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Two main goals are pursued in the present work. First, the global buckling of axially loaded sandwich beams with composite face sheets and aluminum honeycomb cores under humid environments is investigated. An analytical solution with high accuracy is developed based on piecewise low-order shear deformation theory (PLSDT) to estimate the critical buckling loads. A parametric study is carried out to examine the influence of geometric parameters on the buckling loads of simply supported and clamped sandwich beams under different wet conditions. The obtained results indicate that humidity plays a significant role in the buckling behavior of honeycomb sandwich beams. As the second purpose of the present work, the weight minimization of sandwich beams is studied. The optimization variables include the face sheet thickness, core thickness, honeycomb cell size and honeycomb cell wall thickness. Moreover, different failure modes, including global buckling, face sheet dimpling, face sheet wrinkling, core shear instability, and face sheet failure are considered as design constraints. Imperialist competitive algorithm (ICA), a powerful socio-politically motivated global search strategy, is applied to handle the constrained optimization problem. The optimization results show that the presence of humidity in the environment significantly changes the optimal design of sandwich beams and makes them heavier. Furthermore, it is observed that by increasing the length of the structure, the optimal design is more affected by humidity. Moreover, it is found that ICA is a very powerful optimization tool both in obtaining the best values of geometric parameters and in reducing the computational cost. [ABSTRACT FROM AUTHOR]

Mechanical metamaterials are valued for their diverse properties and potential applications. Due to the instability and large deformability of soft mechanical metamaterials (SMMs), geometric reorganization will occur and lead to some unusual properties. It is possible to change the properties of materials by varying the parameters. Conventional SMMs contain a periodic distribution of holes with the same size and shape, which can be changed to a lesser extent. Periodic dispersion of regular through-hole patterns of various sizes or shapes into elastomers, resulting in metamaterials with more mechanical functionality and deformation scenarios. In this paper, we investigated the influence of parameters on the buckling mechanical behavior of SMMs and the buckling mechanical behavior of structures with multiple sizes and geometric shapes. The parameters studied include geometric parameters (pore shape, porosity and area ratio) and physical parameters (Poisson's ratio and compression mode). Simulation of the buckling behavior of SMMs uses the finite element method. The finite element software ABAQUS is used, taking into account the almost incompressible characteristics of materials, the triangular quadratic plane strain hybrid element is selected (CPE6H). Numerical calculation gives the following results: Area ratio, pore shape and compression mode have obvious effects on buckling behavior, but Poisson's ratio has little effect; the influence of parameters on the buckling critical strains varied for SMMs with various pore shapes; very different buckling behaviors will result from swapping out the pattern of holes with the same size or shape for holes with two different sizes or shapes; the expression of buckling behavior is also varied when the mix of hole shapes is modified. These findings demonstrate that the design parameters may be used to achieve the desired buckling behaviors. This is a new method that can be used to control the deformation of structures; modify the properties of the SMMs without changing stiffness; simplify the structures without significantly changing the material properties. The design path of mechanical metamaterials is increased. [ABSTRACT FROM AUTHOR]

Fiber-reinforced elastomeric isolators (FREIs) have been proposed as a cost-effective solution for expanding the use of seismic isolation to normal-importance structures. By using lightweight fiber reinforcement and eliminating the attachment plates, FREIs reduce cost while improving the isolation efficiency and reducing tensile stresses in the rubber. However, the flexural flexibility of the fiber allows cross-sectional distortions (i.e., warping) to occur, which significantly impacts the stability of these devices. This paper evaluates the buckling of rectangular, circular, and annular FREIs, taking into account shear warping effects. A planar buckling theory previously proposed by the authors is adapted for the three-dimensional problem, and effective warping rigidities and warping-related areas are derived for the above bearing geometries, accounting for rubber compressibility. To assess the adequacy of the proposed buckling theory and derived warping properties in predicting the buckling of FREIs, a parametric finite element study is conducted. The critical load predictions of the proposed analytical formulation are found to be in excellent agreement with those of the numerical simulations. It is shown that traditional estimations of the buckling load that neglect warping are significantly unconservative. Finally, design recommendations and resources are provided for practice-oriented applications. [ABSTRACT FROM AUTHOR]

AbstractThis study develops a novel analytical method to evaluate if box sections, with unequal wall thicknesses under bending, will undergo local buckling prior to reaching their yield strength since the analytical determination of critical local buckling stresses for such sections remains unexplored due to the lack of local buckling coefficients, warranting further investigation in scholarly discourse. Despite not directly computing the local buckling stresses, the developed method specifies a possible critical local buckling stress range by incorporating reference, critical, and equivalent section models, all formulated and developed with uniform wall thicknesses. The formulated method proficiently discerns the occurrence of local buckling by conducting a comparative assessment of the yield strength of the box section material against both the lower (min) and upper (max) bound stresses of the critical local buckling stress range. If local buckling persists unclear after the initial benchmark, the method reaches the final conclusion by comparing the constant wall thickness of the critical section with the web thickness of the box section. The developed method validated against finite element results obtained from linear elastic eigenvalue buckling analyses can be applied to the problem of determining whether such box sections subjected to bending will experience local buckling. [ABSTRACT FROM AUTHOR]

The lightweight fabrication of thin-walled cabin sections is popular for advanced ships, and the dimensional tolerance generated by welding buckling significantly influences the fabrication accuracy and schedule with poststraightening. A typical thin section employed in the superstructure of a high-tech passenger ship is considered the research object. Conventional fabrication procedures and welding conditions were examined beforehand with combined thermal elastic-plastic and elastic FE computations based on the theory of welding inherent deformation, while welding buckling was represented with identical behavior compared with fabrication observation. Actually, there are usually two methods to prevent welding buckling with advanced fabrication. Stiffeners with optimized geometrical features and excellent elasticity moduli were assembled to enhance the rigidity of the ship thin section, and less welding inherent deformation with advanced welding methods can be employed to reduce mechanical loading. Computational results show that either less in-plane welding inherent strain or higher structural rigidity can reduce the magnitude of welding-induced buckling, and avoid the generation of welding-induced buckling during the lightweight fabrication. [ABSTRACT FROM AUTHOR]

This article considers a bidirectional functionally graded (BDFG) beam with various distributions of volume fraction. The impact of these distributions on the buckling and bending response of BDFG beam with general boundary conditions is investigated via a quasi-3D solution. It is assumed that the beam is exposed to a set of in-plane varying compressive loads and there mechanical characteristics change in both directions. Also, the BDFG beam is considered to be exposed different external mechanical loads. Hamilton's principle is employed to derive the governing equations, which are then solved using analytical solution to obtain buckling and bending characteristics. The precision of the current formulation is investigated via a comparison with available data in literature. Some numerical results are presented and discussed to assess the effect of different parameters such type of volume fraction, boundary condition, varying load, and beam geometry on the buckling and bending of BDFG beam. [ABSTRACT FROM AUTHOR]

This paper investigates the effect of friction on the buckling behavior of a thin, shallow, elastic spherical shell under uniform external pressure based on an axisymmetric model of the finite element method. The study examines a combination of different geometric parameters with three different types of boundary conditions: clamped, hinged, and frictional ends with a wide range of friction coefficients. Friction has a significant influence on the buckling response of the spherical shell for all geometric parameters. In general, the critical pressure decreases as the friction coefficient or geometric parameter decreases. The buckling behavior of the frictional end with small friction coefficients presents an obvious difference compared to the results of high coefficients. For certain geometric parameters, the buckling mode of the spherical shell is transited because of changing the friction coefficient. A buckling map that describes the dependence of critical pressure on both friction coefficient and geometric parameter combined with buckling mode is generated. This map can be applied to the design of the spherical shell against buckling. [ABSTRACT FROM AUTHOR]

In complex cardiovascular surgical reconstructions, conduit materials that avoid possible large-scale structural deformations should be considered. A fundamental mode of mechanical complication is torsional buckling which occurs at the anastomosis site due to the mechanical instability, leading surgical conduit/patch surface deformation. The objective of this study is to investigate the torsional buckling behavior of commonly used materials and to develop a practical method for estimating the critical buckling rotation angle under physiological intramural vessel pressures. For this task, mechanical tests of four clinically approved materials, expanded polytetrafluoroethylene (ePTFE), Dacron, porcine and bovine pericardia, commonly used in pediatric cardiovascular surgeries, are conducted (n = 6). Torsional buckling initiation tests with n = 4 for the baseline case (L = 7.5 cm) and n = 3 for the validation of ePTFE (L = 15 cm) and Dacron (L = 15 cm and L = 25 cm) for each are also conducted at low venous pressures. A practical predictive formulation for the buckling potential is proposed using experimental observations and available theory. The relationship between the critical buckling rotation angle and the lumen pressure is determined by balancing the circumferential component of the compressive principal stress with the shear stress generated by the modified critical buckling torque, where the modified critical buckling torque depends linearly on the lumen pressure. While the proposed technique successfully predicted the critical rotation angle values lying within two standard deviations of the mean in the baseline case for all four materials at all lumen pressures, it could reliably predict the critical buckling rotation angles for ePTFE and Dacron samples of length 15 cm with maximum relative errors of 31% and 38%, respectively, in the validation phase. However, the validation of the performance of the technique demonstrated lower accuracy for Dacron samples of length 25 cm at higher pressure levels of 12 mmHg and 15 mmHg. Applicable to all surgical materials, this formulation enables surgeons to assess the torsional buckling potential of vascular conduits noninvasively. Bovine pericardium has been found to exhibit the highest stability, while Dacron (the lowest) and porcine pericardium have been identified as the least stable with the (unitless) torsional buckling resistance constants, 43,800, 12,300 and 14,000, respectively. There was no significant difference between ePTFE and Dacron, and between porcine and bovine pericardia. However, both porcine and bovine pericardia were found to be statistically different from ePTFE and Dacron individually (p < 0.0001). ePTFE exhibited highly nonlinear behavior across the entire strain range [0, 0.1] (or 10% elongation). The significant differences among the surgical materials reported here require special care in conduit construction and anastomosis design. [ABSTRACT FROM AUTHOR]

A family of locking-free Kriging-based Timoshenko beam elements with a new implementation of the discrete shear gap technique was recently developed (referred to as K-beam-DSG1 elements). Performance of the K-beam-DSG1 elements has been shown to be very satisfactory in the linear static analysis of beams for a wide variety of thicknesses. This paper presents further development of the K-beam-DSG1 elements to free vibration and bifurcation buckling analyses of prismatic and non-prismatic beams. Consistent Kriging-based mass matrices are used for free vibration analysis and similarly, consistent Krigingbased geometric stiffness matrices are used for buckling analysis. The results show that for most of the cases, the K-beam-DGS1 elements yield remarkably accurate natural frequencies and critical compressive loads using a reasonable number of elements to discretize the beam. For an axially functionally graded fixed-fixed supported beam, however, the elements fail to predict the critical load accurately. [ABSTRACT FROM AUTHOR]

This study investigates the elastic buckling behavior of oblate hemi-ellipsoidal shells (OHES) subjected to non-uniform external hydrostatic pressure. The virtual work-energy of OHES consists of virtual strain energy due to membrane, bending, in-plane stress resultants, and virtual work of hydrostatic pressure. For buckling analysis, the geometric stiffness matrix is obtained from the strain energy due to in-plane stress resultants. A finite element procedure via a C1 continuity axisymmetric element is applied to solve the critical hydrostatic pressure from the eigenvalue buckling problem. The buckling pressure of the hemi-ellipsoidal dome subjected to uniform external pressure is verified with the previous research and FEM commercial software. Present results also indicate that the maximum in-plane stress of the hemi-ellipsoidal shell shapes are near the apex point as the axisymmetric buckling shape. In the case of hydrostatic pressure, the critical hydrostatic pressure of OHES is determined and are in good agreement when compared with the experimental results in published research. Furthermore, the shape ratio influences the difference in critical load results between uniform pressure and hydrostatic pressure, especially when the shape ratio is higher than 0.5 and the a / t ratio is less than or equal to 100. Seawater depth limitations in subsea engineering are also presented and found that the shell thickness and shape ratio are the major factors affecting critical seawater depth. [ABSTRACT FROM AUTHOR]

In this paper, buckling and nonlinear post-buckling behaviors of a bidirectional porous (BDP) beam are investigated under bidirectional hygrothermal environment. Euler–Bernoulli beam theory with the von Kármán nonlinearity is employed to derive the nonlinear variable coefficient governing differential equations based on Rayleigh quotient method. Analytical solutions of critical buckling load and load–deflection equilibrium path in post-buckling are deduced for the single directional varying (SDV) porous beam. The general numerical solutions for bidirectional varying (BDV) porous beam are obtained by differential quadrature finite element method (DQFEM) with Newton–Raphson iteration method based on the variation principle. The high accuracy of the present numerical method with higher computing efficiency is verified by comparison with published reports and the analytical results in this work. Parametric analysis on effects of the porosity bidirectional distributions, porosity coefficients, distributions of hygrothermal environment and boundary conditions on buckling load and post-buckling response is carried out to enhance the buckling and deformation resistances in design, manufacture and usage of porous structures. The results show that the bidirectional porosity pattern, linear and nonlinear hygrothermal distribution and boundary conditions play a significant role on buckling critical external load and critical hygrothermal increments, buckling form and post-buckling path. [ABSTRACT FROM AUTHOR]

To meet the complex and diverse demands for low-stress mechanical measurements of fabrics and other flexible materials, two integrated multidimensional force sensors with the same structure but different ranges were explored. They can support both rapid and precise low-noise, high-precision, low-cost, easy-to-use, reliable, and intelligent solutions for the complex measurement of fabric mechanics. Having analysed the mechanical relationship of the parallel beam theory, and considering the specific requirements of fabric measurement, a novel multi-dimensional force sensor is designed, capable of measuring tensile, shear, and buckling properties. Finite element analysis is used to simulate the mechanical performance of this sensor for fabric-loading/unloading measurement, and the sensitivity of the mechanical quantity transfer, the amount of sensor deformation, the stress distribution, and the degree of inter-dimensional coupling have been investigated and verified. The basis for subsequent digital processing is achieved by a low-offset, low-temperature-drift, low-power-consumption analogue front end, 24-bit ADC circuit, and signal conditioning electronics, suitable for the measurement of fabric mechanics under low stress, which is like the end-user requirements. The sensor information channel is supported by a host microcontroller with a DSP and a floating-point processing instruction set. Information processing is performed in time-sharing with the support of a multitasking real-time operating system. The purpose of designing this sensor is to facilitate the development of a new testing instrument, which will adopt the advances of current instruments whilst eliminating their shortcomings. [ABSTRACT FROM AUTHOR]

In the current research, we delve into the intricate realm of bifurcation analysis for Föppl–von Kármán plates, employing a precise numerical tool. This innovative numerical approach melds the power of spectral discretization with the prowess of a high-order continuation method-based Taylor series development (HODC). It is worth noting that combining the high-order continuation method with such discretization techniques offers an efficient path-following approach, complete with adaptive step lengths, capable of tackling a wide array of nonlinear problems. Despite the extensive applications of nonlinear elasticity, the spectral method remains relatively uncharted territory within this context. However, our deep-rooted understanding and expertise in the field drive us to embrace this method alongside high-order development continuation for bifurcation analysis of Föppl–von Kármán plates. The governing equations governing thin elastic plates experiencing significant elastic deflections manifest as a pair of coupled nonlinear differential equations, famously known as the von Kármán (vK) equations, presented in a strong form with two principal unknowns: deflection (w) and the Airy stress function (F). Leveraging Chebyshev decomposition matrices, we approximate these fourth-order elliptic nonlinear partial differential equations. Subsequently, we harness high-order development continuation techniques to morph these nonlinear systems into linear ones. Our rigorous evaluation and validation of this numerical approach's precision and performance come to fruition through a comprehensive buckling analysis encompassing multiple illustrative examples. [ABSTRACT FROM AUTHOR]

• Time-varying buckling and post-buckling of tapered columns in fire. • Temperature-dependent material properties. • The convective–radiative condition. • Geometric nonlinearity and yield strength. • Effects of transient localised fire on the tapered column. This paper presents time-varying flexural buckling and post-buckling responses of tapered columns under a transient fire of which the temperature is non-uniform along the length. First, the transient temperature field within the column is determined by solving a dimensionally reduced transient heat transfer problem considering the convection-radiation boundary conditions and temperature-dependent (TD) material properties. Subsequently, the von Kármán geometric nonlinear theory is applied to obtain the nonlinear equilibrium equation. The nonlinear heat transfer and equilibrium equations are solved by the differential quadrature (DQ) method. According to a yield criterion, the ultimate load at which the material failure occurs is predicted. The influences of a transient localised fire on the temperatures, buckling and post-buckling responses of tapered steel tubular columns are discussed. [ABSTRACT FROM AUTHOR]

The main goal of this article is to extend the Carrera unified formulation (CUF) in polar coordinates to analyze the mechanical and thermal buckling of functionally graded (FG) circular plates with axisymmetry. The governing equations are derived using CUF in polar coordinates for FEM. The fundamental nuclei, and accordingly, the elemental matrices for a 3-node line axisymmetric element are proposed. Mechanical and thermal buckling under uniform, nonlinear temperature rise with and without the effect of convection has been investigated. The results have been verified with several plate theories and the finite element method using the second-order axisymmetric 2D elements. [ABSTRACT FROM AUTHOR]

Buckling failure is a major concern in lightweight lattice core sandwich structures (LCSSs). This study proposes an efficient method for designing LCSSs with superior buckling strength under uniaxial compression. In this approach, the buckling-resistant non-uniform shapes of single struts with different slenderness and inclination are first identified, and then they are directly used to replace uniform struts in LCSSs. This method can save considerable design time compared to conventional methods, which require conducting optimizations on entire LCSSs. Numerical results demonstrate that four designed representative non-uniform LCSSs can gain over 15% improvement in buckling strength compared to their counterpart uniform LCSSs. This improvement is even comparable to the solutions from optimizations on entire LCSSs. Two LCSSs with non-uniform struts are 3D printed, and the test results validate at least 10% improvement in compressive strength. Based on the proposed method, various LCSSs with superior buckling strength could be designed for different loadings. [ABSTRACT FROM AUTHOR]

• Nonlinear torsional buckling of toroidal shell segments is presented using the Ritz energy method. • The corrugated core sandwich toroidal shell segments with FG-GRC coatings are considered. • The thermal forces are added to improve the homogeneous model for the corrugated core. • Ritz energy method, Donnell shells theory, and Pasternak's foundation model are applied. • Effects of corrugated core, material and geometrical parameters on the buckling behavior of shells are investigated. An investigation on the nonlinear torsional buckling of corrugated core sandwich toroidal shell segments with functionally graded graphene-reinforced composite (FG-GRC) laminated coatings in temperature change is mentioned in this paper using the Ritz energy method. The complex configuration of sandwich toroidal shell segments with double curvatures and the combination of the corrugated core and the FG-GRC coatings create the special behavior of structures. A homogenization model for corrugated structures and the extended Halpin-Tsai model can be applied to estimate the stiffnesses of shells. The effects of uniform temperature change are taken into account by supplementing the thermal forces into the total forces of shells. The Donnell shell theory and Pasternak's foundation model are used to establish the total potential energy of the structures. Ritz energy method is applied, and the closed condition and circumferential stress are taken into account, the postbuckling curve expressions of torsion-deflection and torsion-twist angle are obtained in explicit forms. The numerically obtained examples can show the significantly beneficial effects of FG-GRC laminated coatings and corrugated core on nonlinear buckling responses of structures. [ABSTRACT FROM AUTHOR]

Most studies have focused on determining optimal dimensions of metal- or composite-based rectangular hollow sections (RHSs) by considering only the design requirement of strength. Different from those, an analytical procedure for the determination of optimal sectional dimensions of polymer-based RHS beams by accounting for both adequate-strength and local buckling for the first time has been presented in the context of this study. Analytical expressions which give the optimal sectional dimensions simultaneously satisfying the adequate-strength and local buckling conditions have been derived for two different loading configurations such as a pure major axis bending and a combined axial compression and major axis bending. The analytical procedure proposed in this study depends on the idea of preventing the polymer-based RHS from buckling prior to its compressive strength. This has been achieved by increasing the critical buckling stress of the RHS up to its compressive strength via optimizing its sectional dimensions. During the optimum design, different elastic and plastic material behaviors of polymers in tension and in compression have been taken into calculations. The results attained analytically have been validated against numerical predictions obtained from linear elastic eigenvalue buckling and postbuckling analyses implemented in Abaqus engineering finite element code. Thus, the analytical procedure reported in this study can be used as a benchmark in identifying the optimal dimensions of RHS members manufactured from polymers. Communicated by Davide Spinello. [ABSTRACT FROM AUTHOR]

This study investigates the structural behavior of a particular mechanical joint subjected to bending and perturbation and the selection of overlapping lengths for this CHS structure arrangement. We began this research by meticulously validating the methodology through a rigorous replication of a prior experimental study, establishing its reliability as a solid foundation. Subsequently, the process was applied to pile-in-pile (PIP) slip joints with varying overlapping lengths. The primary aim was to determine the optimal overlapping length, a critical parameter in this analysis, encompassing the evaluation of stiffness, bending capacities, and joint efficacy. These investigations reveal a clear correlation between increasing overlapping length and heightened joint stiffness. An optimal overlapping length that strikes a harmonious balance between stiffness, bending capacity, and joint efficiency was identified. These findings hold substantial promise for enhancing the joint design of tubular sections, particularly within the context of wind-turbine structures. Using this novel joint can be promising in increasing the efficiency and reliability of CHS structures in future construction and performance. [ABSTRACT FROM AUTHOR]

Composite structures can achieve greater performance through variable stiffness design. In consideration of inevitable manufacturing defects introduced by the Automatic Fiber Placement machine, modified models are established to calculate equivalent properties for materials with gaps or overlaps. A modeling method for variable stiffness structures with defects is proposed based on the modified models. This approach significantly reduces the dependence on mesh size for analysis accuracy, thereby improving modeling and calculation efficiency. Upon validation of the proposed modeling method, a Hierarchical Kriging surrogate modeling is employed to optimize the buckling performance of a variable stiffness wing box with defects. The impact of different manufacturing strategies on optimization results is also investigated. The findings demonstrate that the variable stiffness design improves the wing box buckling performance under a combined torsion-bending condition. Finally, the potential of utilizing overlaps without cut-restart is analyzed for weight reduction in the design of variable stiffness wing boxes. [ABSTRACT FROM AUTHOR]

The interaction behavior between local and global buckling modes in high-strength steel box-section columns has received limited research attention. Currently, there is a lack of a validated equivalent geometric imperfection that can be effectively employed in nonlinear plastic analysis to estimate the interaction buckling resistance. This research aims to find equivalent geometric imperfections that can be used in geometrical and materially nonlinear analysis using imperfections (GMNIA) to estimate the interaction buckling resistance of square welded box-section columns made of high-strength steel. It extends prior investigations by the authors on equivalent imperfections for normal-strength steel welded box-sections. A developed and validated numerical model is used to perform parametric studies to estimate the accurate buckling capacity using previously developed and verified combinations of imperfections and residual stresses. The accurate buckling capacities are used to calibrate equivalent local and global imperfection combinations that can be used in FEM-based design. A reliability assessment study is also performed to check the safety level of the proposed imperfection combinations. [ABSTRACT FROM AUTHOR]

The quest for safe lower bounds to the elastic buckling of axially loaded circular cylindrical shells has exercised researchers for the past 100 years. Recent work bringing together the capabilities of nonlinear numerical simulation, interpreted within the context of extended linear classical theory, has come close to achieving this goal of defining safe lower bounds. This paper briefly summarizes some of the important predictions emerging from previous work and presents new simulation results that confirm these earlier predictions. In particular, we show that for a specified maximum amplitude of the most sensitive, eigenmode-based geometric imperfections, normalized with respect to the shell thickness, lower bounds to the buckling loads remain constant beyond a well-defined value of the Batdorf parameter. Furthermore, we demonstrate how this convenient means of presenting the imperfection-sensitive buckling loads can be reinterpreted to develop practical design curves which provide safe, but not overly conservative, design loads for monocoque cylinders with a given maximum permitted tolerance of geometric imperfection. Hence, once the allowable manufacturing tolerance is specified during design or is measured post-manufacturing, the greatest expected knockdown factor for a shell of any geometry is defined. With the recent research interest in localized imperfections, we also attempt to reconcile their relation to the more classical, periodic, and eigenmode-based imperfections. Overall, this paper provides analytical and computational arguments that motivate a shift in focus in defect-tolerant design of thin-walled cylinders--away from the knockdown experienced for a specific geometric imperfection and towards the worst possible knockdown expected for a specified manufacturing tolerance. [ABSTRACT FROM AUTHOR]

This paper aims to analyze the effects of porosities, tangential constraints of boundary edges and elevated temperature on the buckling and postbuckling behaviors of thin functionally graded cylindrical shells subjected to uniform torsion. The porosities are assumed to exist within functionally graded material (FGM) according to even and uneven distributions. The properties of constituents are assumed to be temperature dependent and effective properties of porous FGM are determined using a modified rule of mixture. Mathematical formulations are established within the framework of classical shell theory taking into account von Kármán–Donnell nonlinearity and elasticity of tangential edge constraints. Multi-term analytical solutions are assumed to satisfy simply supported boundary conditions and Galerkin method is used to determine buckling torsional load and load–deflection relation for postbuckling analysis. Numerical results show that porosities have remarkably deteriorative influences on the torsional buckling resistance and postbuckling load capacities of FGM cylindrical shells. This study also reveals that tangential edge constraints have pronouncedly beneficial and detrimental effects on the postbuckling strength of torsion-loaded porous FGM cylindrical shells at room and elevated temperatures, respectively. [ABSTRACT FROM AUTHOR]

A new utilization of entropy in the context of buckling is presented. The novel concept of connecting the strain energy and entropy for a pin-ended strut is derived. The entropy of the buckling mode is extracted through a surrogate model by decomposing the strain energy into entropy and virtual temperature. This concept rationalizes the ranking of buckling modes based on their strain energy under the assumption of given entropy. By assigning identical entropy to all buckling modes, they can be ranked according to their deformation energy. Conversely, with identical strain energy assigned to all the modes, ranking according to entropy is possible. Decreasing entropy was found to represent the scaling factors of the buckling modes that coincide with the measurement of the initial out-of-straightness imperfections in IPE160 beams. Applied to steel plane frames, scaled buckling modes can be used to model initial imperfections. It is demonstrated that the entropy (scale factor) for a given energy roughly decreases with the inverse square of the mode index. For practical engineering, this study presents the possibility of using scaled buckling modes of steel plane frames to model initial geometric imperfections. Entropy proves to be a valuable complement to strain energy in structural mechanics. [ABSTRACT FROM AUTHOR]

Negative Poisson's ratio in auxetic structures plays a crucial role in energy absorption and impact mitigation. Origami-based lattices within the realm of auxetic structures offer the advantage of facile fabrication and design. Nevertheless, the utilization of periodic lattices in origami-based auxetic structures constrains the available design space for achieving diverse mechanical properties. Addressing this limitation, our study introduces origami-based auxetic structures with functionally graded thickness, utilizing origami-based lattices known as Tachi–Miura polyhedra. We investigated the impact of functionally graded thickness on buckling behavior and force responses through dynamic loading experiments employing 3D-printed test pieces. The experimental results indicate that functionally graded thickness induces partial auxetic deformation in lattices, and the resulting nonsymmetric deformation prevents global buckling, thereby averting bounded forces observed in structures with uniform thickness. These findings extend the applicability of auxetic structures, spanning from energy absorption to the design of cushioning structures. [ABSTRACT FROM AUTHOR]

The ability of biomolecules to exert forces on their surroundings or resist compression from the environment is essential in a variety of biologically relevant contexts. For filaments in the low-temperature limit and under a constant compressive force, Euler buckling theory predicts a sudden transition from a compressed state to a bent state in these slender rods. In this paper, we use a mean-field theory to show that if a semiflexible chain is compressed at a finite temperature with a fixed end-to-end distance (permitting fluctuations in the compressive forces), it exhibits a continuous phase transition to a buckled state at a critical level of compression. We determine a quantitatively accurate prediction of the transverse position distribution function of the midpoint of the chain that indicates this transition. We find that the mean compressive forces are non-monotonic as the extension of the filament varies, consistent with the observation that strongly buckled filaments are less able to bear an external load. We also find that for the fixed extension (isometric) ensemble, the buckling transition does not coincide with the local minimum of the mean force (in contrast to Euler buckling). We also show that the theory is highly sensitive to fluctuations in length in two dimensions and the buckling transition can still be accurately recovered by accounting for those fluctuations. These predictions may be useful in understanding the behavior of filamentous biomolecules compressed by fluctuating forces, relevant in a variety of biological contexts. [ABSTRACT FROM AUTHOR]

The woven structure made of naturally curved (in-plane) ribbons has smooth geometry and fewer geometric imperfections, but there is no study of its buckling mechanical properties under vertical loads. The aim of this paper is to investigate buckling mechanical properties of spherical woven structures. Three spherical woven structures with different ribbon types and six new spherical woven structures with different ribbon widths and thicknesses were designed and the quasi-static vertical compression tests were carried out. The buckling load of spherical woven structures were studied by nonlinear finite element and ring buckling theory. Results indicate that the failure mode of the spherical weave structure under vertical loading can be divided into two stages, where a flat contact region forms between the spherical weave structure and the rigid plate and inward dimple of ribbons. Spherical weave structures using naturally curved (in-plane) ribbon weaving have better buckling stability than those woven with straight ribbon. Based on theoretical and finite element analysis, we propose a buckling load equation and buckling correction factor equation for the new spherical weave structure under vertical compression load. The formula is validated and has good agreement with the test results, which could help to design the stability of spherical weave structures with in-plane ribbons. [ABSTRACT FROM AUTHOR]

Large infrastructure projects can efficiently use large diameter bars as longitudinal reinforcement in reinforced concrete elements. In earthquake-prone zones, critical regions of these elements must be detailed for ductility and hysteretic energy dissipation. Longitudinal bars in these regions are expected to sustain large-amplitude strain cyclic reversals before bar fracture occurs, in a mode of failure defining the collapse prevention limit state. To date, no successful large strain-amplitude cyclic loading testing has been reported on large-diameter reinforcing bars to observe the large-strain amplitude fatigue life of such bars, which often involves plastic bar buckling. This paper describes a test program designed to determine the plastic buckling/straightening fatigue life of ASTM A706 Grade 60 No. 18 bars (Ø57 mm) reinforcing bars subjected to cycles of reversed plastic strains. The design and implementation of the loading apparatus, critical for the gripping of the bars, the metallurgical characterization of the bars, and several key test results are discussed in the paper. Finally, the paper discusses a general unidimensional fatigue damage index precursor to bar fracture following a few plastic buckling and straightening cycles. [ABSTRACT FROM AUTHOR]

This paper studies electro-thermal buckling in a flexoelectric microbeam. This first-of-a-kind study focuses on two case-specific types of buckling in microbeams, which are essential to microstructures. Because of the electric fields and high temperatures in their environments, microbeams are susceptible to electro-thermal buckling more often than mechanical buckling. In addition, microstructures can exhibit flexoelectricity. As such a thorough understanding of electro-thermal bucking is extremely important. In this paper, we begin with extracting the equations governing flexoelectric microbeams from size-dependent flexoelectric theories. We then derive closed-form solutions for said equations. We explore various boundary conditions and, with respect to the load, analyze the various pre-buckling and buckling modes. Our study shows that buckling does not occur in some boundary conditions, and electrical curvature is very important in isotropic and homogeneous flexoelectric microbeams. In the end, the paper presents electro-thermal buckling results for specific boundary conditions as well the probability of buckling. [ABSTRACT FROM AUTHOR]

In this paper, the quantum effects of fine scaling on the buckling behavior of carbon nanotubes (CNTs) under axial loading are investigated. Molecular mechanics and quantum mechanics are respectively utilized to study the buckling behavior and to obtain the molecular mechanics coefficients of fine-scale nanotubes. The results of buckling behavior of CNTs with different chiralities with finite and infinite dimensions are given, and a comparison study is presented on them. The differences between finite and infinite nanotubes reflect the quantum effects of fine scaling on the buckling behavior. In addition, the results show that the dimensional changes highly affect the mechanical properties and the buckling behavior of CNTs to certain dimensions. Moreover, dimensional changes have a significant effect on the critical buckling strain. Beside, in addition to the structure dimensions, the arrangement of structural and boundary atoms have a major influence on the buckling behavior. [ABSTRACT FROM AUTHOR]

The present study investigates the global buckling behavior of sandwich beams with graded lattice cores. The continuous equivalent theory is utilized to construct a discrete graded lattice core sandwich beam for a continuously varying gradient beam, whose material properties vary with position. A theoretical model of sandwich beams with graded lattice cores is established using the energy method. Finite element models are developed in ABAQUS to validate the theoretical results. Furthermore, four sets of specimens were manufactured and tested to validate the theoretical analysis methods used. The effects of the graded parameters and geometric parameters on the critical buckling load of sandwich beams with graded lattice cores are discussed. The graded lattice sandwich beams exhibit global buckling when the graded parameter is small, with the influence on buckling performance being minor. However, as the graded parameter increases, the graded lattice sandwich beams experience local buckling, and their buckling resistance weakens. Therefore, graded parameters that are too large and cause local buckling should be avoided in gradient design. [ABSTRACT FROM AUTHOR]

The buckling and postbuckling behaviors of functionally graded graphene platelets-reinforced composite (FG-GPLRC) circular plates are studied based on the classical nonlinear von Karman plate theory. The effective Young's modulus of the composite is estimated using the modified Halpin–Tsai micromechanical model, and the effective Poisson's ratio is estimated by the rule of mixtures. Governing equations of the problem are derived based on the Hamilton principle and the numerical solutions of critical loads and postbuckling deflection–load relationships are calculated using the shooting method. Different from the existing linear buckling analysis based on the Terriftz criterion, the study with considering the global deformation of the plates, we analyze the influencing factors of the critical buckling loads and postbuckling paths of the FG-GPLRC circular plates subjected to uniformly distributed radial pressure. The results show that the content, geometric parameters and distribution pattern of GPL have great influences on the critical buckling loads and the post-buckling bearing capacities of the circular FG-GPLRC plates. [ABSTRACT FROM AUTHOR]

The thermal buckling response of square plates with variable angle tows under simply supported conditions is modeled numerically. The path of variable angle tow is modeled as a function of lateral location. The classical lamination theory utilizes fiber paths to calculate thermal loads and stiffness matrices. Using Kirchhoff plate theory and finite element theory, the global material stiffness matrix and the global geometric stiffness matrix of the plate under thermal buckling loads are obtained. By using these matrices, eigenvalues or critical buckling temperature is obtained and the buckling response of the plate is examined. The theoretical results are validated by studies in the literature and finite element models. It has been seen even in an unoptimized span of a sample composite material, variable angle tows (VATs) were 8,60% more resistant to thermal buckling than common composite layups. [ABSTRACT FROM AUTHOR]

The possible failure modes of cold-formed steel (CFS) lipped angle (LA) compression members are yielding, local, flexural torsional, or flexural buckling, and any possible interaction among these buckling modes. In general, the strength estimated by current design guidelines are conservative for these members when flexural-torsional buckling (FTB) is the first global buckling mode because the postbuckling strength of this mode is not accounted for in the global buckling strength equations. The initial part of this paper reports the results of an experimental and numerical study of CFS-LA members undergoing independent FTB. Modifications are suggested to global buckling strength equations based on these results. Subsequently, the reduction in the ultimate strength from strength corresponding to independent buckling modes for LA members undergoing interaction between buckling modes such as local-flexural torsional, flexural-flexural torsional, local-flexural, and local-flexural torsional-flexural are studied systematically using finite-element analysis results. A simple and more accurate interaction equation that accounts for these interactions among buckling modes in CFS-LA compression members is proposed. [ABSTRACT FROM AUTHOR]

In the process of horizontal well construction, the working environment in the well is very complicated. It is difficult to determine the actual deformation and force of the coiled tubing in the wellbore from the load change at the wellhead along. In addition, the coiled tubing wrapped around the reel and entering the wellbore through the injection head may cause an initial residual bending. In this paper, the mathematical model of the coiled tubing under axial load during buckling deformation is established, and the analytical solution with the time term is derived by reasonable simplification of the model. The effect of residual bending on the post-sinusoidal buckling of the coiled tubing in the horizontal well was investigated using the separation variable method. The effect of residual bending variations on the well wall contact forces is analyzed. The research shows that the initial parameter Г is the main factor influencing the post-sinusoidal buckling of the coiled tubing with residual bending. The larger the parameter value Г, the greater the effect of the residual bending on the post-sinusoidal buckling deformation of the coiled tubing, and the earlier the critical point of the mixed sinusoidal-helical buckling of the coiled tubing appears. The compression velocity of the coiled tubing has a significant effect on the well wall contact force. The faster the compression, the greater the contact force. By introducing the time term and the separation variable, this paper provides a new method and theoretical basis for further study of the process of entering sinusoidal-helical buckling of the coiled tubing with initial residual bending. [ABSTRACT FROM AUTHOR]

In order to solve the problem that U-shaped steel sheet piles (USSSPs) are prone to buckling when inserted, we propose a local stiffened U-shaped steel sheet pile destabilization critical load calculation method, namely 'dynamic alignment coefficient method', and analyze the influence of stiffening area, stiffening position and number of stiffening plates on the stiffening effect.The study shows that when the total stiffening area is certain, there is a scheme of stiffening plate arrangement to maximize the critical load value of USSSPs with determined length,and reveals the law of local instability caused by the small width of single stiffening plate when the number of blocks is too large. The critical load value of the member can be increased by 13.55% with the variation of the single stiffener plate arrangement position for 10 m long USSSPs, and the optimized theoretical scheme of stiffener plate arrangement for 10 m and 30 m long USSSPs with different total stiffener area is obtained. [ABSTRACT FROM AUTHOR]

In this paper, a new model for porous structures in functionally graded plates (FGPs) is introduced that under significant differences in constitutive material properties and high porosity ratios, the difference in elasticity modulus of the suggested pattern reaches twice as many as the previous model. This study is based on the finite strip method, incorporating Eringen nonlocal elasticity and third-order shear deformation theory, to create standard and geometric stiffness matrices for mechanical and thermal buckling analyses of functionally graded porous nanoplates (FGPNPs). The procedure is founded on Lagrangian and Hermitian shape functions to account for significant shear deformation effects in thick plates, and all in-plane displacements are applied in the geometric matrix based on the virtual work principle. Various factors like boundary conditions, porosity distributions, temperature variations, and nonlocal parameter are investigated for their impact on the mechanical and thermal buckling loads of FGPNPs. The findings reveal the substantial influence of size effects on thick porous nanoplate evaluations. Mechanical analysis shows that O-, V-, X-shaped and uniform patterns exhibit the best performance against mechanical loads, respectively. Despite the material properties deteriorating with increased porosity ratios, thermal resistance is improved. The new uniform pattern performs the best under uniform loading, and V-shaped porous structures excel at strength against nonlinear loading. However, the X-shaped model exhibits the lowest thermal resistance in both conditions. [ABSTRACT FROM AUTHOR]

Design of mechanical metamaterials is typically realized by repeating microstructured building blocks or unit cells. Microstructures of these unit cells can be identical, whereas individual design of each cell and various combinations of unit cells definitely offer more freedoms and possibilities for combinatorial design of metamaterials. Unfortunately, this combinatorial design problem is prohibitively challenging, if not impossible, due mainly to its huge number of combinatorial cases. This paper poses and addresses the combinatorial optimization of a metabeam, aiming at maximizing its critical buckling load. The problem was conceptualized and solved by combination of ML accelerated surrogate modeling and optimization algorithm, and buckling and post-buckling performance of the optimal design was validated by high-fidelity simulations and experiments. The efforts provide efficient tools for combinatorial design of mechanical metamaterials. We publicly share all the data and codes for implementation. [ABSTRACT FROM AUTHOR]

Buckling is typically the governing failure mode of thin‐walled shells. In particular, geometric and material imperfections have a major influence on the buckling behavior. Small variations of imperfections have large effects on the load‐bearing behavior. However, the design of shells is still characterized by a deterministic way of thinking, in which uncertainties have not yet been sufficiently considered. Even in probabilistic approaches, false assumptions are often generated due to the small amount of experimental data. The focus of this paper is an appropriate uncertainty quantification based on the available data. Therefore, the concept of polymorphic uncertainty modeling is presented on axially loaded shells with different types of imperfections. Finally, an idea for a novel design concept for shells based on a fuzzy‐valued safety level is introduced. The paper is intended to initiate a rethinking of the methodology for the numerical design of shells with an appropriate uncertainty quantification. [ABSTRACT FROM AUTHOR]

This paper investigates the size-dependent vibration and buckling behavior of nanoplates described by the nonlocal Kirchhoff model analytically. The nonlocal and local constitutive relations, governing equations and boundary conditions are comprehensively discussed. A shifted governing equation in terms of local stress resultants with associated local boundary conditions is chosen in the current work. The direct separation of variables method is formulated based on the Hamiltonian dual form of the governing differential equation to address the eigenvalue problems of nonlocal rectangular plates with each edge either simply supported or clamped. The closed-form eigen-solutions are acquired for the first time for the cases where two adjacent clamped edges exist. The validity and accuracy of the present approach are verified by comparison with published analytical and numerical results. Parametric studies are performed to investigate the influences of nonlocal parameter and boundary conditions on the size-dependency of natural frequencies and critical buckling loads of nanoplates. [ABSTRACT FROM AUTHOR]

The classical theory of elastic critical buckling stress works well for slender columns and thin flat plates under compression; however, the situation is different for longitudinally compressed thin-walled circular cylindrical shells, and the issue has plagued us despite considerable efforts over the last 100 years. We noticed that all such buckling analyses thus far, both linear and nonlinear, in terms of the main philosophy, inherited and were confined to Euler's pioneering solution for the slender column model that focuses on the longitudinal buckling deformation mode and should be classified as the 'longitudinal open-loop' eigenmode because the deformations of the two longitudinal ends are physically independent of each other. In view of this, for an ideal linear-elastic buckling model of a thin-walled perfectly circular cylindrical shell under uniform longitudinal compression on the foundation of the longitudinal open-loop eigenmode solution, it is also necessary to consider a 'circumferential closed-loop' eigenmode simultaneously to physically avoid violating the reality of its ideal periodic deformation on the entire perimeter and to mathematically redefine the biunique and precise relationship for each distinct eigenmode by the critical circumferential wavelength. Originating from such a case study, the mathematical uniqueness issue hidden in the general solution of the Donnell equation is further discussed. The authenticity of the competing eigenmode characterized by the Koiter circle is also discussed. Furthermore, a preliminary attempt was conducted to interpret the discrepancy between theoretical and experimental buckling loads, mainly initiated by the characteristic type of longitudinally generated circumferential local inward displacement in initial geometric imperfections, using the insights herein. [ABSTRACT FROM AUTHOR]

The stability behaviour of unsymmetrical laminated structures made of fibre-reinforced plastics is significantly influenced by bending–extension coupling and the comparatively low transverse shear stiffnesses. The aim of this work is to improve the analytical stability analysis of unsymmetrically laminated structures. With the discrete plate theory, the stability of laminated structures can be reduced to single laminated plates. The structure is divided into individual segments, and the surrounding structure is modelled by rotational elastic restraints. The governing equations for single plates under specific boundary conditions can be solved exactly with Lévy-type solutions. In this study, Lévy-type solutions for the mentioned boundary conditions under biaxial compressive load is described for the classical laminated plate theory, the first-order shear deformation theory and the third-order shear deformation theory (TSDT). In addition to transverse shear, bending–extension couplings of unsymmetrical cross-ply and antisymmetrical angle-ply laminates are considered. For the implementation of boundary conditions for the rotational restraints in the context of TSDT, a new set of conditions is formulated. The investigation shows very good agreement of the buckling load with comparative finite element analyses for different layups. [ABSTRACT FROM AUTHOR]

This paper deals with the determination of numerical and experimental buckling loads for circular plates. In the study, plates made of isotropic material and laminated composites were taken into consideration. For the experimental part of the study, a buckling apparatus for circular plates (BACIP) was designed and manufactured to apply radial compression on plates simply supported along the outer edge, which was the most important aspect of the study. Experimental buckling loads were determined by connecting this apparatus to a tension machine. ANSYS software based on the Finite Element Method (FEM) and the analytical buckling load formula found in textbooks were also used for the determination of the numerical and analytical buckling loads. The effects of parameters such as plate thickness, number of layers, cutout sizes, and so on on critical buckling loads were investigated within the scope of the work. Comparisons of analytical, theoretical and experimental buckling loads were presented in both graphical and tabular form. The results of the experimental and theoretical buckling were found to be comparatively compatible. [ABSTRACT FROM AUTHOR]

This study investigates the buckling and free vibration behavior of functionally graded saturated porous (FGSP) using a refined quasi-3D theory that ensures zero transverse shear stress at the top and bottom surfaces of the plate. The material properties depend on the porosity coefficient according to three patterns. Hamilton's principle and Biot's poroelasticity theory are employed to derive the equations of motion, which are then solved using Navier's technique. After examining the accuracy of the suggested approach, the effect of fluid compressibility on natural frequency and critical buckling load is investigated in the undrained condition. Also, the effect of porosity, geometrical parameters, and elastic foundation on the vibration and buckling response of FGSP plates are examined. The study reveals that saturating the pores with fluid leads to increased plate stiffness. This translates to higher critical buckling loads and fundamental frequencies. [ABSTRACT FROM AUTHOR]

A novel four-node quadrilateral element with eleven degrees of freedom per node is approximated using the C1-order non-conforming Hermite and Lagrange functions and the novel refined Quasi-3D plate hypothesis for buckling and free vibration analysis of non-uniform thickness bi-directional functionally graded sandwich porous (BFGSP) plates resting on variable elastic foundations (VEF) in a hygro-thermal environment. Material and mechanical properties that change in both the length and thickness directions with three different laws of porosity, which are made up of a fully ceramic core layer and two bi-directional functionally graded (2D-FG) material ones, may be used a lot in the aerospace engineering and military industries. In order to analyze the buckling and free oscillation behaviors shown by the plate with arbitrary boundary conditions, a series of mathematical methods created in Matlab's software are used. The computation program's correctness is verified by comparing numerical findings to dependable assertions. In addition, a comprehensive analysis of the impact of factors on the buckling and free oscillation responses is conducted. The findings reveal that the novel porosity patterns, the hygro-thermal environment, the elastic medium characteristics, and the boundary conditions have a substantial impact on the mechanical behaviors of the non-uniform thickness 2D-FG sandwich porous plates. The results of this article can be used as a useful reference for engineers when calculating and designing structures of this type in engineering practice. [ABSTRACT FROM AUTHOR]

This paper is concerned with a novel problem of determining the maximum spanning capacity of an elastic catenary arch under its own weight against in-plane buckling. The arch supports may be fixed or pinned or rotationally restrained. The arch is assumed to have a uniform cross-section throughout its entire length and the arch length is assumed to be inextensible. Additionally, catenary arches with a crown hinge are considered. The specific shape of a family of catenary curves is specified by the height-to-span ratio (or the horizontal force) which is to be determined for maximum buckling capacity of the arch. The Hencky bar-chain model is adopted for the elastic buckling analysis as it avoids the need to formulate the governing equation for buckling and it is also a simple model to understand and for coding. From the maximum in-plane buckling load of the optimal arch solution, the maximum spanning capacity of the arch can then be derived. Presented herein are the maximum spanning capacities, optimal arc length to span ratios and maximum buckling loads of catenary arches with various support and crown conditions. [ABSTRACT FROM AUTHOR]

Honeycomb sandwich panel is a common hot structure in aircraft, and pits of different shapes are easily formed on its surface during service. In order to study the effect of different shapes of pits on the eigenvalue buckling performance of the honeycomb sandwich panel, three kinds of parametric finite element model for honeycomb sandwich panel with pit defects were built, namely circular pit, quadrate pit, and equilateral pit. Influence of key parameters on the eigenvalue buckling performance of the honeycomb sandwich panel was analyzed under both constant temperature and variable temperature environment. The results show that with the increasing of diameter or dopth of the pit defect, the critical buckling load increases under both the two temperatures environment. By using contrastive analysis method, the influence of the three kinds of pit defects on the structure was obtained when the pit defects have the same area or the same perimeter. When the pit defects have the same area, the structure with circular pit has the largest critical buckling load and when the pit defects have the same perimeter, the structure with equilateral pit has the largest critical buckling load, and both the differences among them are negligible. [ABSTRACT FROM AUTHOR]

A new beam element only having the translational displacement degrees of freedom is developed to analyze fracture and buckling behaviors of bilayer beams or columns with delamination using the multilayer modeling method. By comparing their degrees of freedom, it is found that the present beam element is equivalent to the conventional Timoshenko beam element. The upper and lower layers are both divided into one or several sublayers, which are modeled by the developed beam elements. The element stiffness matrix, load vector, and geometric stiffness matrix using the linear interpolation polynomial are derived by the principle of minimum potential energy. To illustrate the effectiveness, accuracy, and efficiency, both the fracture and buckling analyses are conducted. Four typical fracture specimens (i.e., homogeneous and asymmetric double cantilever beams, single leg bending, and asymmetric end-notched flexure specimens) are analyzed using the developed beam element, and the obtained energy release rate and its components using the virtual crack closure technique are compared with those of analytical and conventional two-dimensional (2D) finite element solutions. Further, buckling analysis of bilayer beam-columns with delamination is conducted, focusing on the effect of the number of sublayers. The results show that the developed beam element is capable of effectively and efficiently calculating the convergent stress intensity factor ratio, total energy release rate and its components, and critical buckling load of delaminated bilayer beams or columns with relatively few elements, but without introducing the interface continuity condition in comparison to the conventional modeling method. [ABSTRACT FROM AUTHOR]

In this present study, we are interested in the use of a precise theory of shear deformation for the buckling analysis of plates with functional gradation simply supported such as the refined theory of plates with four variables. Several parameters of comparison have been used, dimensional and nondimensional. The displacement field is compatible with this study, the nonuse of shear correction factors is satisfied, and the choice of material is very precise in such a way are variable according to the thickness of the plate and on the other hand to make comparison with other researcher and confirms that this study gives precise results and converges. The transverse shear stresses vary through the thickness, the results found is also studied and discussed. [ABSTRACT FROM AUTHOR]