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As a first attempt, optimum stacking sequences of thick laminated composite plate is obtained to maximize its buckling load via employing the finite element (FE), genetic algorithms (GAs) and particle swarm optimization (PSO) methods. The higher-order shear deformation theory (HSDT) is used to obtain governing equations of the plate. The finite element method (FEM) is employed to solve these equations and to gain buckling load of the plate. The FEM solution is linked with a developed optimization algorithm which is a mix of genetic algorithms (GAs) and particle swarm optimization (PSO) techniques. Some examples are solved to show applicability and usefulness of the proposed hybrid method for maximizing buckling load of the plate via finding optimum stacking sequences of the plate. Also, influences of different parameters on the optimum stacking sequences of the thick plate are studied. [ABSTRACT FROM AUTHOR]

Semi-analytical models for the linear buckling analysis of unstiffened laminated composite cylinders and cones with flexible boundary conditions are presented. The Classical Laminated Plate Theory and the First-order Shear Deformation Theory are used in conjunction with the Donnell’s non-linear equations to derive the buckling equations. Axial, torsion and pressure loads can be applied individually or combined in the proposed models. The stiffness matrices are integrated analytically and for the conical shells an approximation is proposed to overcome non-integrable expressions. Comparisons with the literature show that the classical base functions available for axial compression cannot capture the buckling modes for non-orthotropic laminates. For torsion loads these classical shape functions do not catch the buckling modes even when applying the assumption of pure orthotropy, and it is shown how the proposed models correlate well with experimental data from the literature and finite element results. The use of elastic constraints at the boundaries allows the simulation of different boundary conditions in a versatile way and it is shown how those constants can be adjusted in order to change from one type of boundary condition to another. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents the buckling analysis of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) plates under various in-plane mechanical loads, using the element-free kp-Ritz method. The first-order shear deformation plate theory is applied and a set of mesh-free kernel particle functions are used to approximate two-dimensional displacement fields. Effective properties of materials of the plates reinforced by single-walled carbon nanotubes (SWCNTs) are estimated through a micromechanical model based on either the Eshelby–Mori–Tanaka approach or the extended rule of mixture. Comparison study and numerical simulations with various parameters are conducted to assess efficacy and accuracy of the present method for analysis of buckling of SWCNT-reinforced composite plates. Results demonstrate that the change of carbon nanotube volume fraction, plate width-to-thickness ratio, plate aspect ratio, loading condition and temperature have pronounced effects on buckling strength of CNTRC plates as well as the boundary condition. [Copyright &y& Elsevier]

Abstract: Dynamic buckling analysis of FGM plates has not been accomplished so far. In the present paper, vibration and dynamic buckling of FGM rectangular plates with surface-bonded or embedded piezoelectric sensors and actuators subjected to thermo-electro-mechanical loading conditions are investigated. A finite element formulation based on a higher-order shear deformation theory is developed. Both initial geometric imperfections of the plate and temperature-dependency of the material properties are taken into account. Dynamic buckling of plates already pre-stressed by other forms of loading conditions is assumed to occur under suddenly applied thermal or mechanical loads. A nine-node second order Lagrangian element, an efficient numerical algorithm for solving the resulted highly non-linear governing equations, and an instability criterion already proposed by the author are employed. A simple negative velocity feedback control is used to actively control the dynamic response of the plate. Results show that generally, initial geometric imperfections lead to an increased fundamental bending natural frequency and decreased buckling loads. Furthermore, buckling mitigation due to utilizing integrated piezoelectric sensors and actuators is mainly achieved in extremely high gain values. Therefore, the piezoelectricity effect on the buckling load is small in applicable voltages. It is also noticed that the temperature-dependency and initial geometric imperfections remarkably affect the buckling loads. [Copyright &y& Elsevier]

Abstract: A solution is proposed to the buckling problem formulated for a rectangular sandwich plate having all the edges fully clamped (CCCC plate) and subjected to a uniaxial compressive loading. The analysis of the out-of-plane deformation of the buckled plate is based on the equations of the first order shear deformation theory (FSDT). Galerkin method has been employed to solve the problem. Variations of the plate deflection and angles of rotation between the unloaded edges have been approximated using the solution to the bending problem for the shear deformable beam with clamped ends. The approximation of these variables between the loaded edges has been performed using trigonometry series. The solution to the problem is reduced to the calculation of the eigenvector of corresponding homogeneous system of linear equations and determination of its least component. Verification of the solution obtained has been performed using finite-element analysis. [Copyright &y& Elsevier]

Abstract: A semi-analytical method is developed for pre-buckling and buckling analyses of thin, symmetrically laminated composite panels with an elliptical cutout at an arbitrary location and orientation under general thermo-mechanical loading conditions. Both the pre-buckling and buckling analyses are based on the principle of stationary potential energy utilizing complex potential functions and complete polynomials. The complex potential functions capture the steep stress gradients and local deformations around the cutout, and the “complete” polynomials improve the global buckling response of the laminate. The complex potential functions in the pre-buckling state automatically satisfy the in-plane equilibrium equations, thus reducing the first variation of the total potential energy in terms of line integrals only. Because the complex potential functions for out-of-plane displacements are augmented by the “complete” polynomials, the area integral terms in the second variation of the total potential energy, referred to as the Treftz criterion, are retained in the buckling analysis. The kinematic boundary conditions are idealized by employing extensional and rotational springs (elastic restraints) with appropriate stiffness values. Based on the numerous validation problems, this analysis is proven credible for predicting the buckling load of rectangular and non-rectangular panels with a cutout. [Copyright &y& Elsevier]

Abstract: The objective of the present work is to study the effects of flexural boundary conditions on buckling and postbuckling behavior of axially compressed quasi-isotropic laminate, (+45/−45/0/90)2 s with various shaped cutouts (i.e., circular, square, diamond, elliptical–vertical and elliptical–horizontal) of various sizes using the finite element method. The FEM formulation is based on first order shear deformation theory and von Karman’s assumptions are used to incorporate geometric nonlinearity. The 3-D Tsai-Hill criterion is used to predict the failure of a lamina while the onset of delamination is predicted by the interlaminar failure criterion. It is observed that the laminates clamped and simply supported on all edges have the highest and lowest buckling and postbuckling strength, respectively, irrespective of cutouts shape and size. It is also noted that a fully clamped laminate with large size elliptical–vertical cutout can take higher compressive buckling load than the laminate without cutout for same boundary condition. [Copyright &y& Elsevier]

The vibration behaviors of functionally graded carbon nanotube (FG-CNT) reinforced composite rectangular plates subjected to in-plane loads are studied in this paper. Three types of carbon nanotube (CNT) distributions are researched in this investigation. Reddy’s third-order shear deformation theory (HSDT) is applied to evaluate the displacement fields of the plate. The equation of motion of the structural system is formulated with use of the Hamilton’s principle. The plates investigated in this study are simply-supported on two opposite edges and therefore, in order to solve the coupling set of equations of motion, the state-space Levy method is applied. Based on the Levy solution, the natural frequencies and vibration mode shapes of FG-CNT reinforced composite plates subjected to in-plane loads with different boundary conditions are presented for different thickness-length ratios and aspect ratios. Moreover, the critical in-plane loads for the buckling of different FG-CNT plates are calculated and compared. [ABSTRACT FROM AUTHOR]

Abstract: Capacity of nonlinear large deformation is favored for structures because of its indication of potential failure. Such behavior is achieved mainly through material ductility, for example yielding of steel, or so-called pseudo-ductility at the price of progressive failures of structural components. A strategy is proposed in this paper for structures made using brittle fiber reinforced polymer (FRP) materials to achieve such behavior at structural level without the failure of materials. The concept is to take advantage of the post-buckling process of certain structural components in compression, during which the structure loses its redundancy and structural deformation increases as the applied load is sustained. The concept is introduced and illustrated using the analysis of a simple truss. Experiments are then reported which visualize the proposed concept on two FRP truss structures. Experimental results from the first truss demonstrate nonlinear large deformation similar to material ideal elastic–plasticity and those from the second truss exhibit a response analogical to material strain hardening. Possible applications and developments of this concept are further suggested. [Copyright &y& Elsevier]

Thin-walled composite beams of complex sectional contour are widely used along with the traditional elements of reinforced structures. Based on the generalized theory of elasticity of thin-walled beams, the mathematical model of flexural–torsional deformation of open-profile thin-walled composite beams of non-uniform cross section under thermo-mechanical loading has been developed. To confirm the reliability of developed approach to determination of the spatial displacements of thin-walled composite beams of non-uniform cross section, several experimental studies were conducted. Based on the analysis of the range of typical profiles, for the further analysis we selected several compound cross sections for which the analytical dependences were obtained regarding displacements of their characteristic points. Our studies can serve as a base for development of the practical recommendations for the optimal designing and manufacturing of thin-walled anisotropic profiles, as well as proposing the measures to reduce the value of deformations caused by the production process. [ABSTRACT FROM AUTHOR]

The problems of a multi-mode buckling approach which is based on Koiter’s theory of a hybrid column are presented in this paper. An interaction of global buckling modes with the local ones is discussed. There are many different local and global buckling modes. Their selected combinations are dangerous and cause a reduction in the load-carrying capacity. All walls of the hybrid column were plane and made of many layers. The outer layers were thermal barriers and made of a TiC ceramic layer or an AL-TiC-type FGM. The inner layers were composed of aluminium layers and a few carbon-epoxy laminate layers. The classical laminate theory is used to define the ABD matrix which described the relations between applied loads and the associated deformations. The layup configuration of the hybrid column is general, so the coupling submatrix B is non-trivial. This submatrix has a significant impact on the value of local buckling load, whereas its effect on the value of global buckling load can be neglected. The main topic discussed in this paper is whether and how individual elements of the B submatrix can change the load-carrying capacity of a hybrid column. A detailed discussion is conducted for simple supported columns with opened cross-sections subjected to mechanical loads only. Thermal effects are neglected. [ABSTRACT FROM AUTHOR]

Abstract: This paper discusses the influence of thermal distortion to compression failure load of polymer matrix composite panels in fire. The thermal gradient along the thickness of the panel, caused by low thermal conductivity, induces transverse deformation field even without external mechanical loads, known as thermal distortion. The deformation field of thermal distortion obtained from combined thermal–mechanical analysis is presented in terms of non-dimensional parameters that represent thermal and mechanical properties, including those in phase transition at high temperature range, and dimensional lengths. A failure model is proposed to assess the transition from Euler buckling to plastic compression failure under the influence of thermal distortion. For large slenderness ratio, the panel is failed by Euler buckling. For small slenderness ratio, the panel is failed by plastic failure mechanism, where the analysis quantifies the influence of thermal distortion to the reduction of load-bearing capacity. The compression failure mechanism under the influence of thermal distortion is discussed for developing quantitative approach to design polymer matrix composite structures in fire. [Copyright &y& Elsevier]

The present paper deals with the linear and non-linear dynamic instability of functionally graded materials (FGMs) plate subjected to non-uniform loading. Due to this loading, the in-plane stress distributions within the FG plate in pre-buckling state are evaluated using plate membrane analysis. The FG plate is modeled using higher order shear deformation theory (HSDT) considering von-Kármán geometric nonlinearity. The Galerkin’s method is used to reduce the non-linear governing partial differential equations into a set of ordinary differential equations describing the plate non-linear dynamic instability. Bolotin’s method is used to obtain the boundaries of dynamic instability regions. These boundaries are traced by the periodic solution of linear ordinary differential equation (Mathieu-Hill equation) with period T and 2T. Effects of power index, span-to-thickness ratio, aspect ratio, static load factor, boundary conditions and various types of linearly varying loadings and parabolically distributed loadings on the linear and nonlinear dynamic instability are studied. The study of linear and non-linear response in stable and unstable regions are carried out to identify the dynamic instability behaviour such as dependence of forcing frequency, existence of beats, effect of nonlinearity on the response and influence of the initial conditions. [ABSTRACT FROM AUTHOR]