Thermomechanical buckling of laminated composite and sandwich plates using global–local higher order theory

In this paper, a global–local higher order theory has been used to study buckling response of the laminated composite and sandwich plates subjected to thermal/mechanical compressive loads. The present global–local theory satisfies the free surface conditions and the geometric and stress continuity conditions at interfaces, and the number of unknowns is independent of the layer numbers of the laminate. Based on this higher-order theory, a refined three-noded triangular element satisfying C¹ weak-continuity conditions has been also proposed. The present theory not only predicts accurately the buckling response of general laminated composite plates but also calculates the critical buckling loads of the soft-core sandwich plates. However, numerical results show that the global higher-order theories as well as first order theories encounter some difficulties and overestimate the critical buckling loads for the sandwich plates with a soft core.     

Buckling of symmetrically laminated rectangular plates under parabolic edge compressions

Buckling analysis of symmetrically laminated rectangular plates with parabolic distributed in-plane compressive loadings along two opposite edges is performed using the Rayleigh-Ritz method. Classical laminated plate theory is adopted. Stress functions satisfying all stress boundary conditions are constructed based on the Chebyshev polynomials. Displacement functions for buckling analysis are constructed by Chebyshev polynomials multiplying with functions that satisfy either simply supported or clamped boundary condition along four edges. Methodology and procedures are worked out in detail. Buckling loads for symmetrically laminated plates with four combinations of boundary conditions are obtained. The proposed method is verified by comparing results to data obtained by the differential quadrature method (DQM) and the finite element method (FEM). Numerical example also shows that the double sine series displacement for simply supported symmetrically laminated plates having bending-twisting coupling may overestimate the stiffness, thus providing higher buckling loads.     

Buckling of moderately thick rectangular composite plates subjected to partial edge compression

The objective of the present paper is to investigate the influence of partial edge compression on the critical loads of moderately thick laminated plates. Towards this, an eight node isoparametric plate element is developed. The element has five degrees of freedom per node. The computer code developed accepts two sets of boundary conditions, one for pre-buckling stress analysis and the second for stability analysis. This flexibility is proposed to exploit the mid-line symmetry conditions. Two types of partial edge compression, viz., (I) uniform partial edge compression near the corners and (II) uniform partial edge compression at the middle of edges are considered. The effect of percentage of loaded edge length on the critical load of thin and thick composite plates with simply supported and clamped edge conditions is studied in detail.     

Generalized buckling analysis of laminated plates with random material properties using stochastic finite elements

A generalized layer-wise stochastic finite element formulation is developed for the buckling analysis of both homogeneous and laminated plates with random material properties. The pre-buckled stresses are considered in the derivation of geometric stiffness matrix and the effect of variation in these stresses on the mean and coefficient of variation of buckling strength is studied. The mean buckling strength of plates under uniform stress assumption exactly matches with those reported in the literature. However, it is shown that the actual mean buckling strength of plates can be significantly different based on the pre-buckled stress analysis which depends on boundary constraints, principal material directions, aspect and thickness ratios of plates. The statistics of buckling strength is determined using a Taylor series expansion based mean centered first order perturbation technique. The stochastic finite element solutions obtained using layer-wise plate theory is also validated with analytical solutions presented in this paper. Parametric studies are conducted for different aspect ratios, ply orientations and boundary conditions.     

含初始缺陷的加强复合材料圆柱壳的非线性屈曲分析

综合考虑几何非线性、材料非线性、横向剪切效应以及初始几何缺陷等因素，对带有加强筋和加强环的复合材料圆柱壳的屈曲问题进行了分析研究。所得数值结果与有关试验值及其它已知解吻合良好，因而可用于实际工程中加强复合材料圆柱壳的设计计算，同时表明这里给出的本构关系对于弹塑性屈曲分析是适用的，并提出保证结构完整性、改善结构整体屈曲性能的关键是控制制造加工质量，减少初始缺陷。     

Analysis of rectangular laminated composite plates via FSDT meshless method

A meshless approach based on the reproducing kernel particle method is developed for the flexural, free vibration and buckling analysis of laminated composite plates. In this approach, the first-order shear deformation theory (FSDT) is employed and the displacement shape functions are constructed using the reproducing kernel approximation satisfying the consistency conditions. The essential boundary conditions are enforced by a singular kernel method. Numerical examples involving various boundary conditions are solved to demonstrate the validity of the proposed method. Comparison of results with the exact and other known solutions in the literature suggests that the meshless approach yields an effective solution method for laminated composite plates.     

The shear buckling behaviour of thin composite plates with particular reference to the effects of bend–twist coupling

The effect of bend–twist coupling on the shear buckling behaviour of laminated composite plates is examined in this paper using a finite strip procedure. The complex buckled shapes which are associated with shear loading are duly accounted for in the analysis approach through the multi-term facility of the strip formulation employed and, of course, through the appropriate level of structural modelling. The degree of bend–twist coupling in the laminated composite plates is varied by changing the level of anisotropy in the plies and by altering the lay-up configuration of the plies in the laminated stack. Symmetric laminates of a balanced and unbalanced nature are given consideration. It is shown that, for a given degree of anisotropy in the plies of a laminate and for a given laminate thickness, the stacking sequence of the plies significantly alters the degree of bend–twist coupling. The shear buckling performance of composite plates having the same dimensions and being made from the same material are therefore shown in the paper to be quite different. The preclusion of the bend–twist coupling coefficients in the solution procedure of the finite strip method allows the shear buckling orthotropic solution to be determined. Comparisons between the coupled and orthotropic solutions are shown in the paper to be markedly different with respect to critical shear performance level and also buckled mode shape. For square plates or plates with a moderate aspect ratio the influence of bend–twist coupling on buckled mode shape is shown in the paper to be noticeable through increased distortion. For the larger aspect ratio plates it is shown that the presence of bend–twist coupling can cause a complete change in the mode shape from a symmetric to an antisymmetric nature or vice versa. Amplitude modulation is shown in the paper to be clearly evident in the shear buckling mode shapes of long plates.     

壁板结构热屈曲后模态特性试验

高速飞行器在服役期间面临着严酷的气动加热效应,热载荷会引起材料性能变化,会在结构内部产生热应力、热变形及热屈曲,从而改变结构的有效刚度,影响其动力学特性。针对铝合金壁板结构开展热屈曲后模态特性的试验,采用石英灯辐射加热方法模拟气动加热,利用热应变与温度的关系,获得了壁板结构热屈曲临近温度,进而选取屈曲前、屈曲后一系列温度状态开展热模态试验。试验结果表明,模态频率随加热温度的增加先降低,在临近屈曲温度附近达到最低值,热屈曲后随着温度增加又逐渐增加。由于不同阶模态对热载荷的敏感程度不一样,第3阶和第4阶模态在加热过程中发生交换,而模态阻尼随着加热温度的增加呈现增加的趋势。     

Vibration and buckling of cross-ply laminated composite circular cylindrical shells according to a global higher-order theory

Natural frequencies and buckling stresses of cross-ply laminated composite circular cylindrical shells are analyzed by taking into account the effects of higher-order deformations such as transverse shear and normal deformations, and rotatory inertia. By using the method of power series expansion of displacement components, a set of fundamental dynamic equations of a two-dimensional higher-order theory for laminated composite circular cylindrical shells made of elastic and orthotropic materials is derived through Hamilton's principle. Several sets of truncated approximate higher-order theories are applied to solve the vibration and buckling problems of laminated composite circular cylindrical shells subjected to axial stresses. The total number of unknowns does not depend on the number of layers in any multilayered shells. In order to assure the accuracy of the present theory, convergence properties of the first natural frequency and corresponding buckling stress for the fundamental mode r=s=1 are examined in detail. The internal and external works are calculated and compared to prove the numerical accuracy of solutions. Modal transverse shear and normal stresses can be calculated by integrating the three-dimensional equations of equilibrium in the thickness direction, and satisfying the continuity conditions at the interface between layers and stress boundary conditions at the external surfaces. It is noticed that the present global higher-order approximate theories can predict accurately the natural frequencies and buckling stresses of simply supported laminated composite circular cylindrical shells within small number of unknowns.