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• The low-restraint GLARE is taken as a research object and its deformation characteristics and failure mode are studied using uniaxial tensile, bending experiments and numerical simulation in this paper. • Based on experimental observations, it is found that the low-restraint GLARE produces the phenomenon of interlayer slip, and the interlaminar residual stress is much smaller than the cured laminate, whereas the deformation limit and performance are improved. • The results of bending experiments revealed that the load variation of low-restraint laminate is significantly different from the cured laminate during bending. • The low-restraint GLARE does not obviously delaminate and fracture during bending due to the low interlayer residual stress and a certain degree of interlayer slipping, exhibiting a significant improvement in the bending forming limit. • This paper provides theoretical bases for the in-depth analysis of deformation properties and forming laws of low-restraint GLARE, guiding further applications of laminates. Fiber metal laminates (FMLs) possess a better weight reduction effect than traditional metal materials due to the coupling properties of heterogeneous materials, showing promise in the areas of aviation and aerospace. At present, the research on FMLs mainly focuses on the deformation properties after curing while the mechanical properties in the low-restraint state, i.e. the laminates are temporarily not cured and are formed under lower constraint stresses, are not studied in detail. Herein, the low-restraint GLARE is taken as a research object and its deformation characteristics and failure mode are studied using uniaxial tensile, bending experiments and numerical simulation in this paper. Moreover, the influence of key parameters, such as temperature, laminate structure and span length, is investigated, as well as the tensile and bending deformation behavior of GLARE in a low-restraint state is obtained. In addition, based on experimental observations, it is found that the low-restraint GLARE produces the phenomenon of interlayer slip, and the interlaminar residual stress is much smaller than the cured laminate, whereas the deformation limit and performance are improved. This paper provides theoretical bases for the in-depth analysis of deformation properties and forming laws of low-restraint GLARE, guiding further applications of laminates. [ABSTRACT FROM AUTHOR]

• The novel beetle elytra inspired lattice configuration is proposed. • The IBCC exhibits superior stiffness and energy absorption than BCC and OCT under the same relative density. • The bio-inspired topological design and interaction effects of curved rods contributes to the enhanced mechanical performance. • The structure of IBCC with "target" mechanical properties can be inversely designed using genetic algorithm. The elytra of the ironclad beetles possess very strong and toughness performance, to protect the body from catastrophic physical damage, owing to its unique curved geometry and layered microstructure. In this paper, inspired by the elytra of ironclad beetles, a novel configuration of lattice structure (IBCC) was developed. The digital light processing (DLP) with hard-tough resin was used to fabricate the lattice structures. The compression experiment and simulation were performed to investigate the mechanical response and deformation mechanism. The response surface model (RSM) was adopted to build a forward relationship between structure parameters and mechanical properties. A numerical method was developed to inversely design structure parameters of IBCC with "target" mechanical properties using genetic algorithm. The novel lattice structure exhibits superior stiffness and energy absorption than conventional BCC (body-centered cubic) and OCT (Octet) structures, under the same relative density. For example, IBCC shows a maximum 59% improvement (at ρ ¯ =9.60%) of stiffness, and a maximum 25% improvement (at ρ ¯ =7.40%) of SEA, with respect to OCT. Besides, the stress plateau of IBCC is more stable than OCT, even at relatively large compression strain. The superior mechanical response of the IBCC lattice structure is mainly ascribed to bio-inspired topological design and interaction effects of curved rods in the "V-shaped" region. Besides, the effectiveness of the proposed inverse design method is verified by three numerical cases. The proposed bio-inspired design strategy, mechanical enhancement mechanism, and customizable method will be helpful in expanding the prospects of lattice structures in future multifunctional application fields. [ABSTRACT FROM AUTHOR]

• An innovative pipe-strut tensegrity structure is proposed. • A fluid-structure interaction computational theory is investigated. • Examples of pipe-strut tensegrity structures are conducted. • FSI can be regarded as the driving strategy of the proposed structure. • Potential kinematic trend of the structure is preliminarily explored. As a self-equilibrated system under prestresses, the internal forces and geometric configurations of tensegrity structures are highly related. Consequently, by employing active control units internally, the lengths of structural components can be adjusted, enabling control over the structural shape and facilitating its motion and actuation. Fluid actuation, as a common type of driving mechanism, is typically achieved by using external fluid actuators or directly replacing structural components with them. In order to better realize the combination of flexible, efficient and adaptable fluid-driven strategy with lightweight, flexible and adjustable tensegrity structure, this paper proposes an innovative pipe-strut tensegrity structure based on the topology of traditional tensegrity structure. In the proposed structure, conventional cables are replaced by flexible pipes to establish a continuous fluid path. This construction concept promotes the flow of fluid within the structure, enabling the proposed structure to deform or move under the influence of the fluid flow. With structural and hydraulic analyses serving as the theoretical foundation, a simplified calculation theory based on the fluid-structure interaction is thoroughly investigated to analyze this innovative structure. Two specific examples are presented to demonstrate the feasibility of the novel configuration, validate the accuracy of the proposed calculation theory, and verify the possibility of deformation and motion trend of the proposed fluid-driven pipe-strut structure. [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]

Abstract Purlins are usually connected to roof sheeting by sliding-clips, while wall sheeting is often screw-fastened to girts. This paper investigates the buckling of such two types of parallel purlin/girt systems inter-connected by multiple lines of sag rods. One single purlin braced by one sag rod at any place along the span is first analyzed, and its buckling deformation at any cross-section is seen as a flexibility coefficient which is then used to study the buckling of the purlin braced by multiple sag rods along span. A flexibility matrix is constructed, whose eigenvalues are the base of critical equations. In the case where the sag rods are placed with equal spaces along span, the eigenvalues are expressed in explicit forms, of which each represents one buckling mode. Threshold stiffness of the sag rods are presented for multiple sag rod bracings for these two types of sheet-to-purlin connection. Based on the findings of this paper, the differences of buckling behaviors between these two types of purlin systems have been revealed. The effect of local deformation of the web at the sag rod connecting points on the sag rod stiffness is also included. Parallel purlin systems are then investigated in a compact matrix form. After carrying out matrix operations and slight approximations, a key parameter is found to be used to reflect the effect of the number of purlins and zig-zag layout of sag rods in adjacent bays on the effective sag rod stiffness. Highlights • Buckling of parallel purlins braced by multiple lines of sag rods is studied. • Rotational restraints of roof sheeting to purlins are considered. • The reduced effectiveness of the sag rods are revealed systematically. • It's found parallel purlins can be analyzed as if they one single-purlin-system. • Two types of purlin-to-sheeting connections are analyzed and compared. [ABSTRACT FROM AUTHOR]

Abstract An innovative cold-formed steel (CFS) framing wall with infilled lightweight flue gas desulfurization (FGD) gypsum was presented in Part I by Wu et al. (Submitted for publication) [1], in which cyclic loading tests were performed. This paper focuses on axial compressive behavior of the innovative wall. Eight full-scale specimens of infilled and unfilled CFS walls were tested under axial compressive loads. The failure modes, axial load-deformation responses, axial load-strain responses, axial compressive stiffness and axial bearing capacity of the specimens were investigated. In the tests, gypsum-encased wall studs lost their bearing capacity in the limit state of strength failure instead of buckling failure. Clear evidences were obtained that axial bearing capacity and axial compressive stiffness of the walls were significantly improved by infilling the gypsum. Compared with the unfilled walls, the maximum loads of the infilled were enhanced by 1.88–2.99 times. When the infilled specimens reached to their maximum loads in which the encased studs were in or close to yield state, but at that moment, the infilled gypsum cannot make full use of its axial bearing capacity in total sections. In addition, the finite element models of infilled walls were developed and validated using experimental results. Parametric studies showed that wall thickness, CFS thickness, and compressive strength of infilled gypsum had an impact on axial compression capacity of the walls, but the friction coefficient between CFS and infilled gypsum had little effect on axial bearing capacity. In this scenario, a modified superposition method was proposed to quantify axial bearing capacity of the infilled walls, and the reduction factor γ = 0.6 was then suggested in the paper, which shows a good agreement with experimental and numerical values. Highlights • Axial loading tests conducted on infilled CFS shear walls. • Encased wall studs lose their bearing capacity in the limit state of strength failure instead of buckling. • A modified superposition method was proposed to quantify the axial-bearing capacity of the infilled walls. [ABSTRACT FROM AUTHOR]

This paper presents a combining experimental, numerical, and analytical efforts to elucidate the resultant effect of synchronised double blast loadings on square steel plates. Blast tests were performed to investigate the effect of the distance between the two identical charges upon the large inelastic deformation of fully-clamped steel plates at various standoff distances. Detailed three-dimensional finite element simulations using LS-Dyna were performed to provide insights into the equal blast wave collision and transient response of the ductile plates under the double blast loading. An analytical model was developed to predict the large inelastic deflection of the fully-clamped thin plate under either pulse pressure loading or impulsive loading (an instantaneous zero-period impulse). Experimental results found that splitting a 1kg TNT into 2 × 0.5 kg TNT (with a certain separating distance) would lead to greater permanent inelastic deformation of the ductile thin plates (by up to 19.6%). Both numerical and analytical results were validated against experimental data. Results from the parametric study showed that an optimum charging distance exists for maximised plate deflection under a given TNT mass and standoff distance. The results presented in this work shall be useful for evaluating the hazards of multiple blast loadings or for demolition applications. • Double blast loadings due to synchronised detonation of identical TNT charges. • Large inelastic deformation of thin steel plates subjected to double blast loadings were quantified experimentally for the first time. • Splitting a 1 kg TNT into 2 × 0.5 kg TNT (with a certain separating distance) would lead to greater plate deformation. • An analytical model is developed for quick assessment of the transient response of square steel plate under double blast loadings. [ABSTRACT FROM AUTHOR]

Gels are polymers that can imbibe large amounts of solvent and generate large volumetric deformations in a process commonly termed swelling. The swelling-induced deformations can be harnessed to produce pressure against surrounding elastic elements, and therefore lead to spatial shape changes without the need for an external energy source. In the present paper, we consider a thin cylindrical elastic tube that encapsulates a gel and deforms in response to the swelling-induced forces. It is expected that by controlling the spatial stiffness distribution of the tube, the deformed swelling-induced shape can be programmed. We exploit this simple idea to obtain controlled shape change driven by the large volumetric expansion of gels. To this end, we train a machine learning algorithm through many FE simulations that enable solving the inverse problem: for any prescribed swelling-induced target shape, the algorithm provides the spatial stiffness distribution of the thin tube. The results confirm that precise controlled shape change is achievable by exploiting the large swelling-induced volumetric deformations in an autonomous manner (i.e. without the need for any external energy source). This work paves the way for new perspectives in the design of shape-change systems based on the simple yet proper elastic distribution of confining structures. • Controlled swelling of soft gel filled structures. • Swelling-driven shape change of gel-based systems. • Inverse design problem of the soft gel filled structures. • Machine learning for finding the elastic distribution of the thin layer encapsulating a gel core. • Numerical FEM simulation of gel filled structures. [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]

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]

The objective of this paper is to investigate the seismic response of cold-formed steel storage racks with spine br acings using two types of connections: a speed-lock connection, JD1, and a speed-lock connection with two bolts and full flange welding, JD5, using the incremental dynamic analysis (IDA) as a companion paper to the pushover analysis. The racks analyzed are racks using only JD1 and JD5 connections given the insights in terms of their performances observed from the pushover analysis in the companion paper. This paper presented the structural models for the IDA analysis with the hysteretic behaviors of the connections based on the previous experimental studies. With selected ground motion records, a total of 44 IDA curves were produced for each rack model studied: a single entry unit rack (SEU) and a double entry unit rack (DEU). The impact of the ground motion records was studied based on the IDA and associated fractile curves. The response modification factor R were then calculated for each rack and compared with those from the pushover analysis. The collapse mechanisms were also studied from the IDA results and compared with those from the pushover analysis. Moreover, the seismic performances of the racks were evaluated based on nonlinear dynamic response history analysis under the ground motions that were closely matching with fractile curves. [ABSTRACT FROM AUTHOR]

This paper investigates the internal inversion process of mild steel tubes under axial impact analytically, numerically and experimentally using a die. The analytical model which is based on the energy method, is able to predict the shortening length of the tube and the required force for tube inversion considering tube thickness variation. In order to validate the analytical model, some experimental tests are performed on the steel tubes in a gas gun and the required force for tube inversion is obtained using an impact loading measurement system. The tube inversion process is also simulated using the finite element software Abaqus and finally the obtained results are compared with each other. In the present paper, the effect of impact parameters included the projectile mass and velocity, is investigated on deformation mechanism and energy absorption of the tubes in the internal inversion process. The effect of tube thickness and die radius are also studied in the mentioned process. It is observed that in the situation of constant projectile mass, increasing the impact velocity doesn’t have a tangible effect on the inversion force and just increases the tube displacement, but if the impact velocity remains constant, increasing the projectile mass causes increase in the inversion force as well as increased tube displacement. It is also concluded that increasing the tube wall thickness increases the inversion force which makes the tube not to be a good absorbent and decreases the tube displacement. Comparing the experimental, analytical and numerical results provides good agreements between them. [ABSTRACT FROM AUTHOR]

• A novel non-linear numerical model for thin-walled members is presented. • Four classes of H-section members are selected to study the hysteretic behaviour. • The comparison of test results and those of the proposed model is accomplished. • The deformation mode, buckling effects, and material nonlinearity are considered. Based on Gonçalves's geometrically exact beam theory considering cross-section deformation, the warping and distortional deformation of thin-walled members are described in this paper by means of a combination of section deformation modes. By integrating with the J2 elastic‒plasticity theory for the steel, a numerical model is established for the hysteretic behaviour of thin-walled steel members. Four classes of H-section members are selected on account of the design codes, and the influence of section warping and distortion deformation modes on the calculation of the hysteretic behaviour of components with different section types is analysed. The crucial aspect lies in the bending hysteresis behaviour around the strong and weak axes of the cross-section for H-beam steel members subjected to typical thin-walled members with relatively large widths and thicknesses. Test results on the hysteretic behaviour of H-section steel members are compared with those calculated from the proposed model in terms of the hysteric behaviour of components, strength degradation, energy-dissipating capacity, etc. These findings validate the correctness and feasibility of the established non-linear analysis model for thin-walled members. [ABSTRACT FROM AUTHOR]

The response of cold-formed steel roof trusses undergoing large deformations resulting from unconventional loading is not totally known. Roof truss end-connections are one structural component that can cause premature failure. This paper investigates the failure capacities and the energy absorption capabilities of roof truss end-connections. Experimental tests were performed to obtain the capacities of these connections under quasi-static vertical and horizontal (tension and shear) loadings. Numerical simulations were developed to predict the connection response to failure for any configuration. Implicit and explicit dynamic procedures were used in the analysis of the numerical simulations. A deformable screw behavior with failure criterion was used in the numerical modeling to predict the progressive failure of the connection. The paper includes four verifications that validate the deformable behavior of #10 TEK screw used in the simulations. Results showed that the toughness (energy absorbed to failure) of the end-connection is greatly affected by the screw configuration and the direction of loading. [ABSTRACT FROM AUTHOR]

Suitable and fast calculation methods with sufficient accuracy are required to optimise large composite structures. The present paper introduces a progressive stiffness degradation analysis (PSDA), which computes skin buckling onset and strength failure initiation of skin fields separated by stiffeners, as well as the subsequent damage propagation using closed form solutions. This constitutes a simplified, but much faster approach compared to state of the art progressive failure analyses, which incorporate finite element simulations. Therefore, the computational effort can be reduced. This paper illustrates the process of the PSDA and then verifies this simplified approach by means of one example. [ABSTRACT FROM AUTHOR]

Structural design of stiffened plates of the walls of rectangular-sectioned industrial ducts is currently based on the strip method that follows the linear flexural beam theory. The current design method assumes that the displacements generated in the plate are small and the membrane forces that generate in the plate are negligible. This paper addresses the current design method and discrepancies associated with it to present a new design approach that takes into account the effects of large displacements on the load-deformation and load-stress behavior of stiffened plates. Two different sets of formulas are presented based on Finite Element analysis of rectangular plates with relatively long aspect ratios that estimate the maximum stress and deformation in the typical and edge panels of stiffened plates. These formulas are then used to establish design equations for stiffened plates. Based on the findings of this paper, a reduction of 30–40% in the plate thickness could be achieved if the new design approach is selected over the conventional design method. [ABSTRACT FROM AUTHOR]

• The rapid maximum dynamic stress (S max) prediction method of Miura-ori core sandwich panels with impact defects is proposed, which could directly predict S max with few simulations by establishing the relationship with impact deformation in advance. • S max of sandwich panels will increase by 2.635 times with the impact deformation below 32.1 % of Miura cell projection area. • The impact deformation is predicted by the geometric relationship of Miura creases and material properties, and the prediction errors are below 12.5 %. Miura-ori core sandwich panels have great application potential in aviation aircraft. Subject to the impact and vibration loads, the small impact defect will increase the dynamic stress, resulting in fatigue failure. Moreover, the Miura creases complicate the impact deformation, which is extremely time-consuming to analysis the dynamic stress only through simulation. Therefore, a rapid dynamic stress prediction method for Miura-ori core sandwich panels is first proposed based on the predicted impact deformation by arbitrary defects in this paper. The dynamic stress of sandwich panels could be directly calculated with few numerical results by establishing the relationship with impact deformation in advance. The vibration mechanism of sandwich panels with defects is revealed. Although the deformation area is below 32.1 % of Miura cell projection area, the dynamic stress will increase by 1.984–2.635 times with different defects. The impact deformation is predicted by the geometric relationship of Miura creases and material properties, and the prediction errors of hemispherical and drilling defects with arbitrary defect positions are below 12.5 % and 10.6 %, respectively. Taking two types of defects (hemispherical and drilling defects), different defect depths and positions into consideration, the prediction errors of maximum dynamic stress are from -7.9 % to 16.8 % compared to simulation. [ABSTRACT FROM AUTHOR]

• The bi-modular FGMs UMAT is developed for the first time and successfully conducted to validate the perturbation solution. • The rise-to-thickness ratio and corresponding critical load are two factors influencing the snap-through buckling. • The rotation constraint and radial constraint at the shell edge have opposite effects on the snap-through buckling. • The bi-modular FGM effect may speed up or slow down the snap-through buckling. Functionally graded materials (FGMs) enable structures to achieve a smooth transition between different material properties, providing an optimized combination of functions to meet the diversity of engineering needs. However, the presence of bi-modular effect in FGMs is often neglected due to the complexity in the analysis. In this paper, the curvature correction equivalent method based on the von Kármán theory will be applied to the theoretical study for the large deformation problem and the resulting snap-through buckling of functionally graded revolutionary shallow thin shells with bi-modular effect under different boundary constraints. Furthermore, a bi-modular FGMs user material subroutine (UMAT) is developed for the first time to simulate the real material model, thus validating the theoretical solution. The results show that except for the bi-modular effect of materials, boundary constraints of shells also have important influences on the relationship of load vs. central deflection and snap-through buckling. The research of boundary constraints brings new conclusions to snap-through buckling: the rotation constraint and radial constraint at the shell edge have opposite effects on snap-through buckling. This work will contribute to the analysis of the snap-through buckling of functionally graded revolutionary shallow thin shells with an obvious bi-modular effect and under various boundary constraints. [ABSTRACT FROM AUTHOR]

The present paper focusing on the most important energy absorbing system of the circular thin-walled tubes or shells under lateral compression between two rigid plates, which is also a basic mechanical issue, studies the cross-sectional deformation in terms of the compressive force applying to the tube in the large elastic–plastic deformation stage during the lateral compressive process by both theoretical as well as finite element analysis (FEA) methods. Firstly a FEA simulation for the thin-walled tube's lateral compressive process between two parallel plates is carried out to analyze the mechanical response and deformation characteristics, and then it is validated by tube's lateral compressive experiment using digital image processing technology. Following the simulation results, some assumptions are proposed for theoretical derivation. Secondly focusing on the large elastic–plastic deformation stage (Stage II, in this paper), the compressive deformation of thin-walled tubes is divided into elastic and plastic regions according to the von Mises yield criterion. In elastic region the linear strain–displacement relations of shell theory and Hooke's stress–strain relations are employed, and in plastic region the nonlinear large strain–displacement relations of doubly-curved shell theory and the power hardening rule are employed. Then considering both geometric and material nonlinearities, the equilibrium equation, which is a complicate integral equation with the variable upper limit, is derived using the principle of virtual work. It is solved by expanding the integrand as a set of polynomials power series. Then the predicted cross-sectional deformation in terms of the compressive force can be obtained by the iterative method. Finally some lateral compressive simulations involving various tubes with different geometric parameters are carried out, and the theoretical model is validated by comparison of the cross-sectional profiles predicted by theoretical model with those obtained by the simulations as well as other methods. At the same time, the applicable conditions of this model are discussed. This paper will play a positive role in studying the cross-sectional deformation for various shells under lateral compression in different application areas. • Mechanical response and deformation characteristics are presented by FEA, which have been validated by compressive experiment. • A new theoretical is derived to predict the cross-sectional deformation in the large elastic-plastic deformation stage of the laterally compressed thin-walled tubes. • A new method is proposed to solve the unintegrable equation with the variable upper limit during the theoretical derivation. • The applicable conditions of this model are given. [Display omitted] [ABSTRACT FROM AUTHOR]

The nonlinear free vibration behavior of shear deformable sandwich porous beam is investigated in this paper within the context of Timoshenko beam theory. The proposed beam is composed of two face layers and a functionally graded porous core which contains internal pores following different porosity distributions. Two non-uniform functionally graded distributions are considered in this paper based on the equivalent beam mass, associated with a uniform distribution for purpose of comparison. The elastic moduli and mass density are assumed to vary along the thickness direction in terms of the coefficients of porosity and mass density, whose relationship is determined by employing the typical mechanical characteristic of an open-cell metal foam. The Ritz method and von Kármán type nonlinear strain-displacement relationships are applied to derive the equation system, which governs the nonlinear vibration behavior of sandwich porous beams under hinged or clamped end supports. A direct iterative algorithm is then used to solve the governing equation system to predict the linear and nonlinear frequencies which are presented by a detailed numerical study to discuss the effects of porosity coefficient, slenderness ratio, thickness ratio and to compare the varying porosity distributions and boundary conditions, providing a feasible way to improve the vibration behavior of sandwich porous beams. [ABSTRACT FROM AUTHOR]

Because of their geometrical shape, two-pinned steel arches (TPSAs) have special internal force distributions and deformations compared with conventional straight beams. However, the present studies on TPSAs exposed to fire are still quite limited with regard to their fire-induced deflection modes or deflection limits and ultimate temperatures. This paper employs several numerical models to analyse the high-temperature performance of TPSAs at elevated temperatures in terms of the effects of the load ratios, horizontal restraints, rise-to-span ratios, fire fields and geometrical sizes of the cross-section. The results show that TPSAs exposed to high temperatures are more sensitive to the load ratios than the horizontal restraint stiffness and geometrical size of the cross-section. The TPSAs could not develop catenary actions such as those of straight beams in fire; previous investigations have not predicted the behaviour of TPSAs in fire. The in-plane buckling and excessive mid-span sagging of TPSAs are the final failure modes regardless of the location of the fire actions. To date, the acceptable rise-to-span ratio is approximately 0.25–0.35 for TPSAs in fire. Finally, this paper presents a prediction formula for the limit state of TPSAs at elevated temperatures by using trigonometric functions and logarithmic regression. [ABSTRACT FROM AUTHOR]

This paper presents 18 tests conducted on short, medium and long circular Concrete Filled Steel Tube (CFST) columns. To explore the impact of column parameters and confinement effect three L/D ratios, two D/t ratios, two steel qualities and three concrete classes were employed. Some specimens have properties within application limits of EC4 and AISC 360-10 whereas others have properties beyond the application limits. Since new, large and efficient structures require adoption of high strength materials, it is compulsory to push the limits of design specifications. It is shown that 56 MPa and 66 MPa concretes provide very smooth and ductile load-shortening curves which imply high deformation capacity of such concrete classes. Brittle nature of 107 MPa concrete is shown by very sharp transitions from pre-peak to post-peak region and sudden discharge of loading in load-shortening curves. Additionally, 239 experimental data were collected from literature to assess EC4 and AISC 360-10 predictions within application limits and beyond application limits. Instead of focusing on a narrow region of configurations, this paper examines the performance of prediction methods on short, medium and long CFST columns. EC4 predictions indicate much better agreement with the test results. However AISC 360-10 predictions are conservative for all combinations of parameters. The application limits of EC4 can be widened to cover solutions of columns with broader properties. Confinement effect should be handled elaborately in AISC 360-10 formulations. L/D and relative slenderness are key parameters and have direct impact on column behaviour. However D/t does not have direct impact on column behaviour. [ABSTRACT FROM AUTHOR]

This paper focuses on the crushing collapse theory of externally fiber-reinforced twelve right-angle section (TTRS) tubes based on the kinematic approach. This paper presents the crushing energy dissipation mechanism of metal TTRS tubes and derives the expression of mean crushing force. Considering the contribution of the composite-metal wall and the final crushing deformation, which affected by the accumulation of the composite after failure, the expression describing the mean crushing force for externally fiber-reinforced TTRS tubes is presented. The accuracy of the theoretical predictions is validated by finite element simulations, including four different metal wall thicknesses and three different amounts of composite plies. The results indicate that the mean crushing forces calculated by the proposed theory show a good consistency with the simulation results. [ABSTRACT FROM AUTHOR]

This paper compares two distinct approaches for obtaining the cross-section deformation modes of thin-walled members with deformable cross-section, namely the method of Generalized Eigenvectors (GE) and the Generalized Beam Theory (GBT). First, both approaches are reviewed, emphasizing their differences and similarities, as well as their resulting semi-analytical solutions. Then, the GE/GBT deformation modes for four selected cross-sections are calculated and examined in detail. Subsequently, attention is turned to the efficiency and accuracy of the GE/GBT mode sets in typical benchmark problems, namely the calculation of the global–local–distortional first-order and buckling (bifurcation) behaviors of bars with the previously analyzed cross-sections. It is concluded that GE and GBT, both based on the method of separation of variables, yield accurate results although they use different structural models and mode selection strategies. Therefore they offer complementary advantages, which are put forward in the paper. [ABSTRACT FROM AUTHOR]

The paper describes the derivation of a beam finite element method which enables the effects of local and/or distortional buckling deformations to be accounted for. The development of local/distortional buckling reduces the rigidity of the section against axial straining, minor and major axis flexure, as well as twisting. The reduction in rigidity can be determined by an analysis performed prior to the frame analysis, in which tangent rigidities (( EA ) t , ( EI z ) t , ( EI y ) t , ( EI w ) t ) and other tangential stiffness terms are obtained for increasing values of generalised strains ( ε x , κ z , κ y , κ x ). The paper sets out the tangential stiffness matrix for a locally/distortionally buckled element and discusses in detail the determination of tangent rigidities. The companion paper [1] shows that close agreement can be obtained between the beam analysis which incorporates reduced rigidities and analysis using full shell finite element discretisation. The paper is limited in scope to doubly-symmetric open sections. [ABSTRACT FROM AUTHOR]

This paper presents an experimental study that was designed to investigate the compressive behavior of a new type of fiber reinforced polymer (FRP)-concrete–steel composite column system. This composite column system has recently been developed by the author as a special form of double-skin tubular columns (DSTCs), with the column manufactured using two different grades of concrete (referred to as dual-grade concrete (DGC) DSTCs in this paper). In this system, the annular section of the column (i.e. the section between FRP and steel tubes) is filled with normal-strength concrete (NSC) and the core section inside the steel tube is filled with a higher grade concrete mix. Based on the understanding that confinement demand of concrete increases with its strength, the system was designed to maximize the effectiveness of the composite column. To establish the performance levels of this new column system with respect to those of the conventional DSTCs manufactured with normal- and high-strength concrete (NSC and HSC), a comprehensive experimental investigation was undertaken where 28 circular and square DSTCs were tested under concentric compression. Results of the experimental program indicate that the proposed DGC DSTC system exhibits a superior compressive behavior compared to those of the conventional NSC and HSC DSTCs. It is observed that both circular and square DGC DSTCs exhibit extremely high axial load and deformation capacities, which in turn results in a much higher system and concrete ductility compared to those in companion single-grade concrete DSTCs. The results also show that companion square and circular DGC DSTCs can be designed to develop similar axial load capacities under the same level of FRP confinement. It is found that, under these conditions, the axial deformation capacities of square DGC DSTCs exceed those of their circular counterparts. [ABSTRACT FROM AUTHOR]

In this paper, an experimental investigation on the impact performance of FRP–concrete–steel double skin tubular members is presented. Twenty-four tests were carried out to examine the failure modes and the time histories of the impact forces, lateral deformations and strains. The effects of the impact energy and number of FRP layers on the impact behavior of the double skin tubular members were discussed. The results show that FRP–concrete–steel double skin tubular members behave in a ductile manner; there is a long stabilized stage of impact forces and the residual deformation mainly results from the cracking of FRP and concrete, as well as the overall bending deformation. The confinement of the outer FRP layers in the hoop direction to the sandwiched concrete in the composite members is small during the whole impact process. However, increasing the number of the outer FRP layers is somewhat beneficial to improve the dynamic resistance ability. The effect of the impact energy on the dynamic response of the composite members is significant. The difference between the FRP–concrete–steel double skin tubular members, concrete filled double skin steel tubes and concrete filled steel tubes is discussed based on the test results in this paper. [ABSTRACT FROM AUTHOR]

This paper discusses aspects related to the mechanics underlying the distortion of thin-walled members with symmetric and periodic open cross-section, such as those commonly employed in cold-formed steel construction. The Generalised Beam Theory (GBT) framework is employed to determine the cross-section distortional deformation modes and obtain insight into the problem under consideration. Besides reviewing the well known case of reflectional symmetry, the implications of rotational symmetry and periodicity through translation or glide reflection are examined. For each case, computationally efficient procedures to obtain the distortional modes are provided. Several examples are presented throughout the paper, in order to enable a better grasp of the concepts and procedures addressed. [ABSTRACT FROM AUTHOR]

Experimental studies on the behaviour of concrete filled double-skin steel tube (CFDST) subjected to local bearing forces are presented in this paper. Sixteen specimens were prepared and tested with the included angle between bearing member (BM) and compression member of 45° and 90°, whilst both the inner and outer steel tubes of the CFDST specimens are square hollow sections (SHS). The main parameters in the tests were: 1) outside width ratio between BM and compression member: from 0.4 to 0.6; 2) hollow ratio of CFDST: from 0 to 0.6; 3) wall thickness of outer steel tube: 3.05 mm and 3.95 mm; and 4) cross-section of BM: solid and hollow. The failure pattern, load versus deformation curve, bearing capacity and corresponding deformation at bearing capacity of the tested specimens are presented and analyzed. The experimental results show that, while subjected to local bearing forces, CFDST specimens have a high bearing capacity and a good deformation-resistant ability. The calculated bearing capacities of CFDST under local bearing forces using the proposed formulae in the paper are evaluated by comparison with the experimental results. [ABSTRACT FROM AUTHOR]

The present paper is concerned with the analysis of the ratcheting behaviour of elasto-plastic thin-walled pipes under internal pressure and subjected to cyclic axial loading. Understanding the behaviour of this kind of structure at different load levels is of critical importance in a range of engineering applications such as in the design of structural components of power and chemical reactors. Depending on the kinematic hardening, the pipe may exhibit a ratcheting behaviour in the circumferential direction, which leads to a progressive accumulation of deformation. Many different constitutive theories have been proposed to model the kinematic hardening under such kind of loading history. The present paper presents a simple local criterion to indicate whether or not the pipe may exhibit a progressive accumulation of deformation. Such criterion is independent of the choice of the evolution law adopted for the backstress tensor. As an example, a semi-analytic approach using a mixed nonlinear kinematic/isotropic hardening model is proposed to be used in a preliminary analysis of this kind of structure. [ABSTRACT FROM AUTHOR]

The present paper focuses on the constitutive assumptions, both for the isotropic and orthotropic cases, and consistency in the framework of the Generalized Beam Theory. In particular, a novel approach based on energetic arguments, able to automatically select appropriate constitutive relations in accordance with the GBT kinematics, is presented. Furthermore, the concept of consistency of a GBT-based model is established and a consistency analysis is presented. This yields a formal rational basis to investigate the effects of the various families of cross-section deformation modes in terms of predictive capabilities of the GBT model. Some numerical examples illustrate the arguments exposed in the paper. [ABSTRACT FROM AUTHOR]

This paper researches a type of absorber of kinetic collision energy that works on the principle of shrinking and splitting a tube of circular cross section. During collision, a seamless tube is thrust through a cone bush, squeezing the tube. Energy is absorbed by the plastic deformation, and through the friction between the tube and the bush. After passing through the cone bush, the tube presses against a splitter, and further energy is lost to friction and plastic deformation during the splitting process. Grooves on the inner wall of the tube prevent uncontrolled longitudinal tearing of the wall during the splitting. This new combined method of energy absorption enables greater absorption power with compact dimensions. Scaled samples have been tested in the laboratory. The influence of geometry and manufacturing technology of the samples, as well as the benefits of using such an absorber, are presented and discussed in this paper. The results show that the combined absorber has approximately 60% higher absorption power than the shrinking absorber by itself. [ABSTRACT FROM AUTHOR]

In this paper the generalization of the constrained finite strip method ( c FSM) is provided. c FSM is an extension of the semi-analytical finite strip method (FSM), where carefully defined constraints are applied to enforce the thin-walled member to deform in accordance with desired deformations, e.g., to buckle in flexural, lateral-torsional, distortional, or local buckling mode. This paper is a companion to [1] , where the method is introduced and where the primary modes are defined, i.e., modes that are associated with minimal cross-section discretization, when nodal lines are located at folds and ends only. In this paper the so-called secondary modes are defined, i.e., those with no displacements at folds and edges, which thus exist only if flat plates are discretized into multiple strips. Moreover, some practical aspects are also discussed, including how the individual base vector of the deformation spaces can be defined in a practically useful and meaningful manner. The applicability of the method is demonstrated by numerical examples. [ABSTRACT FROM AUTHOR]

In this paper the generalization of the constrained finite strip method ( c FSM) is discussed. c FSM is a special version of the semi-analytical finite strip method (FSM), where carefully defined constraints are applied which enforce the thin-walled member to deform in accordance with specific mechanics, e.g., to allow buckling only in flexural, lateral–torsional, or a distortional mode. In the original c FSM only open cross-section members are handled, here the method is extended to cover any flat-walled member, including those with closed cross-sections or cross-sections with open and closed parts. Moreover, in the original c FSM only 4 deformation classes are defined, here the deformation field is decomposed into additional, mechanically meaningful, sub-fields. Formal mechanical criteria are given for the deformation classes, and implementation of the criteria regardless of cross-section topology is illustrated. In this paper, the primary deformation classes are presented in detail. Primary deformations are associated with minimal cross-section discretization, i.e. nodal lines located at folds and ends only. This paper is accompanied by a companion, where secondary modes and additional practical aspects in the selection of base vectors for the deformation classes are discussed. With the proposed modifications the powerful c FSM capabilities of buckling mode decomposition and identification are extended to essentially arbitrary thin-walled cross-sections. [ABSTRACT FROM AUTHOR]

Slender tubes constituted of hyperelastic materials undergoing large deformations and conveying inertialess flow of Newtonian fluids are a model representation of several systems including those in soft robotics, biology and in industry. In this paper, we undertake a systematic study of this system. The tube's hyperelastic behavior is modeled by five (5) different constitutive laws: Neo-Hookean, Mooney–Rivlin, Fung, Gent and Ogden. Invoking the principles of finite elasticity, we delineate the local pressure — deformation relationship for the tube for each of the hyperelastic models. The structural mechanical field of the tube is then coupled with fluid flow field, which is simplified using the principles of lubrication approximation. The resultant fluid–structure interaction problem then throws up a set of interesting results including the deformation and pressure profile across the tube, and tube laws for five (5) hyperelastic models. Analyzing these results, we posit that the behavior of Neo-Hookean and Mooney–Rivlin tubes is converse of Fung's and Gent's tubes; the latter show a strain hardening behavior whilst the former exhibit a strain softening one. A sensitivity analysis which underscores the relative importance of geometrical nonlinearity in the problem then follows. • Thin walled hyperelastic tubes conveying inertialess flow analyzed. • Five (5) different models of hyperelasticity analyzed and compared. • Tubes undergo large deformations. • Lubrication approximation for fluid flow used to analyze the FSI problem. • Effect of geometric nonlinearity discussed. [ABSTRACT FROM AUTHOR]

• Giving the deformation mode of stiffened conical shell under deep water burst load. • Giving the trapezoidal deformation function for the deformation of the structure. • Giving the solution model of the maximum displacement of the structure. The reinforced cylindrical and conical column structures are widely used structural forms in underwater vehicle structures. In this paper, the reinforced conical shell structure in the transition compartment of underwater vehicles was used as the research object. Based on the shock wave propagation theory and ABAQUS acoustic structure coupling numerical simulation method, the numerical simulation model of conical shell structure under deep-water explosion load was established. The deep-water explosion simulation of conical shell structure under the conditions of different water depths, charges and explosion distances was carried out, and the deformation and failure mode of small depressions in the shell plate between ribs of stiffened conical shell structure was obtained, that was, independent small pits were formed along the axis direction. According to the theory of elastic-plastic deformation of plate and shell structure, the small pits of shell and plate between ribs were approximated as the deformation of trapezoidal plate, and the deformation function of trapezoidal plate was obtained by coordinate transformation. The deformation energy of plate and shell was divided into bending deformation energy and midplane strain energy. By establishing the correlation between explosion energy and deformation energy, the theoretical calculation model of the small pit deformation mode of shell and plate between ribs was obtained. [ABSTRACT FROM AUTHOR]

• Development of a finite element formula in Total Lagrangian framework for large deformation of isotropic and anisotropic membrane structures without restriction to geometry, loading and boundary conditions. • Representation of both invariant-based and stretch-based strain energy density functions, and derivation of actual values of fourth-order elasticity tensor dealing with the complexities of transformation between Cartesian and principal coordinates for stretch-based strain energy density functions. • Employing the exact form of the fourth-order elasticity tensor in finite element method for stretch-based hyperelastic material model. • A comparative study between deformations in terms of invariant-based and stretch-based formulations in possible cases. A nonlinear finite element formulation for large deformation analysis of hyperelastic membranes in Total Lagrangian framework is developed. In many cases, it is convenient to utilize the invariant-based strain energy density function to analyze the structures when employing the finite element method. However, in this contribution, both invariant-based and stretch-based formulations are developed. Formulations are completely general and not restricted to axisymmetric loading and geometry of membrane. Furthermore, initially flat and non-flat membrane can be investigated by this method. Incompressible as well as compressible materials can be modeled. A method for imposing the plane stress condition to the formulation for compressible materials is presented. Moreover, isotropic and anisotropic materials can be considered. Some problems are analyzed and results compared to the available ones in the literature. The comparison between solution based on invariant-based method and stretch-based method with exact fourth-order elasticity tensor obtained in this work demonstrates that the stretch-based method derived in this paper works very well. The presented examples demonstrate that the developed formulations have no restriction or simplification with respect to the modeled object geometry and inherent anisotropy. [ABSTRACT FROM AUTHOR]

• A 3D free-bending process method that can accurately control the process parameters in transition zone is proposed. • An analytical model of finned special-shaped tube bending forming based on exponential hardening behavior is constructed. • The influence rule of the speed parameters in transition section on the forming radius and cross-section deformation is obtained. • FE results are in good agreement with experimental results. In 3D free-bending technology, the bending forming of the tube consists of the transition section and the stable forming section. However, because of the continuous movement of the bending die and tube in the transition section, the forming mechanism of the tube in the transition zone is relatively complex and still unclear. In addition, due to the complexity of the cross-section deformation of the finned special-shaped tube (FSST), its application in the heat dissipation pipeline of aerospace vehicles is severely hindered. To address the above issues, in this paper, a 3D free-bending forming process method, which can effectively coordinate the movement of FSST and the bending die in the transition section, was proposed. Meanwhile, an analytical model of FSST bending forming was established, which can effectively characterize the elastic-plastic evolution of the FSST cross-section and match the bending radius with the cross-sectional bending moment effectively. Then, the effectiveness of the process method and analytical model was verified by finite element model (FEM), and experiments. Further, FEM and experiments were used to investigate the influence of the process parameters of the transition section on the forming radius and cross-section deformation of FSST after springback. The results from this study show that reasonable coordination of the rotation speed of the bending die and the advancing speed of FSST in the transition zone can improve the forming quality of FSST. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents an experimental investigation into the behaviour of ultra light-gauge steel storage rack uprights subjected to compression. Two different types of members with varying lengths are tested and while the combined effects of local and distortional buckling are investigated, special attention is given to longer specimens that fail by flexural–torsional buckling in combination with local and distortional buckling. Deformations experienced during testing by all of the specimens were measured and observations regarding failure modes have been documented. In addition, the geometric imperfections of each member were measured before testing, as were the material properties of the cold-rolled sections and the virgin steel from which the sections were formed. This paper details the observed failure modes, the recorded ultimate strengths and the load-deflection responses. Design capacities calculated from AS/NZS 4084 (2012) [1], RMI (2012) [2] and EN 15512 (2009) [3] specifications are then evaluated and compared to the experimental results obtained.The evaluation of international specificationsdetermined that EN 15512 (2009) [3] is more accurate in predicting ultimate loads of sections undergoing interactive buckling than both AS/NZS 4804 (2012) [1] and RMI (2012) [2]. [Copyright &y& Elsevier]

Abstract: To rehabilitate damaged or sub-standard box girders, techniques utilising the lightweight, high strength and corrosion resistance of carbon fibres reinforced polymers (CFRP) composites have been proposed. This paper presents experimental results for two series of CFRP strengthened and rehabilitated model box girders under quasi-static large deformation 3-point bending. The first series represents strengthening 12 un-degraded rectangular hollow section (RHS) beams from the manufacturer using externally wrapped CFRP sheets. The second series was for rehabilitation of 41 artificially degraded RHS beams strengthened using externally wrapped sheets or bonded plates. The main parameters examined in this paper were the section type, section and member slenderness and the type and number of the CFRP sheets. The flange and web slenderness examined in this paper was in the range of b/t=20 to 66.67 and d/t w =20 to 75. The CFRP sheets were wrapped around the section in the transverse direction with a sufficient overlap. The results show that the combined flexural and bearing strength of the steel box girder can be significantly increased by adhesively bonding CFRP. Expressions for the bearing strength and plastic moment of the composite section were obtained by means of an equivalent thickness approach. The newly derived interaction equations were compared against the present design rules in steel specifications. The average gain in strength due to bonding the CFRP laminate was 65% and 19.9% for the strengthening and rehabilitations series, respectively. The percent increase in strength was mostly affected by the section slenderness where the maximum gain was obtained for the slender section. [Copyright &y& Elsevier]

Abstract: Due to the increased consumption of thin-walled structural elements there has been increasing focus and need for more detailed calculations as well as development of new approaches. In this paper a thin-walled beam element including distortion of the cross section is formulated. The formulation is based on a generalized beam theory (GBT), in which the classic Vlasov beam theory for analysis of open and closed thin-walled cross sections is generalized by including distortional displacements. The beam element formulation utilizes a semi-discretization approach in which the cross section is discretized into wall elements and the analytical solutions of the related GBT beam equations are used as displacement functions in the axial direction. Thus the beam element contains the semi-analytical solutions. In three related papers the authors have recently presented the semi-discretization approach and the analytical solution of the beam equations of GBT. In this approach a full set of deformation modes corresponding to the homogeneous GBT equations are found. The deformation modes of which some are complex decouple the state space equations corresponding to the reduced order differential equations of GBT and allow the determination of the analytical solutions. Solutions of the non-homogeneous GBT differential equations and the distortional buckling equations have also been found and analyzed. Thus, these related papers are not dealing with an element but dealing with analytical solutions to the coupled differential equations. To handle arbitrary boundary conditions as well as the possibility of adding concentrated loads as nodal loads the formulation of a beam element is needed. This paper presents the formulation of such a generalized one-dimensional semi-discretized thin-walled beam element including distortional contributions. It should be noticed that we are only dealing with a basic generalized beam theory and not an extended finite element formulation of an approximate beam element, which allows the addition of special (transverse extension and shear lag) modes. Illustrative examples showing the validity and the accuracy of the developed distortional semi-discretized thin-walled beam element are given and it is shown how the novel approach provides accurate results making it a good alternative to the traditional and time consuming FE calculations. [Copyright &y& Elsevier]

Abstract: This paper presents experiments and theoretical analysis of 16 steel I-section beams strengthened using externally bonded CFRP under quasi-static large deformation 3-point bending. The main parameters examined in this paper were the section and member slenderness and the location of the CFRP plates. The member slenderness examined in this paper was in the range of L e /r y =40–92. The section slenderness examined in this paper was in the range of b/t f =6.25–16.67. The CFRP plates were added either to the tension flange or both compression and tension flanges or even to the whole section including the web. An expression for the yield and plastic moments of the composite section were obtained by means of an equivalent thickness approach for the web and flange. The newly obtained strength results were compared against the present design rules in steel specifications. The CFRP increased the strength by up to 32% for compression and tension flange strengthening whereas the strength increased only by 15% for tension flange strengthening. The per cent increase in strength for short specimens was mostly affected by the section slenderness where the maximum gain was obtained for the semi-compact section. Plastic mechanism analysis was performed to predict the collapse curves. Good agreement was found between the theoretical and experimental post buckling load–deflection curves. [Copyright &y& Elsevier]

Abstract: This paper reports the results of a numerical investigation aimed at providing fresh insight on the mechanics underlying the buckling and (mostly) post-buckling behaviour of short-to-intermediate equal-leg thin-walled angle steel columns exhibiting fixed and pinned (but with the secondary warping prevented) end supports. Although most of the numerical results presented and discussed were obtained through Abaqus shell finite element analyses, the paper also includes some GBT-based critical stresses and buckling mode shapes, whose interpretation help clarifying the distinction between local and global buckling. The shell finite element results displayed consist of (i) elastic post-buckling equilibrium paths and (ii) curves and diagrams providing the evolution, along a given path, of the column deformed configurations and normal stress distributions. [Copyright &y& Elsevier]

Abstract: This paper presents distorting buckling solutions for semi-discretized thin-walled columns using the coupled differential equations of a generalized beam theory (GBT). In two related papers recently published by the authors a novel semi-discretization approach to GBT has been presented. The cross section is discretized and analytical solutions are sought for the variation along the beam. With this new approach the general GBT equations for identification of a full set of deformation modes corresponding to both homogeneous and non-homogenous equations are formulated and solved. Thereby giving the (complex) deformation modes of GBT which decouple the state space equations corresponding to the reduced order differential equations. In this paper the developed semi-discretization approach to generalized beam theory (GBT) is extended to include the geometrical stiffness terms, which are needed for column buckling analysis and identification of buckling modes. The extension is based on an initial stress approach by addition of the related potential energy terms. The potential energy of a single deformation mode is formulated based on a discretization of the cross section. Through variations in the potential energy and the introduction of the constraints related to beam theory this leads to a modified set of coupled homogeneous differential equations of GBT with initial stress for identification of distortional displacement modes. In this paper we seek instability solutions using these GBT initial stress equations for simply supported columns with constrained transverse displacements at the end sections and a constant axial initial stress. Based on the known boundary conditions the reduced order differential equations are solved by using the trigonometric solution functions and solving the related eigenvalue problem. This gives the buckling mode shapes and the associated eigenvalues corresponding to the bifurcation load factors. Thus the buckling modes are found directly by the analytical solution of the coupled GBT-equations without modal decomposition. Illustrative examples showing global column buckling, distortional buckling and local buckling are given and it is shown how the novel approach may be used to develop signature curves and elastic buckling curves. In order to assess the accuracy of the method some of the results are compared to results found using the commercial FE program Abaqus as well as the conventional GBT and FSM methods using the software packages GBTUL and CUFSM. [Copyright &y& Elsevier]

Abstract This paper addresses an improved cross-section analysis approach for calculating the deformation modes of thin-walled cross-sections with circular rounded corners in the framework of generalized beam theory (GBT). In the cross-section discretization, in contrast to the classic GBT one, the circular rounded corners are treated as independent circular walls, and deflection functions of the corresponding circular arches, which play the role of basis functions, are used to approximate the in-plane displacements of any points on the corner mid-line. Because the geometries of the circular corners are accurately modelled by curved elements, the proposed procedure is more efficient than those based on the polygonal approximation of the corner mid-lines. Illustrative cases concerning the employment of the procedure to four cold-formed cross-sections are presented to show its validity and potential. Through comparisons of the proposed procedure against that based on the polygonal approximation, it is shown that it yields accurate results with much coarser cross-section discretization. Highlights • New procedure for determination of the deformation modes for unbranched open sections with circular rounded corners. • Exact discretization of cross-section geometries with curved elements instead of plane elements. • New interpolation scheme for displacement fields for ensuring the kinematic constraints used in GBT cross-section analyses. • Demonstration of the computational efficiency of the procedure through comparison against the classic procedure. [ABSTRACT FROM AUTHOR]

Abstract In engineering, the bending deformations of thin-walled tubes mostly are under three-point loading. However, for the dual rectangle thin-walled tube (DRTWT), the theoretical prediction of the three-point bending collapse is still an unsolved problem. In this paper, the three-point bending collapse of the DRTWT is innovatively investigated using theoretical prediction and experimental verification. The global energy equilibrium theory is applied to derive the bending characteristic of the DRTWT. It is assumed that all the bending energy is absorbed and distributed along the hinge lines and in the toroidal surfaces during the bending collapse. The analytical results show good agreement with the experimental results. Finally, a simplified bumper structure of automobile is created by using beam elements and spring elements with the derived bending characteristics, which can effectively replace the detailed finite element model (FEM) to accelerate the crashworthiness design of automotive structure at the conceptual design stage. Highlights • The bending collapse of the dual rectangular thin-walled tubes is investigated under three-point bending. • The global energy equilibrium theory is applied to derive the bending collapse characteristics. • The analytical results show good agreement with the experimental results. • The simplified finite element model can accelerate crashworthiness design at the conceptual design phase. [ABSTRACT FROM AUTHOR]

Abstract: This paper generalizes the newly developed DSC-Element method for free vibration analysis of skew plates using the first-order shear deformable plate theory. Basically, the DSC-Element method not only embraces the discrete singular convolution (DSC) delta type wavelet kernel as a trial function with the Ritz principle, but also incorporates the concept of the finite element method. The current approach is novel and flexible as contrast to the global numerical methods in treating the complex kinematic supporting edges. The objective of this paper is to examine the efficiency and validity of the DSC-Element method for oblique plates having large skew angles. Parametric studies for the vibration analysis of skew plates with various skew angles, thickness ratios, aspect ratios and continuous or discontinuous periphery supports are presented as well. The natural frequencies are directly compared and discussed with those reported in the open literature. Some frequency solutions for skew plates with mixed edge conditions are also presented. [Copyright &y& Elsevier]

Abstract: This paper addresses the experimental and numerical investigations of the dynamic parameters, natural frequencies and mode shapes, of fixed roof, ground supported, steel storage tanks. Three tall liquid storage tanks with aspect ratios greater than unity are considered. The considered tanks have similar height of 12.190m and different radius of 6.095, 8.00, and 9.144m. The effect of the aspect ratio, along with the liquid level on dynamic parameters is discussed. Finite element models of tanks are constructed using the finite element package ANSYS. The fluid-structure interaction is governed in the models. Yet, before using numerical techniques for analyzing the tank-liquid systems, they should be validated by experimental results. For this purpose, a series of ambient vibration tests are carried out to determine the natural frequencies and, if possible, the modes of the vibration. Comparison between numerical and experimental values shows good agreement. The new feature considered in the paper is the influence of roof on the natural frequencies and the modes of vibration. It is found that the influence of roof on the natural frequency of vibration of the considered tanks is negligible, while it does restrain the tank top against radial deformations and has significant effect on the mode shapes of tank. [Copyright &y& Elsevier]

Abstract: This paper presents a corotational formulation of a three-dimensional elasto-plastic mixed beam element that can undergo large displacements and rotations. The corotational approach applies to a two-noded element a coordinate system which continuously translates and rotates with the element. In this way, the rigid body motion is separated out from the deformational motion. In this paper, a mixed formulation is adopted for the derivation of the local element tangent stiffness matrix and nodal forces based on a two-field Hellinger–Reissner variational principle. The local beam kinematics is based on a low-order nonlinear strain expression using Timoshenko assumption. The warping effects are characterized by adopting Benscoter theory that describes the warping degree of freedom by an independent function. Shape functions that satisfy the nonlinear local equilibrium equations are selected for the interpolation of the stress resultants. This local element, together with the corotational framework, can be used to analyze the nonlinear buckling and postbuckling of thin-walled beams with generic cross-section. The mixed formulation solution is compared against the results obtained from a corotational displacement-based formulation having the same beam kinematics. The superiority of the mixed formulation is clearly demonstrated. [Copyright &y& Elsevier]