysis (FEA) models are built in this paper. First, the model development process considers the initial defections and interface properties, and these models are verified by the experimental results. Two models of typical load-axial displacement curves describe the experimental results: a Bilinear model and a Trilinear model. Second, finite element modeling (FEM) is used to conduct a parametrical analysis that considers 7 parameters, and the results identify the mechanism of the strengthened member. Specifically, the Bilinear model corresponds to an unreinforced or relatively weakly reinforced specimen, and the Trilinear model corresponds to a relatively strongly reinforced specimen. If the exterior restraint system is weak, then the core steel buckles and subsequently yields; this behavior is described by the Bilinear model. If the exterior restraint system is strong (e.g., the length or the bending stiffness of the exterior restraint system is great), then the specimen can continue to bear a higher force after steel yielding until elastic-plastic buckling occurs; this behavior is described by the Trilinear model. Third, the FEA results and previous experimental and theoretical studies are used to obtain the stiffness and load-axial displacement curves, which are helpful for the design process. In general, relatively accurate FEA models are built in this paper that are capable of describing the mechanical behaviors of the novel member. Highlights • Accurate FEA models that consider the initial imperfections, interface properties are built. • The mechanism of the member is revealed by parametric studies. • The stiffness and the load-displacement curves are obtained. [ABSTRACT FROM AUTHOR]

Abstract It is now well recognized that limit states are a much better basis than allowable working stresses for economical, yet safe design of structures. The objective of the present paper is to apply the ultimate limit states as the structural design criteria of a box girder crane. For this purpose, a reference box girder crane structure which was originally designed and constructed based on the allowable working stress criteria and still in operation is selected. The structure is then redesigned applying the ultimate limit state criteria, where other types of limit states such as serviceability limit states and fatigue limit states are also considered. Nonlinear finite element method is applied to analyze the progressive collapse behaviour of the structure until and after the ultimate limit state is reached. While the ultimate strength or maximum load-carrying capacity of the structure has never been realized as far as the allowable working stress based design method is applied, this study starts with identifying it by the nonlinear finite element method. The structural weight was then attempted to minimize by changing structural member dimensions while the ultimate strength remains the same. It is concluded that the ultimate limit state based design method provides more economical, yet safe structures, compared with the allowable working stress based design method. Considerations for the serviceability limit states are addressed in the paper, while those for the fatigue limit states are presented in a separate article. Highlights • An existing box girder crane structure made of mild steel is redesigned. • The limit state approach is used to redesign the reference structure using high tensile steel. • The ultimate strength of the reference structure is identified by the nonlinear finite element method. • By keeping the structural safety at the similar level, the structural redesign is made by minimizing the structural weight. [ABSTRACT FROM AUTHOR]

In traditional end plate column splices, bolts are placed double symmetrically on the four sides of square hollow sections (SHS). In order to reduce the required gap between the façade and the column, the end plate could be flushed on one or two sides of SHS for the column along the façade or at the corner of a building, respectively. However, the analytical solution (Component method) for the traditional column splice is not applicable in this case. This paper addresses the tensile behaviour of asymmetric column splices, where a cover plate is used on the end plate flushed side. Columns are dominantly loaded in compression and bending, but to verify the component's interaction, the column splices are tested in tension in this paper. The tensile behaviour is investigated through the experiment, the finite element (FE) analysis, and the component method. Eight tensile tests were conducted. The FE model is validated against the experiment. A bi-linear model is employed to characterise the column splice yield resistance, which shows a good agreement with the ultimate resistance of the FE model using a constitutive model without strain hardening. The effective length measured from the FE model is approximately two times that calculated by equations. Using the measured effective length, the component method predicts the characterised yield resistance well (average 13% lower). In comparison, the resistance is underestimated by 35% on average if the calculated effective length is used. [Display omitted] • The behaviour of the asymmetric bolted column splice is investigated experimentally. • 3D DIC is used to reveal the internal force distribution at different deforming stages. • The column splice yield resistance is characterised based on a bi-linear model. • The component method is used to predict the column splice resistance. • The effective yield line length is measured from the validated finite element model. [ABSTRACT FROM AUTHOR]

A non-negligible percentage of steel products for civil and industrial constructions is realised with members characterised by a mono-symmetric cross-section. The non-coincidence between the centroid and the shear centre reflects in a quite complex behaviour that is remarkably influenced by the warping effects. Usually, frame design is based on the output data of commercial Finite Element Analysis Packages (FEAPs) but only few of them offer a refined beam element formulation able to reproduce the response of non-bisymmetric cross-section members (like the 7 degrees of freedom, DOFs, beam element). As a consequence, warping effects are usually neglected in routine design, leading in several cases to assess non-correct internal stresses, global displacements and critical buckling multipliers. This paper is focussed on mono-symmetric cross-section members and deals with the influence of the interaction between axial force, bending moments and bimoment in linear elastic range. In particular, the two strategies that FE developers usually adopt, in the 7 DOFs beam formulation, to pass from the local to the global reference system are herein shortly introduced and discussed. The effects of the associated transformation matrices have been investigated in few examples, also reproduced via closed expressions derived from the mixed torsion theory and FE shell models. Paper outcomes show that the results in terms of generalised displacements, internal forces and, consequently, stress distribution along the member cross-section are significantly different, strictly depending on the adopted transformation matrix. The importance of a correct evaluation of the bimoment distribution is stressed also by the fact that the new edition of the EN1993-1-1, expected in the next months, includes also the bimoment contribution for member checks. • Interaction between bending moments and bimoment in linear elastic range for mono-symmetric cross-section members. • The two strategies adopted in 7DOFs beam formulation, to pass from the local to the global reference system are discussed. • Vlasov's theorems are discussed and applied to example of practical interest for structural design. • Displacements and internal forces are significantly different, strictly depending on the adopted transformation matrix. [ABSTRACT FROM AUTHOR]

In this paper the nonlinear finite element approach is used to solve the problems of first ply failure of laminated composite skewed hypar thin shell roofs. The geometrically nonlinear strains terms are incorporated in the present finite element code which is validated through solution of the problems solved and published by earlier researchers. The first ply failure loads of the industrially popular, aesthetically appealing hypar shells are studied meticulously for varying aspect ratios and thicknesses for clamped boundary condition. The paper gives specific recommendations regarding choice of linear and nonlinear approaches for obtaining failure loads in different specific cases. [ABSTRACT FROM AUTHOR]

In the engineering practice, arches, such as arch bridges, are often subjected to localized loading. It is known that the nonlinear in-plane instability of shallow arches is caused by the significant in-plane bending action. The different localized loading produces very different in-plane bending distributions and so the instability of arches under localized loading would be quite different from that under a central point load or under a radial load uniformly distributed over the entire arch. However, there are no studies about the nonlinear instability and post-instability of arches under localized loading reported in the literature. This paper presents nonlinear in-plane analyses for fixed shallow circular arches under a localized uniform radial load. Novel theoretical solutions for nonlinear equilibrium, limit point instability, and bifurcation instability for arches under a localized uniform load are obtained, and new theoretical solutions of the certain modified slenderness switching the instability patterns of an arch under localized uniform loading are also obtained. It is found that the length of localized loading segment significantly influences the in-plane instability and post-instability responses of an arch. The limit point and bifurcation instability loads decrease with a decrease of the length of the localized loading segment. However, the modified slenderness switching instability patterns is found to increase with a decrease of the length of the localized loading segment. Comparisons against the finite element results show the theoretical solutions derived in this paper are accurate. These theoretical solutions provide comprehensive solutions for nonlinear instability and post-instability of fixed arches and they can reduce to those under a central point load or to extend to those under a uniform load over the entire arch. [ABSTRACT FROM AUTHOR]

Multi-strake cylindrical and conical shells of revolution are complex but commonplace industrial structures which are composed of multiple segments of varying wall thickness. They find application as tanks, silos, circular hollow sections, aerospace structures and wind turbine support towers, amongst others. The modelling of such structures with classical finite elements interpolated using low order polynomial shape functions presents a particular challenge, because many elements must be sacrificed solely in order to accurately represent the regions of local compatibility bending, so-called ‘boundary layers’, near shell boundaries, changes of wall thickness and at other discontinuities. Partitioning schemes must be applied to localise mesh refinement within the boundary layers and avoid excessive model runtimes, a particular concern in incremental nonlinear analyses of large models where matrix systems are handled repeatedly. In a previous paper, the authors introduced a novel axisymmetric cylindrical shell finite element that was enriched with transcendental shape functions to capture the bending boundary layer exactly, permitting significant economies in the element and degrees of freedom count, mesh design and model generation effort. One element is sufficient per wall strake. This paper extends this work to conical geometries, where axisymmetric elements enriched with Bessel functions accurately capture the bending boundary layer for both ‘shallow’ and ‘steep’ conical strakes, which are characterised by interacting and independent boundary layers, respectively. The bending shape functions are integrated numerically, with several integration schemes investigated for accuracy and efficiency. The potential of the element is illustrated through a stress analysis of a real 22-strake metal wind turbine support tower under self-weight. The work is part of a wider project to design a general three-dimensional ‘boundary layer’ element. [ABSTRACT FROM AUTHOR]

Concrete-filled steel tubular (CFST) column-wall has a promising prospect in the construction field, especially for multi-story residential buildings. It is very important to have a thorough understanding of its mechanical behaviour and fire resistance. This is a companion paper that carries forward the work by the authors [1]. The previous paper focused on full-scale testing to determine the fire resistance of CFST column-wall, whereas this paper deals with finite element analysis and simplified design method for such composite structural elements. Heat transfer mechanism was analysed by comparing the temperature distributions of CFST column-wall sections with different fire exposures. Structural analysis, such as internal force distribution, strain and stress of different components, interfacial behaviour between steel and concrete was given to describe the deformation behaviour and failure mechanism of CFST column-wall. Based on the FEA model, parametric analysis was carried out to investigate the influence of geometric, load and physical parameters on the fire resistance of CFST column-wall. Since no specific design rules can be found for CFST column-walls, a simplified fire design method was proposed in this paper to calculate the fire resistance of CFST column-wall structure. [ABSTRACT FROM AUTHOR]

This paper provides means for obtaining the first three significant vibration modes for rectangular plates based on mass participation ratios. A non-dimensional frequency parameter is presented which results into the vibration frequency of rectangular plates at each of these three significant modes. Various aspect ratios and four combinations of boundary conditions at the plate edges are studied. A correlation between the nonlinear load-deformation behavior of the plate and its vibrational behavior is also presented accordingly. It is demonstrated that the vibration frequency of the studied rectangular plates increases significantly upon increasing the applied lateral pressure if the large deformation effects are considered in the analysis. The easy-to-follow method of frequency calculation presented in this paper is useful for assessing the dynamic characteristics of rectangular plates with or without lateral pressure that are subject to vibration. [ABSTRACT FROM AUTHOR]

This paper presents results of a numerical finite element parametric study on elastic shear buckling and ultimate shear strength of cold-formed steel channels with longitudinally stiffened slotted webs. The following parameters were varied: channel height, thickness, flange width, flange lip length, longitudinal stiffener size, perforation pattern, aspect ratio, steel yield stress and boundary conditions. Channels with longitudinally stiffened solid webs subjected to shear load were also studied to provide reference data for comparison with the slotted channels. The parametric study described in this paper allowed us to develop equations for predicting the shear buckling coefficient of longitudinally web stiffened solid channels, as well as equations for predicting the elastic shear buckling load and the ultimate shear strength of channels with longitudinally stiffened slotted webs. The developed shear strength equations without and with tension field action are presented in the paper in the traditional and direct strength method formulations. The developed equations account for the studied parameters and showed good agreements with the finite element simulation results. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to investigate the impact of the geometric imperfection on the interaction of buckling modes for thin-walled cold-formed steel members with a quantitative modal identification approach. Previous studies showed that the interaction of buckling modes varies during the loading process and how buckling interacts depends not only on the section itself but also on the geometric imperfections in the member. This interaction could change the failure modes of the member and its strength accordingly. This paper integrates a modal identification approach based on constrained finite strip method to track this interaction out of the shell finite element model for nonlinear collapse analyses. The geometric imperfections are included in the computational shell finite element model using the traditional modal approach with stochastically simulated magnitudes. The simulations are performed on five specially selected cold-formed steel sections that are deemed to be local-dominant, distortional-dominant, local-distortional interacted, P cr -equal interacted, and P n -equal interacted. The deformations of the analyses are categorized into the fundamental deformation modes commonly available to cold-formed members: local, distortional, and global. Sensitivity of imperfection is studied by tracing the variation of mode interaction, in particular, for the failure mode. Peak load and associated mode participations are investigated. In addition, a statistical study of the impact of imperfections on the potential failure mode at peak is provided. The potential correlation of the member strength with mode participation is explored, which will shed light on the coupled instability of cold-formed steel member, in particular on investigating the impact of mode participations to member strength. [ABSTRACT FROM AUTHOR]

This paper presents an improvement of the first-order Generalised Beam Theory (GBT) formulation proposed in [1] , which was developed for naturally curved thin-walled members with deformable cross-section and whose undeformed axis is a circular arc with no pre-twist. In this paper, the restrictions on the cross-section shape are removed (in the previous paper only rather simple cross-sections were dealt with) by proposing and discussing a novel and systematic procedure to obtain the cross-section deformation modes for arbitrary flat-walled cross-sections (open, closed or “mixed”). The proposed procedure retains the nomenclature of the deformation mode subsets defined in [2,3] , even though the kinematic constraints employed to subdivide the modes are much more complex than for prismatic members. A set of representative illustrative examples is presented, involving complex local-distortional-global deformation, to show the efficiency of the proposed procedure when used together with a standard displacement-based GBT finite element. It is demonstrated that extremely accurate results are obtained with rather few DOFs and that the GBT modal solution provides in-depth insight into the structural behaviour of naturally curved members. [ABSTRACT FROM AUTHOR]

This paper presents an experimental investigation and a finite element analysis on web-stiffened cold-formed lipped channel columns with batten sheets connected between the column's two lips at reasonable space. Initially, the paper presents the static compressive test results on 18 specimens under pinned-end restraint conditions with different column length and load eccentricities considered. It is shown that the batten sheets exert significant influence on both the buckling modes and the ultimate strength of the specimens under positive eccentric loading and/or axial loading conditions, while they just have few impacts on that of the specimens under negative eccentric compression. Strengthened by the batten sheets, the columns performed obviously higher ultimate strength under axial and positive eccentric compression compared with the ones without batten sheets and the strengthening effect increase with the increase of column length. Furthermore, the tested specimens were also numerically investigated by finite element program of ANSYS. Geometric and material nonlinearities were both included in the finite element models and it is demonstrated that the numerical analysis can closely predict the ultimate strength and the buckling behavior of the tested columns. Finally, a parametric study was conducted by using program of ANSYS, in which effect of the increasing lip stiffener width and varying batten sheet space were all investigated and it is concluded that the contribution of the batten sheets to the columns’ strength decreased notably with the increasing lip width or batten sheets’ space for axial and/or positive compressed columns. The best choice of the distance between batten sheets (d≤λ/3) for axial compressed lipped channel columns must also be a reasonable choice for positive compressed columns. [ABSTRACT FROM AUTHOR]