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The objective of this paper is to conduct a comprehensive investigation into the buckling and post-buckling behavior of hyperelastic beams through both computational and experimental means. Natural rubber is used in the construction of a beam with a square cross-section. To determine the mechanical properties of natural rubber, a uniaxial tensile test is performed in accordance with ASTM D412. In finite element modeling (FEM), the nonlinear behavior of rubber is modeled using hyperelastic theory and the Yeoh strain energy function. The Static-Riks method is also implemented using Abaqus for the analysis of nonlinear buckling. To validate the present investigation results with FEM, an experimental test of digital image correlation (DIC) is conducted. The critical buckling force obtained via numerical methods exhibits an error of nearly 5% when compared to the corresponding results obtained from experimental testing. In order to ascertain the impact of various design parameters on the buckling behavior of the system, a comprehensive parametric analysis has been conducted. The parameters studied include the cross-sectional thickness, length of the structure, eccentric loads, as well as the mechanical properties of the materials used in the system. Consistent with the FEM outcomes, the critical buckling force exhibited by the hyperelastic beam demonstrates a positive correlation with increasing levels of hardness, cross-sectional thickness, and eccentric loads. The buckling behavior of the system is adversely affected by increasing its length. To ultimately validate the precision and reliability of the model, a supervised neural network (NN) learning method is employed. [ABSTRACT FROM AUTHOR]

In this paper, the nonlinear post-buckling analysis of imperfect two-dimensional quasicrystal cylindrical shells is performed. The nonlinear governing equations are established by considering initial geometric imperfection, higher-order shear deformation theory and phonon-phason fields coupling effect. The load-shortening curves and buckling modes are obtained by the Galerkin's method. Numerical results are compared with the existing results and excellent agreements are obtained. Effects of geometrical parameters, initial imperfection and phonon-phason fields coupling effect on the critical load and imperfection sensitivity of two-dimensional quasicrystal cylindrical shells are discussed in detail. [ABSTRACT FROM AUTHOR]

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]

A novel 3D centrosymmetric lattice that exhibits a large twist angle during compression is proposed by tailoring the twist buckling mode of a body-centered cubic lattice and a simple cubic truss to the first. The imperfections of offset and multimaterial systems are introduced to control the twist direction. Effects of geometrical parameters and material properties on twist behavior are studied. Results suggest that the buckling-driven lattice configuration can twist at an angle of 100° and an average angle per unit axial strain of 6.7°/%. The novel configurations can be used as force switches, safety devices, and temperature-controlled transmission devices. [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]

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]

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]

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]

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]

AbstractTubular structural composites are widely used in applications where high stiffness and low weight are required. This work proposes the study and evaluation of the influence of damage on the structural responses of thin-walled structures made of composite materials, as well as the development of a buckling prediction model using artificial intelligence. The methodology is approached on a few main fronts, namely: i) numerical modeling of the direct problem of the structure in finite elements, ii) modeling and parameterization of delamination in the elliptical shell model; iii) obtaining a database through finite element updating and iv) formulation and construction of the regression and prediction model using artificial neural networks. The numerical results showed that, as expected, the presence of delamination has a significant impact on the occurrence of buckling. The study also showed that it is possible to predict buckling values, with extremely satisfactory results - an error of around 1%, provided that more complex regression methods are used, such as regression by artificial neural networks, since the relationship between damage and buckling values is not trivial. [ABSTRACT FROM AUTHOR]

In the present work, a novel refined three-variable quasi-3D shear deformation theory incorporates a correction factor is developed to analyze the buckling behavior of multi-directional functionally graded (FG) curved beams. The proposed displacement field is formulated in accordance with the Euler-Bernoulli beam theory. The research investigated two types of coated Functionally Graded (FG) nanobeams: Hardcore (HC) FG curved nanobeams and Softcore (SC) FG curved nanobeams. Three different material distributions are taken into consideration: a bidirectional material distribution referred to as "2D-FG," a unidirectional transverse material distribution known as "T-FG," and a unidirectional axial material distribution called "A-FG." Eringen's nonlocal elasticity theory is employed to capture small-scale effects. The total potential energy principle is utilized to derive the equilibrium equations of curved nanobeams. A novel solution, utilizing Galerkin's method, has been developed to effectively address a range of boundary conditions. The curved FG beam is supported by an elastic foundation following the Winkler/Pasternak/Kerr model. A comprehensive analysis has been conducted to examine the impacts of various FG schemes, curved beam geometry, nonlocal parameter, elastic foundations, and various boundary conditions on the dimensionless critical buckling loads. This analysis aims to provide a comprehensive understanding of how each of these factors influences the critical buckling loads of the nanobeams. [ABSTRACT FROM AUTHOR]

This article aims to investigate the buckling and free vibration behaviors of nanocomposite beams reinforced with functionally graded (FG) agglomerated carbon nanotubes (CNTs) in polymeric beams matrix. In order to estimate the material properties of the FG CNTs reinforced beam, the Eshelby–Mori–Tanaka rule on the basis of equivalent fiber is employed. Moreover, the Lagrange's principle is used to achieve the governing equations under supposition of the refined higher order beam theory without need of any shear correction factor. The differential quadrature finite element method (DQFEM) as a robust and precise numerical procedure is utilized to achieve the natural frequencies and buckling loads with various boundary supports. Then, the assessment of the effects of different factors such as of CNTs agglomeration parameters, different patterns of CNTs distribution, length to thickness quotients, and mixed boundary conditions on the vibrational and buckling responses of agglomerated CNTs reinforced beam are explored. It is concluded that the current numerical solution based DQFEM is efficient and accurate for predicting the mechanical behavior of the nanocomposite structures. Moreover, the stability and vibration responses of the NC beams can be significantly affected by tailoring the agglomeration parameters. [ABSTRACT FROM AUTHOR]

The present work discusses buckling and vibration characteristics of axially functionally graded (AFG) graphene platelet (GPL) composite beams exposed to axially varying loads (AVLs). Timoshenko beam composition with five different types of axial grading GPLs subjected to six different types of AVLs are studied. The effective elastic properties are obtained using Halpin-Tsai model and the equations of motion are obtained following the Hamilton's principle. Then the equations are solved for buckling and vibration analysis using the Ritz method. Influences of nature of axial grading of GPLs and load, content of GPL, and structural boundary conditions are investigated through detailed parametric studies. It is found that the grading pattern of GPLs not only influences the buckling load, but also changes buckling mode shapes of the beam at specific type of AVL. Furthermore, results reveal that buckling and vibration characteristics of beam enhanced in case of AFGM-A type for most of the load cases studied. The proposed study will be helpful for the structural engineers to select the nature of graded distribution of GPLs for the given type of AVL and design the structural member. [ABSTRACT FROM AUTHOR]

This research explores the finite integral transform approach for analytical thermal buckling solutions of composite thin plates with all edges rotationally-restrained, which is difficult to handle by other analytical approaches. Performing the transformations defined on the governing thermal buckling equation and the boundaries investigated, which yields the transform coefficient for the deflection. Incorporating the inversion formula to satisfy the remaining boundary restraints yields sets of homogenous linear algebraic equations, which determines the critical temperature and corresponding mode shapes for plates. In addition, we provide new exact solutions for non-Levy-type plates via setting the rotational restrained coefficient. The precision and efficiency of the present solutions were well validated by precise FEM analysis. It is promising to develop the present approach for seeking more analytical solutions for intractable moderately-thick/thick plate problems. Finite integral transform approach for new exact thermal buckling analysis of fully rotationally-restrained composite rectangular thin plates is developed. New analytic exact thermal buckling solutions of plates under non-classical/non-Levy-type boundaries are obtained. Comprehensive benchmark numerical and graphical results are presented. The method is promising to explore new analytic solutions for intractable problems of plates based on different shear deformation theories. [ABSTRACT FROM AUTHOR]

AbstractThe primary aim of this study is to analyze the buckling behavior of carbon-nanotubes (CNT) reinforced plates using a closed-form dynamic stiffness formulation. The dynamic stiffness method (DSM), typically employed for analyzing plate vibrations, is adapted here for the buckling analysis of various configurations of CNT-reinforced composite plates with internal line support and subjected to uniaxial and biaxial in-plane loads. The displacement field is based on the first-order shear deformation theory, and the analytical expressions for governing differential equations and natural boundary conditions are derived via Hamilton’s principle. The dynamic stiffness matrix is developed for individual plate elements, considering Levy-type boundary conditions. These matrices are then combined to form a global dynamic stiffness matrix, which is solved using the Wittrick–Williams (W–W) algorithm to obtain the critical buckling load. A comprehensive comparative analysis is undertaken to ascertain the accuracy and computational efficacy of the present DSM with alternative numerical methodologies, alongside detailed parametric studies to explore plate buckling characteristics. It should be noted that the DSM is known to provide accurate results as it is based on the exact governing differential equation. Therefore, the reported buckling results can serve as a benchmark for future research in this field. [ABSTRACT FROM AUTHOR]

This study aims to develop semi-empirical formulas for foretelling the buckling loads of clamped and simply supported rectangular isotropic panels with central circular perforation exposed to different ratios of biaxial load conditions. The empirical formulas were developed and evaluated using Gene Expression Programming (GEP), Artificial Neural Network (ANN), and Finite Element Method (FEM). A total of 714 data set, generated using the FEM, is used to establish and validate the empirical formulas. This study investigates the effect of perforation sizes, plate aspect ratios, and biaxial load ratios on the buckling strength of perforated panels. The proposed formulas will allow a quick and easy estimation of buckling loads for perforated rectangular panels with acceptable accuracy without the need for sophisticated calculations. The results of the empirical formulas were comparable reasonably well with the results of the finite element analysis (FE) and available literature findings. [ABSTRACT FROM AUTHOR]

Large displacements are expected to occur in existing code-compliant steel moment-resisting frames during a severe earthquake, affecting the functionality of buildings. This study investigated the use of buckling-restrained braces for controlling the displacement response and ensuring an occupiable performance level of the structures. A design procedure for the braces based on the energy balance concept is proposed, where the hysteretic energy demand of the frame before and after attaching the braces is equated. Time-history analysis results show structures designed using the proposed procedure satisfied the targeted performance level, and no significant change in peak floor acceleration response was observed. [ABSTRACT FROM AUTHOR]

AbstractThis present work investigates the buckling load optimization of the laminated composite plates with the elliptical hole under different non-uniform edge loads. The design objective is the maximization of the critical buckling load by determining the optimum fiber orientations in the layers. The stability equations are derived based on the first-order shear deformation theory (FSDT) of the laminated plates. The critical buckling loads are calculated using the finite element method with the nine noded rectangular element having five degrees of freedom per node. The bonobo optimizer (BO) algorithm is employed to optimize the laminated composite plates with the elliptical hole. The computer programming is developed in the MATLAB environment. Besides, the parametric studies are conducted for different types of the non-uniform edge loads, boundary conditions, cutout radius ratio and aspect ratios and the obtained numerical results are compared. Finally, the optimum results show that these factors play an imperative role in the optimum pattern and stacking sequence of the laminated composite plates with hole. The new significant findings can aid the designers in the structural design, and other industrial applications. [ABSTRACT FROM AUTHOR]

The present study is focused on the numerical and experimental investigation of the non-linear buckling behavior and ply-failure analysis of a hybrid composite shell under uniform hydrostatic pressure exposed on its outer surface. Laminated composite shells made of glass fiber reinforced polymer (GFRP) composites with and without multi-walled carbon nanotubes (MWCNT) reinforcement are considered for the investigation. The critical buckling pressure is numerically determined by performing a buckling analysis on a hybrid composite shell with consideration of various non-linearities such as material non-linearity, geometric non-linearity, and geometric imperfection using the commercially available software ANSYS®. The governing non-linear differential equations of composite shell structures are solved using the arc-length approach and non-linear finite element analysis. The nanotubes dispersion, distribution, structural integrity, aspect ratio, functional group, and purity level of CNT reinforcement with epoxy matrix materials are quantified using field emission scanning electron microscopy (FE-SEM). The elastic and plastic properties of the GFRP lamina with and without MWCNT reinforcement are experimentally determined based on ASTM D3039. The critical buckling pressure obtained through experiments on a GFRP composite shell with and without MWCNT reinforcement is compared with the results obtained from the numerical analysis to validate the effectiveness of the present numerical model. Parametric studies are undertaken to investigate the first ply failure analysis, the effect CNT reinforcement, aspect ratio of MWCNT, and different lamination sequences on the critical buckling pressure of the composite shell. It was observed that the Von-Misses stresses developed on the composite structures with ply angles of either all layers as 0° or combination of ply angles with 0° and 90° is always less than those of the structures having ply-angles such as 45° and 60°, irrespective of CNTs reinforcement. Furthermore, the highest critical buckling pressure was obtained with reinforcement of 1.5 wt% MWCNT in the composite shell with ply orientation of [90°]4s. [ABSTRACT FROM AUTHOR]

One of the most important parts of the structural calculation during their dimensioning is the study of static or even dynamic stability which can be treated in different manners as static buckling, parametric resonance, and dynamic buckling. In this work, we deal with dynamic stability by using the dynamic buckling criteria for functionally graded (FG) material shell structure. This paper aims to determine, in the dynamic case of FG structures composite type, the critical dynamic load using dynamic buckling criteria as phase plan and motion equation criterion. The different mechanical properties are taken as continuous functions through-thickness direction according to the volume fraction of the constituents by a simple power law distribution. The effect of variations of volume fractions and shell geometrical parameters is studied. Convergence tests and comparison studies have been carried out to establish the efficiency of the present model. [ABSTRACT FROM AUTHOR]

Lateral-torsional buckling (LTB) is the primary failure mode for thin-walled steel members where the cantilever beams experience nonuniform twisting and buckling about their weak axes. Much research exists in the literature, and modern codes have presented simple formulations for calculating of elastic LTB load of simply-supported beams. However, there are limited numbers of treatments for predicting of elastic LTB load of cantilevers, most of which are numerical, because as different from the simply supported beams, the LTB failure mode of the thin-walled cantilevers is much more complicated. The present study aims to develop a simplified equation for calculating the elastic LTB of the cantilevers with the European standard I-section. First, an analytical model considering first-order bending distribution, load height level, and monosymmetry property of the section has been introduced. Then, a simplified formula for cantilevers has been introduced utilizing the analytical model and two dimensionless coefficients called the slenderness and the load case parameters. The presented analytical solutions were verified with the finite element analysis (FEA), and the effects of slenderness and loading positions on the LTB behavior of cantilevers with European standard I-section have been investigated. It is found analytical solutions are quite compatible with FEA, and the proposed equation could be safely used for calculating the elastic LTB of the cantilevers. [ABSTRACT FROM AUTHOR]

The curved beam finite element approach based on the potential energy formulation is widely recognized as a versatile tool for lateral torsional buckling analysis of arches. However, there exist a variety of potentials, which were developed with distinct assumptions. The diversity of energy-based curved beam theories introduces confusions in practical applications. This paper aims to examine various potential energy formulations as to whether or not they obey the rigid body rule which is a prerequisite for valid second-order analysis. The induced moments at the ends of curved beam element that have been neglected from and/or the distributed moments that should be removed from available potentials are identified to help them become rigid body qualified. Based on the revised potential functional, a curved beam finite element formulation has been developed to effectively predict yet with less effort the out-of-plane critical load for circular and parabolic arches subject to various loading and constraint conditions. The results of numerical examples demonstrate that a potential energy formulation eligible for describing the out-of-plane behavior of curved beam is required to be rigid body qualified by fulfilling two aspects: (i) the neglected end moments that are imperative for satisfying the rigid body rule must be considered unless the virtual work done by them vanishes, and (ii) undesirable distributed moments that may be induced when undergoing the rigid body motion should be removed by considering all essential potential components. [ABSTRACT FROM AUTHOR]

In this research, the optimization of the geometric parameters of a 3-layer composite plate with an elliptical cutout in the center was investigated utilizing an artificial neural network and genetic algorithm for the first time to obtain the minimum ratio of linear buckling load to weight and the ratio of the diameters of the ellipse. After completing 294 simulations in Abaqus finite element software and forming an artificial neural network with two hidden layers, the function obtained in the artificial neural network was used as the objective function in the genetic algorithm, and the optimal values for the angle of the ellipse with the horizon axis, the diameter ratio of ellipses as well as the fiber angle of the middle layer of the composite were obtained. using artificial neural networks, three algorithms, Levenberg-Marquardt, Bayesian regularization; and scaled conjugate gradient backpropagation, were compared and the number of neurons in each algorithm was compared. The results showed that Levenberg-Marquardt's algorithm is more accurate compared to other algorithms. In the end, the optimal values for the angle of the ellipse with the horizontal axis; as the fiber angle of the middle layer of the composite and, the ratio of the oval diameters as α = 12.3001 degree , θ = 5.9481 degree and D = 1.5690. [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 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]

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]

AbstractThis paper presents a three-dimensional (3D) analysis of the post-buckling behavior of functionally graded (FG) plates for the first time using an elastoplasticity-based meshfree formulation. A novel 3D Tchebychev-radial point interpolation approach, which combines radial basis functions with Tchebychev polynomials, is developed to solve the nonlinear post-buckling problem. The incremental plastic deformation is modeled by the Prandtl–Reuss flow rule along the isotropic hardening von Mises criterion. The governing equations are derived using the principle of virtual work by considering the 3D full Green–Lagrange strain components. The Newton–Raphson technique along with the arc-length method is used to determine post-buckling equilibrium paths of FG plates. The effective elastoplastic properties of the functionally graded material are assessed by exploiting the homogenization method, named Tamura–Tomota–Ozawa (TTO) model. It has been demonstrated that the accuracy of the solution is improved by incorporating Tchebychev polynomials into the radial point interpolation method (RPIM) shape function, and the stability and robustness of the results are independent of variations in the shape parameter. Furthermore, it is confirmed that TRPIM, with a slightly higher CPU time compared to RPIM, exhibits a higher convergence rate. The excellent agreement of the results with those existing in the literature shows that the proposed meshfree method can be used as a robust and accurate numerical tool to predict the elastoplastic post-buckling behavior of FG plates. Further numerical assessments indicate that post-buckling paths are significantly affected by factors such as geometric parameters, material gradient, loading ratio, and boundary conditions (BCs). [ABSTRACT FROM AUTHOR]

This article investigates the out-of-plane buckling of functionally graded porous I-shaped circular arches with graphene platelets reinforcements in a uniform temperature field. The accurate expressions of the prebuckling internal forces owing to thermal expansion are derived. The theoretical out-of-plane buckling temperature difference is obtained by the Ritz technique and is verified by finite element results. Notably, with the asymmetrical distribution of pores along the height of the section, the monosymmetry parameter is considered in the out-of-plane buckling energy equation. The effects of graphene platelets weight fraction, porosity coefficient, and porosity distribution patterns on buckling temperature difference are analyzed in detailed. [ABSTRACT FROM AUTHOR]

The effect of layer number, buckling sequence and drive velocity on energy dissipation per buckling event of mechanical metamaterials composed of representative volume element (RVE) is studied. Buckling behaviors of a single RVE encompassing buckling beams are investigated based on an approximate model. The metamaterials are modeled as a tandem model composed of identical N RVEs. The buckling behavior can not induce energy dissipation if N ≤ 2 for the proposed structure. As N or drive velocity increases, energy can be dissipated during elastic buckling. Besides, the dissipated energy per buckling event gradually decreases during one complete loading and unloading process. [ABSTRACT FROM AUTHOR]

The influence of local thinning thickness defects on the buckling of cylindrical shells is investigated. A static buckling model of cylindrical shells with defects is established based on the Hamiltonian system. The complete symplectic eigensolutions of the cylindrical shell are superimposed to derive the buckling modes of the cylindrical shell with defects. A total of seven different cylindrical shells with axisymmetric and non-axisymmetric defects are considered. Local buckling modes can be captured by this new analytical model with symplectic methodology. By constraining the defect volume, the influence of different defect shapes on buckling of the cylindrical shell is investigated. Comparing with step defects and parabolic defects, the analysis concludes that defects of exponential function are more harmful to buckling of cylindrical shells. This article establishes a cylindrical shell model with arbitrary thickness changes under the Hamiltonian system and evaluates the buckling characteristics of cylindrical shells with thickness defects. A new symplectic approach is developed where the symplectic eigensolutions of the complete cylindrical shell are superimposed to obtain the corresponding buckling modes. Local buckling modes can be captured by this new analytical model. The occurrence of local buckling often drives a significant decrease in critical buckling load. The effects of defect parameters including location, depth, and shape on structure buckling are determined and analyzed. [ABSTRACT FROM AUTHOR]

The Finite Strip Method (FSM) was employed to study the buckling behavior of laminated glass fiber-reinforced polymer (GFRP) stiffened plates with different boundary conditions under axial compression. The theoretical formulation was established based on the first-order shear deformation theory (FSDT) for the thin plate and the stiffener. In this formulation, the stiffeners are not required to be placed on the nodal lines. This feature is considered useful in modeling the stiffened plates in which the stiffener elements are placed arbitrarily in complex planforms. Experimental, numerical and analytical studies were conducted to investigate the effects of the plate width-to-thickness ratio, the stiffener thickness-to-width ratio, dimensions, angle, eccentricity, torsional stiffness and geometric configuration of stiffeners on axial buckling capacity. Furthermore, the obtained results of the analytical method were compared with experimental results and ANSYS code to show its accuracy and convergence. The advantages of the present are that number of elements is much less and the mesh refinement process is much more convenient than commercial finite element software and traditional finite element method (FEM). Therefore, time consumed for analysis is less than the codes which work based on the finite element method. [ABSTRACT FROM AUTHOR]

This study investigates the size-dependent buckling behavior of Timoshenko nanobeams resting on Winkler-Pasternak foundations in a non-uniform thermal environment. A non-uniform temperature distribution is established through nonlocal heat conduction. Subsequently, the equivalent thermal load due to the obtained temperature distribution and boundary constraints is derived using the governing equations of the axial thermal deformation of the beams based on the stress-driven nonlocal elastic model. To obtain the critical buckling load of the nanobeams, the quadrature element method is used to numerically resolve the eigenvalue problem. In the numerical simulation section, we have presented a series of examples to analyze the effects of length-to-height ratios, nonlocal scale parameters, and Winkler-Pasternak foundation parameters on the buckling loads of the nanobeams under various boundary conditions. Moreover, we examine the effect of comprehensively considering both the elastic and thermal nonlocality on the thermal loads and finally mechanical buckling loads. [ABSTRACT FROM AUTHOR]

Fiber-reinforced composite tubes have remarkable advantages in energy absorption due to the high specific strength, stiffness, and fracture energy, etc. While, the energy absorption capacity is severely dominated by buckling deformation. To this end, the buckling behaviors and corresponding mechanism of CFRP (carbon fiber reinforced polymer) tubes are systematically investigated in this work. Furthermore, an advanced bionic method referring to bamboo and human bones is adopted to improve the buckling. To effectively analyze the buckling, drop weight impact experiments and corresponding numerical simulations are carried out. The results show that the specific energy absorption (SEA) of CFRP tubes is significantly affected by the diameter-to-height ratio and fiber ply direction, and the influencing mechanism is excessive buckling caused by the geometric characteristics and brittle failure of CFRP. At last, the SEA of CFRP tubes were improved through bio-inspired multi-layered metal/composite hybrid, where the buckling is suppressed reasonably well. The conclusions drawn would be inspiring or guiding the optimal design of high energy-absorbing composite tubes in engineering application. [ABSTRACT FROM AUTHOR]

AbstractThis study presents the buckling and lateral torsional buckling behaviors of thin-walled laminated composite or functionally graded sandwich I-beams. A refined beam model (RBT) based on the 3D Saint-Venant (SV) solution is used in this study to formulate the problem. This model allows for a realistic analysis of beams with arbitrary cross-sections and is free from the limitations of classical beam theories. The displacement models establish a consistent 1D beam theory that accurately captures the essence of the cross-section’s nature. The governing models consider cross-section deformations, including in and out of plane warpings and distortions derived from the 3D SV solution associated with the cross-section vibrational behavior. Furthermore, a user-friendly numerical tool called CSB (cross-section and beam analysis) is used to facilitate the implementation of this method. The numerical results are examined in detail and compared with previous works to investigate the influence of boundary conditions, angle-ply, shear effects, span-to-height ratio, and material distribution on the critical buckling loads of thin-walled I-beams. The results demonstrate that the RBT models accurately and efficiently analyze thin-walled I-beams under different loads and boundary conditions. Furthermore, some of the new results are presented as reference values for the future. [ABSTRACT FROM AUTHOR]

The present investigation has analyzed the buckling of bi-directional functionally graded conical micro-shells bearing axial loading. The dominant equations serve on the basis of the theory of first-order shear deformation in the modified couple stress theory (MCST). The Ritz technique is used so as to solve the governing equations. Bi-directional functionally graded material is the material used to construct the shell, and in a predefined composition profile, the volume fractions pertaining to the constituent materials constantly vary through the conical edge directions and thickness. The model predictions are compared and successfully validated using the ones available in the literature. According to the results, in comparison with the classical theory, the micro-shell buckling load is higher in the MCST. In addition, the contribution of a number of geometrical and mechanical parameters, for example, radius-to-thickness ratio, thickness-to-length scale ratio, length-to-radius ratio, semi-vertex angle, homogenization schemes, and material gradient indexes, to the buckling performance of conical micro-shells has been investigated. It is noteworthy that this investigation is the first effort to present a buckling analysis for the purpose of bi-directional functionally graded truncated conical micro-shells in accordance with the MCST. [ABSTRACT FROM AUTHOR]

AbstractIn this article, a simple refined shear deformation theory that eliminates the use of a shear correction factor was presented for buckling analysis of in-plane bi-directional functionally graded (IBFG) porous plates under various boundary conditions. Unlike any other theory, the number of unknown functions involved is only four, as against five in case of other shear deformation theories. Material properties of IBFG are assumed to vary continuously along with two different directions simultaneously, that is, the longitudinal and transversal ones, respectively. Governing equations and boundary conditions are derived. Analytical solutions were obtained for buckling analysis of (IBFG) porous plates. Several numerical examples are presented to demonstrate the performance and effectiveness of the proposed theory. The effects of material gradations, aspect ratios, and porosity on IBFG plate responses are examined in detail as well. [ABSTRACT FROM AUTHOR]

In this article, analytical solutions for the buckling analysis of simply supported rectangular functionally graded (FG) plates subjected to various forms of non-uniform in-plane loads are presented. Both perfect and porous FG plates with power-law material property variation are considered. The analytical solution is obtained by adopting a two-step approach: First, a rigorous plane-stress solution is developed based on the superposition of Airy's stress functions, and later, these stress solutions are used in the buckling load computation of the FG plate based on Galerkin's technique. One key aspect of the proposed solution is that it can consider different non-uniform waveforms of the in-plane loads at two opposite sides of the plate. Results show that the nature of the edge load has a profound effect on the stress solution of the FG plates. Several tables and graphs are presented to obtain a qualitative and quantitative understanding of the buckling behavior of FG plates influenced by various plate design parameters which include plate aspect ratios, power-law exponent, and porosity index. Comparative studies are also presented to highlight some erroneous results published in the open literature. It can be emphasized that the analytical results reported here can be used as a reference to judge the accuracy of other numerical solutions such as the finite element method. [ABSTRACT FROM AUTHOR]

The buckling behavior of moderately thick and thick stiffened composite plates with different stiffener layouts is formulated based on the higher-order shear deformation theory. This investigation is performed under axial compression using the Finite Strip Method and experiment. The effects of dimensions, orientation, eccentricity, torsional stiffness, position and geometric configuration of stiffeners on the buckling load coefficient are achieved by employing the principle of minimum potential energy. Six grid-stiffened composite plate specimens with ortho-grid, angle-grid, and orthotropic-grid stiffeners are tested. The results of the presented method show good outcomes with those of experimental tests and the finite element ANSYS code. [ABSTRACT FROM AUTHOR]

This paper presents a simple refined plate theory (S-RPT) which contains only three unknown variables in the displacement field for bending and buckling analysis and only one unknown variable in the displacement field for free vibration analysis. Unlike other simplified plate theories, S-RPT in its simplification (1) takes into account the Poisson's ratio variation along the thickness direction (2) takes into account the full coupling of in-plane and transverse displacements. These features make S-RPT applicable to the analysis of bending, buckling, and free vibration of functionally graded porous plates reinforced with graphene platelets (FGP–GPLs). Some simplified plate theories already available in the literature can be regarded as special cases of S-RPT. The S-RPT is first used in isotropic and metal–ceramic functionally graded plates to verify its accuracy. Then, the effect of pore distribution, GPLs distribution, porosity coefficient, aspect ratio, thickness ratio, and GPLs weight fraction on the bending, buckling, and free vibration behaviors are investigated based on S-RPT. [ABSTRACT FROM AUTHOR]

AbstractThis paper investigates the effects of multiple materials configurations on the buckling performance, total mass, and manufacturing cost of an existing omega stiffened composite panel. The buckling response of omega stiffened composite panel is predicted and verified using available data in literatures. The multiple materials are introduced into the omega stiffened composite panel. The material distribution, stacking sequences of panel skin, T sub-stiffeners and omega sub-stiffeners are optimized to improve the critical buckling load with reducing the total mass and manufacturing cost. During the optimization process, three classical loading conditions of the stiffened panel are considered, while ensuring compliance with the constraints imposed by ply manufacturing. A generalized optimization design framework for stiffened panels is employed, and NSGA-II algorithm is utilized to achieve the optimum design of stiffened panels. Results demonstrate that the introduction of multiple materials to the omega stiffened composite panel can lead to improved buckling performance, along with reduced manufacturing cost and total mass. Additionally, the proposed multiple-material optimization design framework can be further applied to the structural design of other types of stiffened composite panels in the future. [ABSTRACT FROM AUTHOR]

Stochastic vibration and buckling analysis of functionally graded sandwich thin-walled beams with I-section based on the first-order shear deformation theory is for the first time proposed in this paper. The material properties of beams in both web and two flanges are assumed to be continuously varied in its thickness. Additionally, the constituent material properties are randomly changed according to the lognormal distributions. These stochastic variabilities are then propagated to the stochastic responses of the thin-walled beam through a beam solver with hybrid series-type approximation functions. To achieve efficient evaluations for stochastic responses including natural frequencies and critical buckling loads, polynomial chaos expansion (PCE) based surrogate model is developed. The efficiency and accuracy of PCE's results are assessed by comparing with those of crude Monte Carlo simulation. Sensitivity analysis is carried out to compare the importance of the uncertainty in material properties to stochastic responses. New results reported in this paper can be interesting benchmarks for scientific and engineering community in the future. [ABSTRACT FROM AUTHOR]

The authors propose an intelligent computational method using the deep feedforward neural network integrated with an improved balance composite motion optimization algorithm to formulate a so-called iBCMO-DNN for solving the stochastic thermal buckling problems of functionally graded porous microplates. In the present approach, the deterministic behaviors of the functionally graded porous microplates were firstly analyzed by the combination of a unified higher-order shear deformation theory, modified strain gradient theory, and Ritz-type series solutions, and then stochastic responses under uncertainty of material properties are obtained by the iBCMO-DNN algorithm. The deep neural network with the long short-term memory model is used as a surrogate method to replace the time-consuming computational model, while the improved balance composite motion optimization is used to search for the optimal solutions. The obtained numerical results for various boundary conditions, uncertainty parameters, and three types of temperature distribution indicated that the proposed method achieves its accuracy and effectiveness in predicting stochastic thermal buckling of the functionally graded porous microplates. The improved balance composite motion optimization algorithm demonstrates a computational time ∼1.7 times faster than its predecessor. Furthermore, integrating a deep neural network into the improved algorithm reduces computational time to about 2/5 compared to the method without it. [ABSTRACT FROM AUTHOR]

Thermal buckling analysis of a simply supported sandwich cylindrical microshell with piezoelectric layers reinforced with graphene platelets is presented in the current study. The motion equations of the piezoelectric microshell are derived in reference to the first-order shear deformation hypothesis alongside the modified couple stress theory. The critical buckling temperature difference of piezoelectric graphene platelets reinforced cylindrical microshells is derived from adopting Navier's approach and the meshless method. The material properties of every layer for microcomposite shell layers reinforced by graphene platelets are estimated using Halpin–Tsai model. The comparison study is conducted to verify upcoming results. The goal is to investigate the effects of the applied voltage, the thickness of the piezoelectric layers, the distribution pattern, the weight fraction, the material length scale parameter, the length to radius ratio, and the thickness to radius ratio on the buckling of piezoelectric graphene platelets cylindrical microshell. [ABSTRACT FROM AUTHOR]

Smart materials and structures at the nanoscale represent the main components in manufacturing plan for nano-electromechanical systems. In this research study, an unconventional shell model based upon the nonlocal couple stress (NCS) continuum mechanics accommodating the both softening and stiffening features of size dependency is formulated to analyze the buckling mode transition phenomenon in nonlinear stability characteristics of functionally graded (FG) piezoelectric nanoshells subjected to thermo-electromechanical load. To accomplish this objective, an efficient numerical strategy based upon the moving Kriging meshfree (MKM) technique is employed via different nodal distribution schemes, including Chebyshev, regular uniform and irregular ones. The established NCS-based numerical model has the capability to incorporate the buckling mode transition phenomenon as well as satisfying the function property of the Kronecker delta via imposing essential boundary conditions with no use of predefined mesh and directly at the associated nodes. It is also demonstrated that by changing the sign of electric actuation from negative to positive, the softening character of nonlocality as well as the strengthening character associated with the couple stress size dependency become a bit more significant. Furthermore, the roles of both unconventional stress tensors are more prominent in the value of the second bifurcation point in comparison with the first one. [ABSTRACT FROM AUTHOR]

AbstractThis paper investigates the vibration and buckling analysis of porous metal foam thin-walled box beams. These beams exhibit a unique structural configuration with symmetrical and asymmetrical porosity distributions along their wall thickness, thereby altering the effective mechanical properties. The first-order shear deformable beam theory is employed and the governing equations are derived using the Hamilton’s principle. Numerical results are presented for porous metal foam thin-walled box beams under simply-supported, clamped–clamped and clamped-free boundary conditions. The effects of various porosity parameters, length-to-side and side-to-wall-thickness ratios on the beams’ performance are also examined. A comprehensive comparison between the porous metal foam thin-walled box beams and their counterparts in the form of equivalent homogeneous are presented. [ABSTRACT FROM AUTHOR]

AbstractThis article investigates the static and dynamic buckling behavior of a double-curved sandwich shell composed of two layers via improved first-order shear deformation theory without using the shear correction is utilized to model the sandwich shell. The sandwich two-layer shell are held together by elastic pins, each layer made from an ultra-light auxetic honeycomb core layer (negative Poisson’s ratio) and is reinforced by a layer of tri-phase polymer, graphene nanoplatelets (GNP), and fiber. The double-curved sandwich shell is supported by a Kerr elastic medium in hygro-thermal environment assuming that temperature and humidity only cause forces to be applied tangentially to the shell and do not change the mechanical properties of the shell material. The motion equations of sandwich two-layer shell are derived by Hamilton’s principle, then the finite element method and Bolotin method are used to derive the dynamic instability region of sandwich two-layer shell. The accuracy of these results is confirmed by a comparison with established statements within the specific conditions of the problem model. The influence of inputs on the static and dynamic stability of sandwich two-layer shell is fully explored and discussed. Additionally, this serves as a crucial foundation for the calculation and design of structures that can integrate a variety of materials with different properties with low cost and simplification. [ABSTRACT FROM AUTHOR]

Buckling analysis of functionally graded piezoelectric nanoshell is studied in this paper based on the higher-order shear and normal deformation theory and accounting thickness stretching effect. The nanoshell is subjected to axial load, applied electric potential and thermal loads. Thickness stretching effect is accounted in the analysis based on higher-order shear and normal deformation theory. Small scale effects are accounted based on the Eringen nonlocal elasticity theory. The Navier solution is used for the buckling analysis of the cylindrical nanoshell with simply-supported boundary conditions. The accuracy and trueness of the present paper is justified using comparison with literature. The importance of the present analysis and corresponding results is justified using presentation of results with and without thickness stretching effect. A large parametric analysis is presented to investigate the influence of significant parameters such as dimensionless small scale parameter, length to radius ratio, thickness to radius ratio, temperature rising and applied electric voltage on critical buckling axial loads. One can conclude that the critical buckling axial loads are decreased with increase of small scale parameters and applied electric potential. [ABSTRACT FROM AUTHOR]

AbstractThe thermal buckling behavior of concrete annular sector plates reinforced with nanocomposites is investigated in this work. The thermal buckling issue is stated using mathematical modeling, taking into account the geometric linearity and material heterogeneity caused by the nanocomposite reinforcement. The governing differential equations that are obtained from the theoretical model are solved using the discrete singular convolution (DSC) technique. To generate accurate buckling load predictions, the DSC method’s great accuracy in handling complicated boundary conditions and discontinuities is used. Furthermore, using mathematical modeling to create extensive datasets, the research aims to train deep neural networks (DNNs) to anticipate thermal buckling reactions. These datasets provide a strong basis for DNN training as they include a wide range of factors, such as geometric configurations, loading situations, and material properties. By combining DNN predictions with DSC solutions, this unique technique for solving this difficult issue seeks to improve the accuracy and efficiency of thermal buckling analysis. The findings show how well sophisticated mathematical methods and machine learning models work together, opening the door to creative solutions for the design and analysis of concrete structures reinforced with nanocomposite under complicated stress. [ABSTRACT FROM AUTHOR]