复合材料层合剪切圆柱曲板在侧压作用下的后屈曲

基于Reddy高阶剪切变形理论的Kármám-Donnell型非线性壳体方程,给出复合材料层合剪切圆柱曲板在侧压作用下的后屈曲分析。将壳体屈曲的边界层理论推广到复合材料层合剪切圆柱曲板受侧压作用的情况。相应的奇异摄动法,用于确定圆柱曲板的屈曲荷载和后屈曲平衡路径。分析中同时考虑非线性前屈曲变形和初始几何缺陷的影响。数值算例给出完善和非完善,中等厚度正交铺设层合圆柱曲板的后屈曲荷载-挠度曲线。讨论了横向剪切变形,曲板几何参数,铺层数,铺展方式和初始几何缺陷等各种参数变化的影响。     

湿热环境中复合材料层合圆柱薄壳屈曲和后屈曲

在宏-细观力学模型框架下,讨论湿热环境对复合材料层合圆柱薄壳在轴向压缩作用下屈曲和后屈曲行为的影响。基于细观力学模型复合材料性能与湿度和温度变化有关。壳体控制方程基于经典层合壳理论,并包括湿热效应。壳体屈曲的边界层理论被推广用于湿热环境的情况,相应的奇异摄动法用于确定层合圆柱薄壳的屈曲荷载和后屈曲平衡路径。分析中同时计及壳体非线性前屈曲变形和初始几何缺陷的影响。数值算例给出完善和非完善正交铺设层合圆柱薄壳在不同湿热环境中的后屈曲行为。讨论了温度和湿度,纤维体积比率,壳体几何参数,铺层数,铺层方式和初始几何缺陷等各种参数变化的影响。     

湿热环境中复合材料层合圆柱薄壳的屈曲和后屈曲

在宏-细观力学模型框架下,讨论湿热环境对复合材料层合圆柱薄壳在轴向压缩作用下屈曲和后屈曲行为的影响.基于细观力学模型复合材料性能与湿度和温度变化有关.壳体控制方程基于经典层合壳理论,并包括湿热效应.壳体屈曲的边界层理论被推广用于湿热环境的情况,相应的奇异摄动法用于确定层合圆柱薄壳的屈曲荷载和后屈曲平衡路径.分析中同时计及壳体非线性前屈曲变形和初始几何缺陷的影响.数值算例给出完善和非完善正交铺设层合圆柱薄壳在不同湿热环境中的后屈曲行为.讨论了温度和湿度,纤维体积比率,壳体几何参数,铺层数,铺层方式和初始几何缺陷等各种参数变化的影响.     

Postbuckling of a shear-deformable anisotropic laminated cylindrical shell under external pressure in thermal environments

A postbuckling analysis is presented for a shear-deformable anisotropic laminated cylindrical shell of finite length subjected to external pressure in thermal environments. The material properties are expressed as linear functions of temperature. The governing equations are based on Reddy’s higher-order shear-deformation shell theory with the von Karman-Donnell-type kinematic nonlinearity. The nonlinear prebuckling deformations and initial geometric imperfections of the shell are both taken into account. The boundary-layer theory of shell buckling, which includes the effects of nonlinear prebuckling deformations, large deflections in the postbuckling region, and the initial geometric imperfections of the shell, is extended to the case of shear-deformable anisotropic laminated cylindrical shells under lateral or hydrostatic pressure in thermal environments. The singular perturbation technique is employed to determine the interactive buckling loads and postbuckling equilibrium paths. The results obtained show that the variation in temperature, layer setting, and the geometric parameters of such shells have a significant influence on their buckling load and postbuckling behavior. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 43, No. 6, pp. 789–822, November–December, 2007.     

热-压电效应对轴压混合层合圆柱曲板后屈曲的影响

基于Karman-Donnell型非线性壳体方程，给出带压电作动器混合层合圆柱曲板在机械荷载、电荷载和热荷载作用下的后屈曲分析．假定温度场为均匀分布，电场仅有沿板厚方向的分量Ez，且假定材料性能常数与温度和电场的变化无关。将壳体屈曲的边界层理论推广到混合层合圆柱曲板受复合荷载作用的情况.相应的奇异摄动法用于确定圆柱曲板的屈曲荷载和后屈曲平衡路径.分析中同时考虑非线性前屈曲变形和初始几何缺陷的影响．数值算例给出完善和非完善，含整体覆盖或内埋压电作动器正交铺设层合圆柱曲板的后屈曲平衡路径。讨论了温度变化、控制电压、铺层方式、面内边界条件和初始几何缺陷等各种参数变化的影响。     

An analytical approach for postbuckling of eccentrically or concentrically stiffened composite double curved panel on nonlinear elastic foundation

This paper presents a detailed analytical investigation on the buckling and postbuckling behavior of laminated composite double curved panels with eccentrically and/or concentrically ortho-grid stiffeners subjected to in-plane compression, lateral pressure, thermal environment, and combined loads. The panels are surrounded by three parameter elastic foundations. Different types of simple-supported boundary conditions are considered. The equilibrium and compatibility equations of panel are derived based on Kirchhoff assumptions incorporating nonlinear von-Karman relations. The stress function and Galerkin method are applied to obtain explicit expressions of the buckling load and load-deflection relations. New results are presented to show effects of the combined loads, position of stiffener, and elastic foundation. As a key finding of these results, the buckling load and the postbuckling curves of concentrically stiffened panels are higher than eccentrically stiffened panels.     

加肋圆柱壳在轴压作用下的屈曲和后屈曲

本文讨论完善和非完善的,纵向加肋和正交加肋圆柱壳在轴压作用下的屈曲和后屈曲性态.依据文[1]提供的圆柱薄壳屈曲的边界层理论及其分析方法,给出了加肋圆柱壳在轴压作用下的屈曲和后屈曲理论分析.本文同时讨论肋骨与壳板材料不同时对加肋圆柱壳屈曲和后屈曲性态的影响.     

中厚板热后屈曲分析

依据Reissner-Mindlin板理论考虑转动惯量和横向剪切变形影响,本文给出中厚板在(1)均布和非均布(线性)热荷载作用下;(2)单向压缩和均布热荷载共同作用下的后屈曲分析。采用摄动法导出完善和非完善中厚板的热屈曲载荷和热后屈曲平衡路径,并与经典薄板理论结果进行了比较。     

Thermoelastic stability analysis of laminated composite plates: An analytical approach

The paper presents Chebyshev series based analytical solutions for the postbuckling response of the moderately thick laminated composite rectangular plates with and without elastic foundations. The plate is assumed to be subjected to in-plane mechanical, thermal and thermomechanical loadings. In-plane mechanical loading consists of uniaxial, biaxial, shear loadings and their combinations. The temperature induced loading is due to either uniform temperature or a linearly varying temperature across the thickness. The mathematical formulation is based on higher order shear deformation theory (HSDT) and von-Karman nonlinear kinematics. The elastic foundation is modeled as shear deformable with cubic nonlinearity. The thermal and mechanical properties of the composites are assumed to be temperature dependent. The quadratic extrapolation technique is used for linearization and fast converging finite double Chebyshev series is used for spatial discretization of the governing nonlinear equations of equilibrium. The effects of plate parameters and foundation parameters on buckling and postbuckling response of the plate are presented.     

Postbuckling characteristics of angle-ply laminated truncated circular conical shells

The postbuckling characteristics of the angle-ply laminated composite conical shells subjected to the torsion, the external pressure, the axial compression, and the thermal loading considering uniform temperature change are studied using the semi-analytical finite element approach. The finite element formulation is based on the first-order shear deformation theory and the field consistency principle. The variations in the stiffness coefficients along the meridional direction due to the changes in the ply-angle and the ply-thickness of the filament wound conical shells are incorporated in the finite element formulation. The nonlinear governing equations are solved using the Newton–Raphson iteration procedure coupled with the displacement control method to trace the prebuckling followed by the postbuckling equilibrium path. The presence of asymmetric perturbation in the form of a small magnitude load spatially proportional to the linear buckling mode shape is considered to initiate the bifurcation of the shell deformation. The influence of semi-cone angle, ply-angle and number of circumferential waves on the prebuckling/postbuckling response of the anti-symmetric angle-ply laminated circular conical shells is investigated.     

反对称角铺设层合板的屈曲和后屈曲

本文以挠度为摄动参数,采用文[1]提供的摄动方法研究了四边简支的完善和非完善反对称角铺设层合板在面内压缩作用下的屈曲和后屈曲性态.本文讨论了面内边界条件、铺设角、铺层数以及初始几何缺陷对层合板后屈曲性态的影响.     

多层复合材料圆柱壳的非线性失稳计算

本文用能量法和有限差分法分析了多层复合材料圆柱壳在轴压、静水压力及扭转等载荷作用下的非线性屈曲和后屈曲性能。本文考虑了柱壳的初始缺陷、几何非线性、材料的物理非线性(剪切模量非线性)等因素对于临界载荷的影响。同时还讨论了横向剪切效应。计算分析结果与一些实验结果比较一致。     

Static collapse: A survey of methods and modes of behavior

The phenomenon of static collapse, henceforth called ‘buckling’, is first illustrated by the behavior of a fairly thick cylindrical shell, which under axial compression deforms at first axisymmetrically and later nonaxisymmetrically. Thus, static buckling encompasses two modes of behavior, nonlinear collapse at the maximum point in a load versus deflection curve and bifurcation buckling. Accurate prediction of critical loads corresponding to either mode in the plastic range of material behavior requires a simultaneous accounting for moderately large deflections and nonlinear, irreversible, path-dependent material. A survey is given of plastic buckling, which spans three areas: asymptotic analysis of postbifurcation behavior of perfect and imperfect simple structures, general nonlinear analysis of arbitrary structures, and nonlinear analysis for collapse at a maximum load and bifurcation buckling of shells of revolution. In the survey of general nonlinear structural analysis, some emphasis is given to strategies for solving the governing nonlinear equations incrementally. Numerous examples, generated primarily with the STAGS computer program, which was developed by Almroth and his colleagues, reveal many complex modes of buckling behavior.     

Compressive and thermal postbuckling behaviors of laminated plates with piezoelectric fiber reinforced composite actuators

This paper studied compressive postbuckling under thermal environments and thermal postbuckling due to a uniform temperature rise for a shear deformable laminated plate with piezoelectric fiber reinforced composite (PFRC) actuators based on a higher order shear deformation plate theory that includes thermo-piezoelectric effects. The material properties are assumed to be temperature-dependent and the initial geometric imperfection of the plate is considered. The compressive and thermal postbuckling behaviors of perfect, imperfect, symmetric cross-ply and antisymmetric angle-ply laminated plates with fully covered or embedded PFRC actuators are conducted under different sets of thermal and electric loading conditions. The results reveal that, the applied voltage usually has a small effect on the postbuckling load–deflection relationship of the plate with PFRC actuators in the compressive buckling case, whereas the effect of applied voltage is more pronounced for the plate with PFRC actuators, compared to the results of the same plate with monolithic piezoelectric actuators.     

中厚板的弹性屈曲和后屈曲

本文采用Reissner假定考虑横向剪切变形的影响,导出弹性矩形板大挠度方程.本文讨论考虑横向剪切变形的矩形板的弹性屈曲和后屈曲.采用文[8]提供的摄动方法,给出了完善和非完善中厚板的后屈曲平衡路径,并与经典薄板理论结果进行了比较.     

Numerical analysis of diamond buckles

The “diamond” modes of collapse are studied with finite element methods. Both linear and nonlinear analyses are performed on the buckling of a cylindrical shell under axial compression. Among the postbuckling shapes of the cylindrical shell, a number of diamond modes (cost nθ; N = 0, 14, 18, 10, 24 and 28) are found to be possible. The analysis is compared to those conducted by Maewal and Nachbar, Crisfield, and Yoshida et al. Agreement is established in conceiving the deformed shape with circumferential number of 14 as the stable postbuckling mode of the cylindrical shell.

The transition from the axisymmetric mode to a diamond mode of collapse is shown to be an instantaneous process triggered in the proximity of the critical state by a small perturbation of the load increment.     

An optimization procedure for maximizing the energy absorption capability of composite shells

Composite cylindrical shells are being used more extensively for structural applications in both rotary- and fixed-wing aircraft where low weight and high strength are important design issues. This paper addresses the energy absorption capability of such shells, under axial compressive loading. A design optimization procedure is developed to improve the energy absorption by maximizing the buckling and postbuckling characteristics of the shells. The sensitivity of both geometric and material properties is investigated by studying thin-walled shells of several thicknesses, made of different types of orthotropic laminates. Constraints are imposed on the longitudinal, normal, and in-plane shear stresses of each ply by utilizing a failure criteria. Design variables include shell diameter and ply orientations. The optimization is performed using the nonlinear programming method of feasible directions. A two-point exponential approximation is also used to reduce computational effort. Results are presented for Graphite/Epoxy, Glass/Epoxy, and Kevlar/Epoxy composite cylindrical shells with symmetric ply arrangements.     

The postbuckling analysis of laminated circular plate with elliptic delamination

Based on the Von Karman plate theory, considering the effect of transverse shear deformation, and using the method of the dissociated three regions, the postbuckling governing equations for the axisymmetric laminated circular plates with elliptical delamination are derived. By using the orthogonal point collocation method, the governing equations, boundary conditions and continuity conditions are transformed into a group of nonlinear algebraically equation and the equations are solved with the alternative method. In the numerical examples, the effects of various elliptical in shape, delamination depth and different material properties on buckling and postbuckling of the laminated circular plates are discussed and the numerical results are compared with available data.     

Nonlinear buckling behavior of 3D-braided composite cylindrical shells subjected to internal pressure loads in thermal environments

The nonlinear buckling behavior of a 3D-braided composite cylindrical shell of finite length subjected to internal pressure in thermal environments is considered. According to a new micromacromechanical model, a 3D-braided composite may be treated as a cell system where the geometry of each cell strongly depends on its position in the cross section of the cylindrical shell. The material properties of the epoxy matrix are expressed as linear functions of temperature. The governing equations are based on Reddy’s higher-order shear deformation theory of shells with a von Karman–Donnell-type kinematic nonlinearity and include thermal effects. The singular perturbation technique is employed to determine the buckling pressure and the postbuckling equilibrium paths of the shell.     

Analytical solution for buckling of Mindlin plates subjected to arbitrary boundary conditions

The study investigates the buckling behavior of isotropic plates subjected to axial, biaxial and pure shear loads. The effect of transverse shear deformation is taken into account by adopting the Mindlin first order shear theory. By applying the extended Kantorovich method, an exact solution is presented without any approximation on the boundary conditions. The procedure is proposed for thin, moderately thick and thick isotropic plates. The obtained results are in good agreement with those available in literature and they demonstrate the accuracy of the proposed procedure.