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Thin-walled cylindrical shell structures are revisited with the objective of increasing the axial load-carrying capacity. By using the postbuckling reserve of rectangular plates, polygonal shells are studied, which combines the response of a plate-like structure with a shell-like structure. These "plate-shells" are shown to be imperfection insensitive for a range of polygonal shell designs. Furthermore, their collapse load exceeds the corresponding load for a circular cylindrical shell. These results are a significant departure from the well-known imperfection sensitivity in the axial compressive response of cylindrical shells. [ABSTRACT FROM AUTHOR]

Additive manufacturing enables the production of lattice structures, which have been proven to be a superior class of lightweight mechanical metamaterials whose specific stiffness can reach the theoretical limit of the upper Hashin–Shtrikman bound for isotropic cellular materials. To achieve isotropy, complex structures are required, which can be challenging in powder bed additive manufacturing, especially with regard to subsequent powder removal. The present study focuses on the Finite Element Method simulation of 2.5D anisotropic plate lattice metamaterials and the investigation of their lightweight potential. The intentional use of anisotropic structures allows the production of a cell architecture that is easily manufacturable via Laser Powder Bed Fusion (LPBF) while also enabling straightforward optimization for specific load cases. The work demonstrates that the considered anisotropic plate lattices exhibit high weight-specific stiffnesses, superior to those of honeycomb structures, and, simultaneously, a good de-powdering capability. A significant increase in stiffness and the associated surpassing of the upper Hashin–Shtrikman bound due to anisotropy is achievable by optimizing wall thicknesses depending on specific load cases. A stability analysis reveals that, in all lattice structures, plastic deformation is initiated before linear buckling occurs. An analysis of stress concentrations indicates that the introduction of radii at the plate intersections reduces stress peaks and simultaneously increases the weight-specific stiffnesses and thus the lightweight potential. Exemplary samples illustrate the feasibility of manufacturing the analyzed metamaterials within the LPBF process. [ABSTRACT FROM AUTHOR]

This paper investigates the instability and buckling characteristics of a porous microplate under the influence of electrostatic fields, taking into account the implications of the intermolecular Casimir forces. Employing the modified couple stress theory, this research formulates equations that encapsulate the interplay between electrostatic and Casimir forces within porous plates. The analysis integrates distributed support loads, employing both Galerkin mode summation and finite element methods to solve static deformation equations and determine pull-in instability voltages and buckling loads. A novel approach is introduced, and equilibrium relationships are derived with respect to displacement to determine both the buckling load and instability voltage. This study effectively compares classical and non-classical theories, scrutinizing the effects of dimensionless length scale parameters and porosity ratios on maximum displacement, pull-in instability voltages, and buckling loads. The results demonstrate that the analytical method converges swiftly and aligns with the findings of the finite element method. The method for deriving equilibrium relationships proves to be accurate in predicting both instability voltage and buckling load. Additionally, the instability voltage exhibits an almost linear relationship with variations in the percentage of porosity, and similarly, the buckling load undergoes linear changes with alterations in porosity percentage. Hence, formulas for the linear relationships are calculated for both of these associations. [ABSTRACT FROM AUTHOR]

This paper focuses on the size-dependent free vibration and buckling behaviors of the axially functionally graded (AFG) graphene platelets (GPLs) reinforced nanocomposite microbeams subjected to axially varying loads (AVLs). With various axial grading patterns, the GPL nano-reinforcements are distributed throughout the polymer matrix against microbeam length, and the improved Halpin–Tsai micromechanics model and the rule of mixture are adopted to evaluate the effective material properties. Eigenvalue equations of the microbeams governing the static stability and vibration are derived based on the modified couple stress Euler–Bernoulli beam theory via the state-space method, and are analytically solved with the discrete equilong segment model. The effects of axial distribution patterns, weight fraction, and geometric parameters of GPLs, as well as different types of AVLs, on the size-dependent buckling load and natural frequency are scrutinized in detail. The results show that the synchronized axial distributions of GPLs and AVLs could improve the buckling resistance and natural frequency more powerfully. [ABSTRACT FROM AUTHOR]

In this paper, the mechanics of shear deformable micro beams is investigated via finite element analysis, and a machine learning technique (Deep Learning Neural Network (DLNN)). DLNN is provided for the first time to accurately model and predict this behavior. Using the Finite Element Method (FEM), the obtained coupled equations of motion for shear deformable micro-scale beams are solved using a combination of Timoshenko beam theory and the modified couple stress theory (MCST). The results are compared with literature for each analysis to show the accuracy and the proposed finite element model. After presenting the mechanical model, by using Finite Element Analysis (FEA), a deep learning neural network model is developed for small-scale structures and the capability of this model in predicting different mechanical behavior under thermo-mechanical loading is investigated. It is shown that the presented model has great accuracy in predicting both static and dynamic behavior of small-scale structures with a significant reduction in the computational cost. The application of DLNN for modeling the machines of small- scale structures is a step forward for predicting the behavior of Nano/Micro Electro Mechanical Systems (NEMS/MEMS). [ABSTRACT FROM AUTHOR]

During seismic events, cyclic demands exceeding the elastic limit load and buckling of steel reinforcing bars significantly impact the global response of thin and lightly reinforced concrete (TLRCW) wall buildings. This study evaluates the cyclic response of low-diameter steel reinforcing bars commonly used in thin RC walls. The experimental program of the study comprises the characterization and reversed cyclic tests of 60 specimens obtained from steel reinforcing bars grade 60 (420 MPa) with nominal diameters of 9.5 and 12.7 mm. An increasing, symmetrical strain protocol was used during the cyclic tests. The study analyses the stress–strain curves obtained in the cyclic tests of steel reinforcing bars and assesses the effect of parameters such as the slenderness ratio, bar diameter, and yield stress on the cyclic response of bars. The onset of buckling and its effects on the cyclic response of steel reinforcing bars, such as pinching and stress reduction in compression are also examined. The degradation of the mechanical properties of steel reinforcing bars obtained during cyclic tests was evaluated and compared to that obtained during monotonic tests. The study shows that low-diameter steel rebars under cyclic loading exhibit lower ductility and premature hardening in tension when compared to bars subjected to monotonic loading. Finally, fundamental properties of low-diameter steel reinforcing bars subjected to cyclic loads were established, such as ductility and hardening capacity. These properties will contribute to enhancing the understanding of the seismic behavior of TLRCW buildings. [ABSTRACT FROM AUTHOR]

This paper aims to study imperfect nanotubes' buckling behavior made of functionally graded materials with porosity and non-uniform cross-section. The nonlocal strain gradient theory is used to define the size effect in nano-scale, and also new higher order tube model and first-order shear deformation theory are utilized to develop the nanotube's formulation. The results are obtained using the generalized differential quadrature method and are compared to the Timoshenko theory with very satisfying convergence. The boundary conditions are considered as clamped, clamped-simply supported, and also simply supported. The results illustrate the effects of the FG power index, porosity, rates of cross-section change, nonlocal, and strain gradient parameters on the buckling behavior of the FG tapered porous nanotube. [ABSTRACT FROM AUTHOR]

Background: The modelling of the sheet metal forming operations requires accurate and precise data of the material plastic behaviour along non-proportional strain paths. However, the buckling phenomenon severely limits the compressive strain range that could be used to deform thin metal sheets. Objective: The main aim of this paper was to propose an effective device, that enables to determine of accurate stress-strain characteristics of thin metal sheet specimens subjected to axial deformation without buckling and with a special emphasis on friction correction. Methods: In this paper, an anti-buckling fixture was proposed to assess the deformation characteristics of X10CrMoVNb9-1 (P91) power engineering steel, and DP500 and DP980 dual-phase steels, under compression loading. The fixture enables monitoring of the friction between the specimen and supporting blocks during the test, and thus the precise stress response of the material could be determined. Results: The effectiveness of the fixture was evaluated under tension–compression cyclic loading and during the compression tests in which high-strength thin metal sheets were successfully deformed up to 10% without specimen buckling. Furthermore, the successful determination of a friction force variation between supporting blocks and the specimen during tests enabled to determine an actual force acting on the specimen. Conclusions: The proposed testing fixture was successfully assessed during the compression and cyclic tension–compression of high-strength thin metal sheets as no buckling was observed. Its advantage lies in adapting to change its length with specimen elongation or shrinkage during a test. The friction force generated from a movement of both parts of the device could be effectively monitored by the special strain gauge system during testing and thus its impact on the stress-strain characteristics could be successfully eliminated. [ABSTRACT FROM AUTHOR]

The snap-through analysis of shallow doubly hinged sinusoidal nano-arches subjected to sinusoidal load, considering the nonlocal effects, by using the stress-driven nonlocal model is concerned. The problem is formulated within the framework of Bernoulli–Euler beam theory including geometrical nonlinearity. Numerical simulations are made to investigate the effects of the geometry of the arch, and the nonlocal parameter on the buckling load and on the buckling deflection. Insights and conclusions regarding the effects of various stages of deformation on the stress resultants, and on the buckling including prebuckling and postbuckling are presented. Variations of the stress resultants along the arch are shown. [ABSTRACT FROM AUTHOR]

Arches are important components in nanostructures and systems. Because of the remarkable strength of nanomaterials, nanoarches are slender, thus enhancing their vulnerability to geometric instability, such as buckling. Although molecular simulations are often employed to analyze nanostructures, their use in routine analysis/design is formidable due to prohibitively exhaustive computation. Equivalent continuum models were developed as alternatives. The buckling and postcritical phenomena of the classical arch also form an important benchmark problem in nonlinear mechanics. This study investigates the buckling and the postcritical behavior of nanoarch subjected to inward pressure using nonlocal (NL), strain gradient (SG) continuum theory. The governing equations are derived in the form of a sixth-order nonlinear integrodifferential equation, unlike the fourth-order for a classical arch. The equation is then solved numerically using a differential quadrature (DQ) with appropriate boundary conditions. An incremental-iterative arc-length continuation is employed for the solution of the resulting algebraic system of equations. The equilibrium paths are traced for the possible instability modes, such as symmetric/antisymmetric bifurcations, snap-through and limit point instability, ascertained with the internal-external force diagrams. A particular instability mode is triggered at a certain threshold/range of the slenderness ratio of the arch, which is significantly influenced by the NL and SG interactions. These interactions not only cause quantitative changes in the instability behavior but also lead to qualitative changes, such as cessation, shift, and conversion of modes, more prominently for SG arches. Similar to classical arches, the prebuckling nonlinearity is shown to be significant. [ABSTRACT FROM AUTHOR]

In the present study, the buckling problem of nonhomogeneous microbeams with a variable cross-section is analyzed. The microcolumn considered in this study is made of functionally graded materials in the longitudinal direction and the cross-section of the microcolumn varies continuously throughout the axial direction. The Bernoulli–Euler beam theory in conjunction with modified strain gradient theory are employed to model the structure by considering the size effect. The Rayleigh–Ritz numerical solution method is used to solve the eigenvalue problem for various conditions. The influences of changes in the cross-section and Young's modulus, size dependency, and non-classical boundary conditions are examined in detail. It is observed that the size effect becomes more pronounced for smaller sizes and differences between the classical and non-classical buckling loads increase by increasing the taper ratios. [ABSTRACT FROM AUTHOR]

The purposes of this paper are to study bending, buckling, and vibration by considering micro-scale effects using the Kirchhoff thin-plate theory and to consider small deflections, neglecting higher-order nonlinear terms. The governing equations for the bending, buckling, and vibration of the system are obtained using the equilibrium method coupled with the Kirchhoff thin-plate theory and a modified couple stress theory (MCST). The concept of the equivalent bending stiffness (EBS) of micro-thin plates is proposed to describe the scale effect. The Navier method is used to obtain analytical solutions for the bending, buckling, and free vibration of thin plates under simply supported boundary conditions with scale effects. The numerical results are presented to investigate the influence of scale effects on deflection, critical buckling load, buckling topography, and thin-plate natural frequency. The results show that the scale effect increases the equivalent stiffness of the thin plate, which leads to a decrease in deflection, a larger critical buckling load, and an increase in natural frequency, but does not affect the buckling topography. The MSCT is invalid when the thickness is greater than 10 times the scale effect parameter, thus defining the scope of application of the scale effect. This research study may contribute to the design of micro-scale devices such as MEMSs/NEMSs. [ABSTRACT FROM AUTHOR]

The nonlocal strain gradient and classical shell theories are used to derive the governing equations of functionally graded cylindrical nanopanels (open cylindrical shells). The properties of the nanopanel are graded as a power-law distribution through the thickness direction. The linearization stability equations are obtained using an adjacent equilibrium criterion. Governing equations are solved by Galerkin method to investigate the effects of the material length scale parameter, the nonlocal parameter, the geometric parameters, and the material properties on the buckling behavior of functionally graded cylindrical nanopanels. Numerical results are compared and discussed with available data. The solution of the closed cylindrical shell is recovered when the span angle is taken as 360 degrees. [ABSTRACT FROM AUTHOR]

Due to wide-ranging applications of piezoelectric nanostructures as the next generation of smart devices, this article analyzes size-dependent buckling and free vibration performance of fluid-conveying functionally graded-graphene nanoplatelets reinforced composite (FG-GPLRC) porous cylindrical nanoshell embedded in piezoelectric layer and subjected to the temperature gradient and a uniform electrical field based on modified couple stress theory incorporated into first-order shear deformation theory. Classical continuum theories are unable to capture the size effects on small-scale structures; thus, it is required to employ a nonclassical theory. To accomplish this purpose, modified couple stress theory is utilized to present a size-dependent shell model in which its displacement field is formulated by first-order shear deformation theory. The mechanical properties of the GPLRC layer are estimated based on modified Halpin-Tsai micromechanics and the rule of mixtures. Hamilton's principle is employed to develop governing equations of motion and boundary conditions. Eventually, an analytical solution is prepared based on the Navier method to obtain critical voltage, critical buckling load, and natural frequency in the case of simply supported nanoshell, whereas, for other boundary conditions, the differential quadrature method is employed to solve the problem semi-analytically. The numerical illustration reveals that graphene reinforcement and porosity affect free vibration and buckling behavior of the nanoshell significantly. Moreover, it is concluded that the effect of fluid flow on vibration behavior nanoshell is more noticeable. [ABSTRACT FROM AUTHOR]

Size-dependent functionally graded material thin plate buckling and post-buckling problems are considered using the framework of the MCST (Modified Couple Stress Theory). Based on modified couple stress theory and power law, the post-buckling deflection and critical buckling load of simply supported functionally graded material thin plate are derived using Hamilton's minimum potential energy principle. The analysis compares the simulation results of linear buckling and nonlinear buckling. Innovatively, a power-law distribution with scale effects is considered. The influences of scale effect parameters l and power-law index parameters k on buckling displacement, load, and strain energy of plates have been investigated. In this article, it is found that the critical buckling displacement, critical buckling load, and buckling strain energy increase with increases in the power-law index parameters k. The membrane energy decreases as the power-law index parameter increases. If the upper and lower layers are swapped, the opposite result is obtained. In comparison, the scale effect parameter is more influential than the power-law exponent. The critical buckling displacement in the x-direction is not affected by scale effects. The critical buckling load, the membrane energy, and buckling strain energy increase as the scale effect parameter increases. Scale effects increase material stiffness compared with traditional theory, and the power-law index parameters affect FGM properties such as elastic modulus, Poisson's ratio, density, etc. Both scale effects parameters and power-law index parameters have important effects on the mechanical behavior of materials. [ABSTRACT FROM AUTHOR]

A new microstructure-dependent non-classical model for Kirchhoff plates is developed by using a reformulated strain gradient elasticity theory that incorporates both the strain gradient and couple stress effects. The equation of motion and the boundary conditions are simultaneously obtained through a variational formulation based on Hamilton's principle. The new plate model contains one material constant to account for the strain gradient effect and one material length scale parameter to capture the couple stress effect. The newly developed non-classical plate model includes the plate model incorporating the couple stress effect alone and the plate model based on the classical elasticity as two special cases. To illustrate the new model, the buckling, static bending and free vibration problems of a simply supported rectangular plate are analytically solved by directly applying the general formulas derived. The numerical results reveal that the presence of the strain gradient and couple stress effects leads to reduced plate deflections, enlarged critical buckling loads and increased natural frequencies. These microstructure effects are significant when the plate is very thin, but they are diminishing as the plate thickness increases. These predicted trends of the size effects at the micron scale agree with those observed experimentally. [ABSTRACT FROM AUTHOR]

A Mindlin plate theory for micro-nano structures was proposed based on the couple stress theory. A length parameter was introduced to consider the size effect, and the constitutive equations for the micro-nano Mindlin plate were derived in view of the transverse shear deformation. The buckling and free vibration governing equations in terms of displacements and the slope functions of the shear deformation micro-nano plate were further deduced with the force equilibrium conditions. The analytical solutions of buckling and free vibration for the shear deformation micro-nano plate were obtained through separation of the displacement and rotation variables in space and time domains. Two scenarios of boundary conditions were analyzed: SSSS (simply supported by 4 edges) and SCSC (2 opposite edges simply supported and other 2 edges clamped). A MATLAB program was developed to compute the critical buckling and natural frequencies with different values of dimensional parameters, aspect ratios and length-to-thickness ratios. The research results, in comparison with those from the ABAQUS finite element analysis and previous literatures, are consistent with the latter ones. The examples show that, the size effects significantly influence the buckling load and the natural frequency. [ABSTRACT FROM AUTHOR]

In this paper, the finite element method is utilized to evaluate the behavior of the armchair phosphorene nanotubes under the compressive loading. The energy equations of the molecular and structural mechanics are used to obtain the elemental properties. The critical compressive forces of various armchair phosphorene nanotubes are computed with clamped-clamped and clamped-free boundary conditions. Results show that the stability of armchair phosphorene nanotubes increases with increasing nanotube aspect ratio, particularly under clamped-clamped boundary conditions. Finally, the buckling mode shapes of armchair phosphorene nanotubes under different boundary conditions are compared. Our work offers valuable insights into how these nanotubes respond to mechanical stress, helps determine elemental properties, and investigates the effects of nanotube geometry and different boundary conditions on their stability. This knowledge has broad applications in fields like nanotechnology, materials science, and nanomechanics, advancing the understanding of nanoscale materials and their potential for various practical uses. The finite element method is utilized to evaluate the behavior of the armchair phosphorene nanotubes under the compressive loading. [Display omitted] • FE method is utilized to evaluate the behavior of the armchair PNTs under the compressive loading. • The elemental properties are obtained by the energy equations of the molecular and structural mechanics. • The buckling forces of the armchair PNTs with different radii and lengths are computed. • The stability of armchair PNTs increases by increasing the nanotube aspect ratio. • The clamped-clamped nanotubes are more stable than clamped-free ones. [ABSTRACT FROM AUTHOR]

• The proposed model satisfied the consistency condition of the plastic multiplier under any loading patterns. • Results of the proposed model were consistent with the material and structural test results. • The proposed model had equivalent convergence to existing models. Mild steels are frequently used in building structures because of their high strength, productivity, processability, and weldability. One key feature of mild steels is their yield plateau, which is followed by a hardening region in the stress–strain relationship. During large earthquakes, building members can experience a large plastic strain whose amplitude is difficult to predict beforehand. Constitutive equations applicable to the full-range strain field are necessary for accurate structural safety evaluation. This study provides novel constitutive equations for the plateau region, capable of reproducing a yield plateau. A set of hardening constants was proposed to satisfy the consistency condition of the plastic multiplier under any loading pattern. The closed form of the stress–strain relationship was derived to calibrate the material constants. The material constants were calibrated using two types of material test results. The results of the proposed model were consistent with the material test results under cyclic loading at various strain amplitudes. This was validated by comparing the shear buckling and lateral torsional buckling test results of an H-shaped beam with the finite element analysis (FEA) results. The numerical demonstration also highlighted the significance of not only material constitutive laws but also the introduction of residual stress and initial imperfections in reproducing the pre- and post-buckling behaviors. The convergence of the residual force for the proposed model was equivalent to those of the authors' previous model and the Chaboche model. These results indicate that the proposed model can predict hardening phenomena at the material and structural levels in the plateau and hardening regions. [ABSTRACT FROM AUTHOR]

• A novel multiscale analysis is developed to assess the buckling behavior of MWCNT-reinforced laminated composites. • Integration of microstructural factors like MWCNT clustering, alignment, and curvature in evaluating composite material performance. • Comprehensive assessment of the influence of moisture and temperature on the buckling performance of MWCNT composites. • Results successfully compared and validated with existing experimental and theoretical data. • Offers significant insights for the design and optimization of MWCNT-reinforced composites. This study introduces a detailed method for analyzing the buckling behavior of laminated composite structures strengthened with multi-walled carbon nanotubes (MWCNTs). We propose a multi-scale analysis that combines analytical and computational techniques to assess the mechanical performance of MWCNT-reinforced composites under combined moisture, temperature, and mechanical stress conditions. The Halpin-Tsai equations are used to calculate the overall stiffness properties of the nano-enhanced matrix, considering factors like MWCNT clustering, alignment, and curvature. Additionally, we incorporate the nanoscopic, size-dependent features of MWCNTs into our model. The Chamis micromechanical formulas are applied to determine the individual elastic properties of the nanocomposite layers, considering the impacts of temperature and moisture. We then explore how variables such as MWCNT content and size, along with temperature and moisture levels, influence the critical buckling load of MWCNT-based laminated composite beams and plates using our multi-scale model. Our results are successfully compared with existing experimental and theoretical data to validate our approach. The developed method offers significant insights for the design and optimization of MWCNT-reinforced composites, potentially benefiting various engineering fields, including aerospace and automotive industries. [ABSTRACT FROM AUTHOR]

The prebuckling deformation of structures is neglected in most of the conventional buckling theory (CBT) and numerical method (CNM), because it is usually very small in conventional concepts. In the preceding paper (Su et al., 2019), we found a class of structures from the emerging field of stretchable electronics, of which the prebuckling deformation became large and essential for determining the critical buckling load, and developed a systematic buckling theory for 3D beams considering the effects of finite prebuckling deformation (FPD). For bulk structures that appear vastly in the advanced structures, a few buckling theories consider the effects of the prebuckling deformation in constitutive equations by energy method, which are significantly important but not straightforward and universal enough. In this paper, a systematic and straightforward theory for the FPD buckling of bulk structures is developed with the use of two constitutive models. The variables for the prebuckling deformation serve as the coefficients of the incremental displacements, deformation components, and stress in the buckling analysis. Four methods, including the CBT, CNM, DLU (disturbing-loading-unloading method) method and FPD buckling theory, are applied to the classic problems, including buckling of an elastic semi-plane solid and buckling of an elastic rectangular solid, respectively. Compared with the accurate buckling load from the DLU method, the FPD buckling theory is able to give a good prediction, while the CBT and CNM may yield unacceptable results (with 70% error for the buckling of an elastic semi-plane solid). [ABSTRACT FROM AUTHOR]

In this contribution, we analyze buckling and free vibration of simply-supported cross-ply/angle-ply single-walled carbon nanotubes reinforced composite CNTRC laminated nanoplates in thermal environment. The nonlocal strain gradient theory within the third-order shear deformation plate theory are adopted to capture the size-dependent effects of CNTRC laminated nanoplates. Several types of reinforcement material distributions, a uniform distribution and functionally graded distributions, are inspected. Material properties are temperature-dependent and performed using Touloukian principal. The influence of CNTs reinforcement patterns, composite structure, nonlocal parameter, length scale parameter, carbon nanotubes orientation, and the geometric parameters on buckling loads and natural frequencies is examined. [ABSTRACT FROM AUTHOR]

This article aims to investigate buckling characteristics of a functionally graded magneto-electro-thermo-elastic nanoshell based on nonlocal strain gradient theory (NSGT). Accounting for nonlocal and strain gradient size-dependency, NSGT has two scale coefficients. The nanoshell is subjected to external electric, magnetic, mechanical, and thermal fields. The temperature distributions are considered as uniform and linear thorough the nanoshell thickness. All material properties including elastic, piezoelectric, and magnetic properties are defined based on a power-law distribution type. Seven coupled governing equations are derived for the nanoshell based on Hamilton's rule and then solved applying Galerkin's approach. The dependency of the buckling behavior of the nanoshell on applied thermal load, temperature distribution, electric voltage, magnetic potential, material gradient index, scale parameters, and shear deformation will be explored. [ABSTRACT FROM AUTHOR]

We developed and obtained close-form solutions for the buckling growth rate of microtubule (MT) bundles using the Timoshenko beam theory. We took into consideration the surface effects and the Poisson's ratio of the microtubules surrounded by neighbouring filaments in the viscous cytosol. We developed the motion equation by using the modified couple stress theory (MCST) which will take into account the small-scale effects of the microtubules. We then proceeded by studying the effects of various parameters on the buckling growth rate of microtubule bundles. Our results show that the internal material length scale parameter has a decreasing effect on the buckling growth rate of the microtubule bundle. And as microtubule added in the bundle increases, the buckling growth rate reduces further due to the effects of the surrounding microtubule-associated proteins (MAPs). On the contrary, the Poisson's ratio has an increasing effect on the value of the buckling growth rate of the microtubule bundle. We also investigated the effects of other parameters such as surface energy on the buckling growth rates of microtubule bundles and showed the validity of our model by comparing our results with those obtained by previous researchers. [ABSTRACT FROM AUTHOR]

In this paper, the buckling behavior and nonlinear vibrations of graphene nanosheets in the magnetic field are studied analytically. By considering mechanical and magnetic interactions, new relationships have been proposed for the forces exerted by the magnetic field. The nonlinear governing equation is derived using Kirchhoff's thin plate theory in conjunction with the nonlocal strain gradient theory of elasticity and von Karman's nonlinear strain-displacement relation. The nonlinear governing equation is discretized using the Galerkin method. According to the method of multiple scales, the approximate analytical solutions are extracted. For the three considered boundary conditions, nonlinear natural frequencies and amplitude-frequency curves are computed for different values of magnetic field and nonlocal parameters. The results show that increasing the nonlocal parameter and applying a magnetic field reduces the flexural stiffness and increases the in-plate compressive force which results in reducing the natural frequency. In addition, excessive magnification of the magnetic field causes static buckling. The value of the critical magnetic field is highly dependent on the type of boundary conditions. [ABSTRACT FROM AUTHOR]

The reinforcement in marine RC structures will inevitably be corroded under long-time erosion of chloride ions, which will weaken steel mechanical properties and then structural seismic resistance. The new metallurgical technology is adopted for manufacturing high-strength steel bars (HSSB), but that may affect the corrosion resistance of steel bars at the same time. This paper experimentally investigates the effects of corrosion on monotonic and low-cycle fatigue properties of HSSB HTRB600 and normal strength steel bars (NSB) HRB400E. The HRB400E and HTRB600 steel bars were corroded to different corrosion rates by electrochemical accelerated corrosion technique. The monotonic tensile and compressive, as well as low-cycle fatigue tests of corroded steel bars were conducted to investigate the effects of corrosion on steel mechanical properties, of which corrosion levels (0–20% target corrosion mass loss), slenderness ratios (L / D =6, 8, 10, 12) and strain amplitudes (2%, 4%) are considered. Test results show that, the corrosion morphology of steel bars under electrochemical accelerated corrosion is basically consistent with that observed under natural corrosion. Compared with uncorroded HRB400E and HTRB600 steel bars, 20% corrosion mass loss leads to 38% and 35% decrease in tensile strength, as well as 33% and 28% reduction in buckling stress, respectively. The HTRB600 steel bars present slightly superior monotonic tensile and compressive corrosion resistance than HRB400E steel bars. Corrosion obviously decreases the low-cycle fatigue (LCF) life of steel bars, resulting in reductions of 44% and 36% in LCF life at 20% corrosion mass loss for HTRB600 and HRB400E steel with a L / D of 6, respectively. Moreover, the HTRB600 steel bars present more significant corrosion degradation in total hysteretic dissipated energy, compared with HRB400E steel bars. The combined effect of corrosion and inelastic buckling further exacerbates the deterioration of LCF performance of steel bars. The corresponding deterioration models are proposed to determine the LCF life and energy dissipation capacity of corroded steel bars. • Carry out monotonic and low-cycle fatigue tests of corroded HTRB600 and HRB400E steel bars. • Compare corrosion morphology between electrochemical accelerated and natural corrosion. • Establish mechanical deterioration model of corroded steel bars. • Investigate and compare the effects of corrosion on monotonic and LCF performance of HTRB600 and HRB400E steel bars. [ABSTRACT FROM AUTHOR]

• Axial compression behaviour of BFRP tubes with three different cross-sections was studied. • The stress–strain curves of the BFRP tubes was classified into three stages of elastic, elastic–plastic, and plastic. • Three types of compressive failure modes were observed in the BFRP tubes. • Two design-oriented three-stage theoretical models were proposed for BFRP tubes with different cross-sections. • A stability equation was derived for predicting the compressive strength of slender BFRP tubes. This study analyzed mechanical properties and stability of pultruded basalt fiber-reinforced polymer (BFRP) tubes under compressive axial loading for large-span space and truss structures applications. This study assessed the compressive strength of BFRP tubes with three different cross-sectional shapes and investigated the failure modes under compression with slenderness ratios ranging from 20 to 150. The results demonstrated that short BFRP tubes can achieve a compressive strength of up to 122.36 MPa with a compressive elastic modulus of 40.39 GPa. Three types of compressive failure modes were observed in the BFRP tubes, including local material, critical, and overall buckling failures. Furthermore, based on the analysis of experiment results, two design-oriented three-stage theoretical models were proposed for BFRP tubes with three different cross-sectional shapes. The proposed models were able to predict both the stress–strain and load-lateral deflection curves by taking into account the post-peak softening behavior of the stress–strain curve. In addition, a stability equation was also derived for predicting the compressive strength of slender BFRP tubes and was validated by experiments. The predictions derived from proposed models were consistent with experiment results. [ABSTRACT FROM AUTHOR]

In this paper, an efficient formulation for the topology optimization of extruded beams is developed considering linearized buckling, displacement, and stress constraints. The proposed method relies on a computationally efficient extended\generalized finite element (XFEM\GFEM) formulation for the forward problem, recently developed for the analysis of beams. In this method, a coarse 3D finite element (FE) mesh is enhanced with global enrichment functions, enabling a substantial reduction in the number of degrees of freedom with comparable accuracy to a traditional 3D FE fine mesh. The material distribution at the cross-section is optimized utilizing the material density approach with the Solid Isotropic Material with Penalization (SIMP) method. Our objective is to minimize the total weight of the beam, subject to performance constraints including buckling, displacement, and stress. The forward problem enables the application of general loading and boundary conditions. Thus, both buckling and lateral–torsional buckling are automatically considered. The optimization problem is solved using a gradient-based optimization approach, with analytical gradients derived by using the adjoint variable method. Several numerical examples are presented to investigate the accuracy and efficiency of the proposed formulation. A parametric study showed that the optimized cross-section is strongly dependent on the length and permissible buckling load. In addition, it is shown that a simultaneous formulation leads to significantly different designs, with different structural behavior, compared to results obtained by considering only a subset of the performance constraints. Finally, we verify the model on a beam warping problem under pure torsion, in which the cross-section optimization converges to a known analytical solution. Compared with traditional FEM, two orders of magnitude in terms of execution time are reported in favor of the proposed XFEM\GFEM approach. • A new approach for the topology optimization of extruded beams is proposed. • The forward problem is solved using an efficient numerical scheme relying on the extended finite element method. • The approach simultaneously considers buckling, stress, and displacement constraints. • We show that the beam's length significantly affects the optimal shape. • The proposed XFEM\GFEM approach shows significant time savings compared with 3D FE. [ABSTRACT FROM AUTHOR]

The present study addresses a simplified topology optimization method to improve load bearing capacity. Topology optimization taking account of structurally nonlinear and complex behavior is an important topic from the viewpoint of mechanics. However, most methodologies require complex analytical derivation of sensitivity analysis and high computational cost to obtain the optimal solution. In light of this, we propose a practical design method employing the principal direction of Cauchy stress and the directional statistics, to improve load bearing capacity indirectly with much lower computational cost than those based on complex nonlinear structural analysis. Finally, we discuss setting of optimization problems, and demonstrate the accuracy and performance of the proposed method with a series of numerical examples. [ABSTRACT FROM AUTHOR]

This paper investigates the weight minimization of stiffened panels simultaneously optimizing sizing, layout, and topology under stress and buckling constraints. An effective topology optimization parameterization is presented using multiple level-set functions. Plate elements are employed to model the stiffened panels. The stiffeners are parametrized by implicit level-set functions. The internal topologies of the stiffeners are optimized as well as their layout. A free-form mesh deformation approach is improved to adjust the finite element mesh. Sizing optimization is also included. The thicknesses of the skin and stiffeners are optimized. Bending, shear, and membrane stresses are evaluated at the bottom, middle, and top surfaces of the elements. A p-norm function is used to aggregate these stresses in a single constraint. To solve the optimization problem, a semi-analytical sensitivity analysis is performed, and the optimization algorithm is outlined. Numerical investigations demonstrate and validate the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, the vibration and buckling behavior of a functionally graded piezoelectric porous cylindrical microshell under thermo-electro-mechanical loads are explored on the basis of modified couple stress theory and higher-order shear deformation theory. First, the model of a functionally graded piezoelectric porous cylindrical microshell composed of piezoelectric materials with gradient change in the thickness direction was described. Second, the governing equations of the microshell were derived by Hamilton's principle and Maxwell equation. Third, the modal frequency and buckling equations of the microshell with simply supported ends were obtained on the basis of harmonic trigonometric functions. Finally, the effects of parameters on the modal frequency and buckling behavior were carried out by case studies. The results show that the modal frequency of the microshell can be adjusted by changing the porosity volume fraction, power index, applied voltage, axial load and geometric dimensions. It is also found that the vibration of the microshell is suppressed by positive voltage and axial compression but is strengthened by negative voltage and axial tension, and the material length scale parameter increases stiffness. In addition, the effects of applied voltage and axial load on the buckling behavior are larger than those of temperature. Results can be used to guide the design and application of piezoelectric devices. [ABSTRACT FROM AUTHOR]

To assess the stability and postbuckling behavior of thin composite panels with additional repair lap plates, it is proposed to use relations that consider the unsymmetry of the structure. An analytical solution of the geometrically nonlinear problem is presented for smooth composite panels, whose shape is close to a square, loaded by tangential flows. The initial relations of the problem consider the possible unsymmetry of the structure and include mixed stiffnesses. The boundary conditions in this case correspond to a hinged support. An explicit expression is obtained for the critical stresses of the loss of stability under the action of tangential forces. Relations for the stress-strain state of a square composite panel at its geometrically nonlinear behavior are given. Examples of determination of the critical shear forces are presented, and the expediency of consideration of unsymmetry of the structure in verification calculations of thin composite panels is shown. [ABSTRACT FROM AUTHOR]

In this paper, a numerical investigation on the global buckling capacity of the axially compressed steel columns with hot-rolled I crosssection at elevated temperatures is presented. Geometrically and materially non-linear finite element model and the ABAQUS software were used to determine the buckling resistance. The numerical ABAQUS model was validated using experimental results available in the literature, and then the validated numerical model was used to generate a database of load-carrying capacity. The parametric study covered three different cross-section classes (class 1, 2 and 3), ten different non-dimensional slenderness ̄λ = 0.5, 0.6, 0.7, 0.9, 1.1, 1.3, 1.5, 1.7, 1.9, 2.0), three different temperatures (400°C, 500°C, 600°C), and two stress-strain constitutive relations including (the nonlinear material model adopted in the European guidance for structural fire design EN1993-1-2, and a Bilinear material model), with and without residual stress. The influence of the model parameters on the load capacity of steel columns at elevated temperatures was evaluated. The results of the parametric study were compared with the results of the simplified calculation model presented in EN1993-1-2. [ABSTRACT FROM AUTHOR]

The roof slab of a nuclear reactor supports all the components and sub-systems. It needs to resist the seismic loads in accordance with load-carrying criteria. The static stress analysis of the reactor roof slab reveals that high-stress concentration was present in the pump penetration shell (PPS) that supports the primary sodium pump. This paper presents an assessment of collapse load and the optimization of the pump penetration shell through the reliability approach, accounting for material non-linearity, geometrical non-linearity and randomness in loading. In addition, the load-carrying capacity of PPS was determined considering two different materials: IS2062 and A48P2. The design of experiments (DoE) was formulated considering the flange angle and flange thickness as parameters. An empirical model for load function was formulated from the results of the collapse load obtained for various combinations of design parameters. The above function was used to perform the reliability-based geometry optimization of the PPS of the roof slab. [ABSTRACT FROM AUTHOR]

• Size-dependent responses of 2D FG porous microbeams are studied using the modified strain gradient theory. • Two different porosity distribution models for 2D FG microbeams are considered. • Material length scale parameter (MLSP) is varied in both the axial and thickness directions as well as porosity. • The effects of small size, MLSP, porosity, gradient indexes and boundary conditions are investigated. • The effect of variable MLSP is significant and should be considered for analysis of 2D FG porous microbeams. Finite elemen model for the structural behaviours of bi-directional (2D) FG porous microbeams based on a quasi-3D theory and the modified strain gradient theory (MSGT) is presented. As the main novelty of this study, in order to capture accurately the size effects, the MSGT is employed with three material length scale parameters (MLSPs) rather than the modifed couple stress theory (MCST) with only one MLSP. The material properties including three MLSPs are varied in both the axial and thickness directions as well as porosity. By using a quasi-3D theory, which inludes normal and shear deformations, the governing equations for static, vibration and buckling analysis are derived and solved by Hermite-cubic beam element for various boundary conditions. Through numerical examples, effects of variable MLSP and porosity as well as gradient index in two directions on the deflections, natural frequencies and buckling loads of 2D FG porous microbeams are examined. [ABSTRACT FROM AUTHOR]

Purpose: The purpose of this paper is to attempt the buckling analysis of a laminated composite skew plate using the C0 finite element (FE) model based on higher-order shear deformation theory (HSDT) in conjunction with minimax probability machine regression (MPMR) and multivariate adaptive regression spline (MARS). Design/methodology/approach: HSDT considers the third-order variation of in-plane displacements which eliminates the use of shear correction factor owing to realistic parabolic transverse shear stresses across the thickness coordinate. At the top and bottom of the plate, zero transverse shear stress condition is imposed. C0 FE model based on HSDT is developed and coded in formula translation (FORTRAN). FE model is validated and found efficient to create new results. MPMR and MARS models are coded in MATLAB. Using skew angle (α), stacking sequence (Ai) and buckling strength (Y) as input parameters, a regression problem is formulated using MPMR and MARS to predict the buckling strength of laminated composite skew plates. Findings: The results of the MPMR and MARS models are in good agreement with the FE model result. MPMR is a better tool than MARS to analyze the buckling problem. Research limitations/implications: The present work considers the linear behavior of the laminated composite skew plate. Originality/value: To the authors' best of knowledge, there is no work in the literature on the buckling analysis of a laminated composite skew plate using C0 FE formulation based on third-order shear deformation theory in conjunction with MPMR and MARS. These machine-learning techniques increase efficiency, reduce the computational time and reduce the cost of analysis. Further, an equation is generated with the MARS model via which the buckling strength of the laminated composite skew plate can be predicted with ease and simplicity. [ABSTRACT FROM AUTHOR]

The bending and buckling of functionally graded nanoplates in intelligent devices (e.g., nanorobots) were studied based on the nonlocal strain gradient theory. The motion equations in general cases were derived, and then reduced to bending and buckling in special cases. The effects of the nonlocal scale parameter, the material characteristic scale parameter, the gradient index and the geometric size on the bending deflection and the critical buckling load were acquired and analyzed in detail. The results show that, the maximum bending deflections under different higher-order continuum mechanics theories increase with the gradient index. The deflection goes lower for the square nanoplate. The thicker the nanoplate is, the smaller the bending deflection will be. The maximum deflection increases with the nonlocal scale parameter but decreases with the material characteristic scale parameter. The critical buckling load decreases with the gradient index, and increases with the thickness and the aspect ratio. When the nonlocal scale parameter increases, the critical buckling load will decrease, but will increase with the material characteristic scale parameter. The softening and hardening mechanisms exist in higher-order bending and buckling of the functionally graded nanoplates, and the coupling effect between 2 internal characteristic parameters also occurs. When the nonlocal scale is greater than the material characteristic scale, the nonlocal effect will dominate in the mechanical properties of functionally graded nanoplates, otherwise the strain gradient effect will play a leading role. The analytical solutions also show that, when the nonlocal scale is equal to the material characteristic scale, the results based on the nonlocal strain gradient theory will degenerate into the corresponding classical ones. [ABSTRACT FROM AUTHOR]

Instabilities in nanosized, externally pressurized spherical shells are important for their applications in nano and biotechnology. Mechanics at such length scale is described by nonlocal and Strain Gradient (SG) field theories. However, analysis of shell buckling is involved and becomes even more complicated in presence of nonlocal and SG interactions. This paper demonstrates that such analysis can be largely simplified by a shallow segment representation of the shell by assuming short wave lengths for the incipient buckling modes. The governing equations are derived and linearized equations are solved to obtain a closed form solution for the critical external pressure causing buckling for a pressurized nonlocal shell. Nonlocal interactions are shown to reduce, whereas the SG interaction increases the critical pressure. The relative reduction/increase becomes more prominent for higher modes of buckling and for increasingly thinner shell. A constricting relationship between the two set of wave numbers expressing the buckling modes is also shown to be modified by the nonlocal and SG scale parameters. Consequent wave numbers increase/decrease, accompanied by decreasing/increasing number of wavelengths, thereby further justifying the shallow segment representation employed herein. [ABSTRACT FROM AUTHOR]

The present study explores the buckling and failure behavior of the silicon carbide (SiC) ceramic cylindrical shell under hydrostatic pressure using experimental and nonlinear numerical methods. An innovative experiment setup is designed and built. The hydrostatic test of the SiC ceramic cylindrical shell is carried out. The buckling deformation of the shell is captured by a high-speed camera and the strain response is recorded by strain gauges. In order to compare with the experimental results, the failure behavior of the SiC ceramic cylindrical shell subjected to hydrostatic pressure is simulated using a nonlinear numerical approach. Both the ultimate tensile strength and ultimate compression strength of the material are taken into consideration. The maximum equivalent stress is used as the failure criterion. The buckling mode simulated by the numerical method is in good agreement with the deformation shape observed in the test. As for the buckling pressure, the deviation from the experimental result is only 3.62%. Both the experimental and numerical results show that the failure of the SiC ceramic cylindrical shell under hydrostatic pressure is a typical coupling failure of strength damage and structural instability. • In this study, the buckling and failure behavior of the SiC ceramic cylindrical shell under hydrostatic pressure is investigated. To accomplish this, an innovative experiment setup is established, which combines a hydrostatic chamber, strain instruments, and a high-speed camera. A hydrostatic test is performed on the SiC ceramic cylindrical shell with one end fixed and the other end simply supported. Additionally, a nonlinear numerical simulation is conducted to predict the progress of the structure failure behavior under hydrostatic pressure. The following conclusions are drawn from the study: • The buckling of the SiC cylindrical shell subjected to hydrostatic pressure is a critical behavior. Prior to the critical buckling pressure, the strain response of the SiC cylindrical shell shows significant nonlinearity. • The maximum equivalent stress criterion is found to be an accurate way to evaluate the strength damage of the SiC ceramic cylindrical shell under hydrostatic pressure. The ultimate buckling strength of the SiC ceramic cylindrical shell is mainly determined by the ultimate compressive strength of the material. • Once the material damage occurs in the SiC ceramic cylindrical shell under hydrostatic pressure, even a slight increase in the external load can lead to structural collapse. • It is revealed that failure of the SiC ceramic cylindrical shell under hydrostatic pressure is a typical coupling failure involving both strength degradation and structural instability. [ABSTRACT FROM AUTHOR]

The axial load and buckling of interphase spacers (IPSs) in power transmission lines are investigated during vibration following ice shedding. IPSs are used to maintain the clearance between different phases of transmission line conductors. Axial forces act on the IPSs during conductor motion, potentially leading to buckling. Two numerical approaches are proposed to study this phenomenon. The first one involves a dynamic model that simulates ice shedding from conductors separated by spacers and provides the axial load that acts on the spacers during the vibration. The material properties are obtained from material tests on fiber-reinforced plastic (FRP) samples, which is the material used to manufacture modern IPSs. The other numerical approach simulates the buckling behavior of IPSs under the axial load obtained from the previous model and provides the deformed shape of the IPS together with the stresses that develop during buckling. An experimental set-up is designed for buckling tests on small-scale FRP samples, and it is applied to validate the buckling model. Buckling may damage the spacer, but it is not necessarily harmful if stresses are small enough and the deformation is elastic during buckling. By understanding the behavior of IPSs under dynamic forces and obtaining the maximum deformation and stress during buckling, it may be possible to improve the design and performance of these components in power transmission lines. [ABSTRACT FROM AUTHOR]

In recent years, composite columns have gained much attention in offshore and marine engineering. This paper, with the motivation of a better design for circular straight double skin steel tubes confined concrete (DSSTCC) columns, theoretically explores the local buckling of the internally stiffened inner skin in this column. Firstly, the force analysis of a DSSTCC stub column was conducted, and its common failure modes were outlined. Based on the similar structural performance of the inner tube and the fixed circular arch, a concise buckling analysis model was built up. Then different buckling modes of clamped circular arches under the uniform radial load were presented. The ultimate load-carrying capacity of internally stiffened inner tubes under different buckling modes was also discussed, which shows relatively high dependence on the structural stability. Next, the calculation method of the expected ultimate hoop compressive stress was given, and the main computational procedure of the cross-sectional slenderness limit for internally stiffened inner skins was illustrated. In addition, a very simple prescriptive equation that considers the elastic modulus, the yield stress, and the formed arch's central angle value was fitted to estimate the cross-sectional slenderness limit for inner tubes with internal stiffeners, with which a slender cross-section can be delineated from an effective one. Meanwhile, the elastic buckling stress of the inner tube was also given. Finally, the applicability of the proposed methodology to materials with the bilinear model, the bilinear plus nonlinear hardening model, the idealized multilinear model, or the Ramberg-Osgood model was investigated, thereby demonstrating its good adaptability to these four common nonlinear constitutive models. • A buckling analysis model for inner tubes with internal stiffeners is proposed. • The ultimate hoop resistance of an internally stiffened inner tube is given. • An empirical formula is fitted to estimate the slenderness limit for inner tubes. • The elastic buckling stress of an inner skin with a slender cross-section is given. • The proposed method has a good applicability to other nonlinear constitutive models. [ABSTRACT FROM AUTHOR]

Abstract The study investigates the effect of eccentric load on the stability and postcritical states of thin-walled CFRP channel section columns under compression. Test specimens are subjected to compression on a testing machine provided with a fixture for applying eccentric compressive loads. Loading forces, deflection and strains of the column walls and web are measured. The experiments also involve examination of the operating performance of a structure undergoing buckling and determination of its postcritical equilibrium paths describing the relationship between load and deflection. Based on experimental results, numerical models of composite structures are designed and verified by the FEM. The scope of the numerical analysis involves performing a linear analysis of stability, which allows for determining the buckling mode depending on the amplitude of compressive load eccentricity and corresponding critical loads. The next stage of the analysis involves performing a nonlinear analysis of the structures with implemented geometric imperfections reflecting the lowest buckling modes. Based on obtained results, postcritical equilibrium paths of the developed FEM models are determined. Obtained equilibrium paths are then compared with experimental characteristics of real structures. The numerical results and experimental findings show a satisfactory agreement. [ABSTRACT FROM AUTHOR]

Highlights • A unified size-dependent plate model for buckling analysis of nanoplates is developed. • The governing equations are derived based on nonlocal strain gradient theory incorporating surface effects. • Various higher-order plate theories as well as Kirchhoff and Mindlin plate theories are included. • Analytical solutions for critical buckling load of rectangular nanoplates under various boundary conditions are obtained. • The effects of small scale parameters, geometric parameters, boundary condition, shear deformation and surface energy are studied. Abstract Based on the nonlocal strain gradient theory and surface elasticity theory, a unified size-dependent plate model is developed for buckling analysis of rectangular nanoplates. The developed model is capable of capturing nonlocal effect, strain gradient effect as well as surface energy effects simultaneously. Moreover, by selecting appropriate shape function, the present model can be reduced to not only Kirchhoff and Mindlin plate models but also various higher-order shear deformation plate models. The non-classical governing equations and associated boundary conditions are established by using the principle of minimum potential energy. Analytical solutions for critical buckling load of rectangular nanoplates under various boundary conditions are obtained. Verification of the proposed model is carried out by comparing the degenerated results with those reported in open literature. The effects of nonlocal parameter, material length scale parameter, geometric parameters, shear deformation and surface energy on the buckling behavior of rectangular nanoplates under different boundary conditions are discussed in detail. The numerical results show that the critical buckling load evaluated by nonlocal strain gradient theory is lower than that predicted by classical continuum theory when the nonlocal parameter is larger than the material length scale parameter, and is higher than that evaluated by classical continuum theory when the nonlocal parameter is smaller than the material length scale parameter. However, when taking surface effects into account, the critical buckling load is mainly affected by surface effects at large length-to-thickness ratio, and depends on the combined effects of nonlocality, strain gradient and surface energy at small length-to-thickness ratio. [ABSTRACT FROM AUTHOR]

Abstract Damage tolerance is of critical importance to laminated composite structures. In this paper, we present a new semi-analytical method for predicting the strain at which delamination propagation will initiate following sublaminate buckling. The method uses a numerical strip model to determine the thin-film buckling strain of an anisotropic sub-laminate created by delamination, before evaluating the strain energy release rate for delamination propagation. The formulation assumes that all energy is available for propagation in a peeling mode (Mode I); avoiding an approximate mixed-mode criterion. Results are compared with twelve experimentally obtained propagations strains, covering a variety of laminates each containing a circular PTFE delamination. Comparison shows agreement to within 12% for balanced sublaminate tests in which delamination propagation occurred before intra-ply cracking. The method can be used to significantly improve the damage tolerance of laminates, opening up new opportunities for structural efficiency using elastic tailoring, non-standard ply angles and material optimisation. [ABSTRACT FROM AUTHOR]

This study investigated the seismic demand of continuity plates (CP) in Special Moment Frames (SMFs), including built-up I-shape beams. Six reference experiments for SMF connections were considered, including beams with unequal depths on both sides of the column, to compare the seismic demand for CP with the corresponding value of the AISC code formula. The effects of beam shape properties, connection type, shear strain of the panel zone (PZ), different construction detailing and straight/inclined CP in dual/trapezoidal PZ were included in this study. In addition, companion analytical studies were performed to evaluate CP seismic demand. The results of the experiments and numerical analyses showed that the AISC code underestimates seismic demand for CP in joints with beams having sizes outside the geometries of hot-rolled structural sections. Poor seismic performance of the code-designed CP led to premature yielding and out-of-plane local buckling of CP, which were observed in the reference experiments and confirmed by numerical models. Finally, an equation for CP seismic demand was developed based on findings of this research. It was demonstrated that the proposed seismic demand met the required seismic criteria using this equation, and it also kept CP within the safe structural margins. [ABSTRACT FROM AUTHOR]

Abstract Elevated cylindrical metal silos are often supported on a ring beam which rests on discrete column supports. The ring beam plays an important role in redistributing the majority of the discrete forces from the column supports into a more uniform stress state in the cylindrical wall, which is necessary to reduce the potential for buckling of the shell wall. Traditional design treatments assumed that the discrete support forces can be fully redistributed by the ring beam, producing circumferentially uniform axial membrane stresses in the silo shell. But it has previously been shown that only a very stiff ring beam can produce even relatively uniform axial membrane stresses in the shell. The ring beam stiffness must be evaluated relative to the stiffness of the silo shell in compatible deformation, since even a thin shell is extremely stiff in its own plane. A test for the ring beam to shell stiffness ratio was previously devised by the authors to determine the ring beam stiffness needed to achieve uniform membrane stresses. This new study assesses ring beams of practical dimensions and stiffness, to evaluate their effectiveness in smoothing the shell axial membrane stresses towards the uniform condition and then to find their effect on the buckling resistance of the shell. This study explores the stress resultants in a closed section ring beam of practical dimensions that is less stiff than the ideal stiffness using a finite element parametric study of the flexible ring beam and connected silo shell. The results show that the ring beam stress resultants, relative to those in an isolated ring beam under the same loading, can be directly related to the established shell to ring beam stiffness ratio (ψ). This treatment may be used to significantly enhance current design practice which, according to the Eurocode EN 1993-4-1 for silos, assumes that the shell applies the full uniform transverse loading onto an isolated ring beam. Highlights • Closed form design equations for the isolated ring beam were algebraically derived. • The interaction between the cylindrical shell and the supporting ring beam was explored. • Complementary FE analyses show that shell-ring stiffness ratio is applicable for practical design. • Simple algebraic expressions empirically amend the algebraic equations for stress resultants and displacements for design. [ABSTRACT FROM AUTHOR]

Abstract The progressive instability behaviour of compressed dry-stone rectangular pillars loaded with an eccentric load is assessed experimentally and compared with the theory. Photoelastic compression tests were designed and executed on polymethyl-methacrylate brickwork pillars to reveal, i) the load-bearing capacity of the structure and the load-lateral displacement relation, ii) the effect of the eccentricity in the stress distribution along the structure, iii) the collapse mode of the system at high eccentricity. By employing a no-tension material model with linear behaviour in compression, new analytical, closed-form expressions for deformed shape of the structure, location of the neutral axis in a generic cross section and axial displacement are provided. The photoelastic stress analysis outcome fully confirms the analytical predictions for both low and high eccentricity loadings. [ABSTRACT FROM AUTHOR]

Gusset plates are extensively used for connecting various components in a steel structure which play a crucial role in transfer of forces and maintaining structural integrity. Behaviour of gusset plates is very complex and the determination of the required thickness of a gusset plate is not straight forward. Presently, Whitmore's theory is used to check the thickness of a gusset plate which is provided based on empirical considerations and past experience. Whitmore's theory may be unconservative and may not be reliable. Hence, an effort has been put to rationally determine the thickness of gusset plates that are commonly used in roof trusses and towers. In this investigation, initiation of rupture is considered as failure rather than complete rupture of gusset plate. It is assumed that rupture initiates when the principal tensile stress on the edge of a bolt hole approaches the ultimate strength of the material. The principal tensile stress on the edge of a bolt hole is obtained by geometric and material non-linear finite element analysis of gusset plates. The minimum thickness required to prevent initiation of rupture is noted. The thickness required for preventing buckling of gusset plates is calculated using Modified Thornton's theory. The maximum thickness obtained from the non-linear finite element analysis, Whitmore's theory and Modified Thornton's buckling theory is specified as the minimum required thickness of gusset plates. [ABSTRACT FROM AUTHOR]