Postbuckling behavior of rectangular moderately thick plates and sandwich plates

ＰＯＳＴＢＵＣＫＬＩＮＧＢＥＨＡＶｉＯＲＯＦＲＥＣＴＡＮＧＵＬＡＲＭＯＤＥＲＡＴＥＬＹＴＨＩＣＫＰＬＡＴＥＳＡＮＤＳＡＮＤＷＩＣＨＰＬＡＴＥＳＣｈｅｎｇＺｈｅｎ－ｑｉａｎｇ（成振强）ＷａｎｇＸｉｕ－ｘｉ（王秀喜）ＨｕａｎｇＭａｏ－ｇｕａｎｇ（黄茂光）...     

Elasto-plastic analysis for the buckling and postbuckling of rectangular plates under uniaxial compression

Full-range analysis for the buckling and postbuckling of rectangular plates under in-plane compression has been made by perturbation technique which takes deflection as itsperturbation parameter.In this paper the effects of initial geometric imperfection on the postbuckling behaviorof plates have been discussed.It is seen that the effect of initial imperfection on the inelasticpostbuckling of plates is sensitive.By comparison,it is found that the theoretical results ofthis paper are in good agreement with experiments.     

Buckling and postbuckling behavior of antisymmetrically angle-ply laminated composite plates

The buckling and postbuckling behaviors of perfect and imperfect antisymmetricallyangle-ply laminated composite plates under uniaxial compression have been studied byperturbation technique which takes deflection as its perturbation parameter.In this paper,the effects of in-plane boundary conditions,angles,total number oflayers and initial geometric imperfection on the postbuckling behavior of laminated plateshave been discussed.     

考虑剪切变形的各向同性,正交各向异性矩形板的屈曲和后屈曲

本文讨论考虑横向剪切变形的各向同性、正交各向异性矩形板的屈曲和后屈曲性态。应用Reissner理论,采用文[1]提供的摄动方法,给出了完善和非完善各向同性、正交各向异性矩形板的后屈曲平衡路径,并与薄板理论结果作了比较。     

非线性弹性基础上矩形板热后屈曲分析

给出非线性弹性基础上矩形板在均匀和非均匀（抛物型）热分布作用下的后屈曲分析。采用摄动——Ｇａｌｅｒｋｉｎ混合法给出完善和非完善矩形板热屈曲载荷和热后屈曲平衡路径。数值计算结果表明，非线性弹性基础上矩形板具有不稳定的热后屈曲平衡路径，且对初始几何缺陷是敏感的     

Buckling and postbuckling of moderately thick plates

This paper gives the basic differential equations for finite deflections of elastic plates according to Reissner’s approximate stress distributions. The buckling and postbuckling problems of elastic rectangular plates, including the effect of transverse shear deformation, are solved and discussed, by using perturbation method suggested in ref. [8]. The postbuckling equilibrium paths of perfect and imperfect moderately thick rectangular plates are presented and compared with the results based on thin plate theory.     

中厚板统计分析的随机边界元法

本文建立了分析含随机材料参数并具厚度不均匀性的中厚板问题的随机边界元法,基于Taylor级数展开技术,分析和到广义位移的均值和一阶偏差的积分方程,其中将材料参数的随机性和厚度的不均匀性作为等效荷载处理,从而得到广义边界位移或面力的均值和协方差,并进一步求出部点广义位移和内力的均值和协方差,最后用本文方法计算了两个数例,并对所得结果进行了分析,探讨。     

非均质中厚板的无网格LRPIM动力学分析

用局部加权残值法建立了非均质中厚板的局部径向点插值离散系统方程,采用无网格局部径向点插值法分析了非均质中厚板的自由振动和强迫振动问题。用径向基函数耦合多项式基函数来近似试函数,用四次样条函数做为加权残值法中的权函数。所构造的形函数具有Kronecker delta性质,可以很方便地施加本质边界条件。该方法不需要任何形式的网格划分,所有的积分都在规则形状的子域及其边界上进行。在计算过程中,取积分中的高斯点的材料参数来模拟问题域材料特性的变化。计算结果表明,利用该方法计算非均质中厚板的自由振动和强迫振动问题可以得到具有较高精度的解。     

钢衬壳后屈曲问题分析

本文用两种方法分析了核电站预应力混凝土安全壳中的内衬壳（钢衬壳）在温度应力作用下的后屈曲问题。认为钢衬壳模型是钢衬板模型的一种特殊缺陷形式，用Ｋｏｉｔｅｒ初始后屈曲渐近分析理论研究了钢衬壳的后屈曲问题。另外，本文从大挠度偏微分方程出发导出控制钢衬壳后屈曲的带有参数的非线性方程组，且用伪弧长法追踪其后屈曲平衡路径。文中用两种方法分析了四点铆固钢衬壳的后屈曲性态，并进行了比较。     

Buckling and postbuckling of stiffened cylindrical shells under axial compression

Buckling and postbuckling behaviors of perfect and imperfect,stringer andorthotropically stiffened cylindrical shells have been studied under axial compression.Based on the boundary layer theory for the buckling of thin elastic shells suggested in ref.[1],a theoretical analysis is presented.The effects of material properties of stiffeners andskin,which are made of different materials,on the buckling load and postbuckling behaviorof stiffened cylindrical shells have also been discussed.     

Thermal buckling analysis of truss-core sandwich plates

Truss-core sandwich plates have received much attention in virtue of the high values of strength-to-weight and stifness-to-weight as well as the great ability of impulseresistance recently. It is necessary to study the stability of sandwich panels under the influence of the thermal load. However, the sandwich plates are such complex threedimensional(3D) systems that direct analytical solutions do not exist, and the finite element method(FEM) cannot represent the relationship between structural parameters and mechanical properties well. In this paper, an equivalent homogeneous continuous plate is idealized by obtaining the efective bending and transverse shear stifness based on the characteristics of periodically distributed unit cells. The first order shear deformation theory for plates is used to derive the stability equation. The buckling temperature of a simply supported sandwich plate is given and verified by the FEM. The efect of related parameters on mechanical properties is investigated. The geometric parameters of the unit cell are optimized to attain the maximum buckling temperature. It is shown that the optimized sandwich plate can improve the resistance to thermal buckling significantly.     

Application of the modified iteration method to nonlinear postbuckling analysis of thin circular plates

In this paper,the modified iteration method is further generalized to the study ofaxisymmetrical postbuckling of thin circular plates and hereby a new approximate analyticsolution of the problem is obtained.Further utilizations of this method to postbucklinganalyses of plates of more complicated structure are expected.     

The vibration and stability analysis of moderate thick plates by the method of lines

The method of lines based on Hu Hai-chang's theory for the vibration and stability of moderate thick plates is developed. The standard nonlinear ordinary differential equation (ODE) system for natural frequencies and critical load is given by use of ODE techniques, and then any indicated eigenvalue could be obtained directly from ODE solver by employing the so-called initial eigenfunction technique instead of the mode orthogonality condition.Numerical examples show that the present method is very effective and reliable.     

各向异性弹塑性中厚度板壳的有限元分析

本文在文献［２，３］的基础上，提出了一个解各向异性弹塑性中厚度板壳问题的有限元方法。考虑材料各向异性的特点，采用了Ｈｉｌｌ推广的Ｈｕｂｅｒ－Ｍｉｓｅｓ屈服准则；借用Ｏｗｅｎ的剪切修正系数，正确计及了叠层复合材料壳体的横向剪切效应；为了避免“自锁”现象，文中采用了９节点的Ｈｅｔｅｒｏｓｉｓ二次壳单元；特别是本文利用插值外推的思想，提出了一个带预测的弧长增量控制法，显著提高了确定变形路径的计算效率。几个数值算例表明本文给出的有限元方法对于各向异性中厚度板壳的弹塑性分析有较好的精度，尤其是对具有复杂变形路径的结构计算，收敛速度提高更快。     

复合材料加筋板壳结构的后屈曲强度及破坏分析程序系统

本文介绍适用于复合材料（含各向同性材料）层合加筋板壳结构的后屈曲强度及破坏分析的程序系统（ＣＯＭＰＯＳＳ程序系统）的功能特点、原理和结构，通过一个受压剪载荷作用的加筋层合矩形板的破坏分析，并与试验结果作了比较，说明该程序系统的正确、可靠性     

求解不连续中厚板自由振动的微分容积单元法

基于区域叠加原理和微分容积法,发展了一种新型的数值方法——微分容积单元法,用以分析具有不连续几何特征的中厚板的自由振动。根据板的不连续情况将其划分为若干单元,在每个单元内用微分容积法将控制微分方程离散成为一组线性代数方程．在相邻的单元连接处应用位移连续条件和平衡条件,引入边界约束条件后得到一套关于各配点位移的齐次线性代数方程,由此可导出求解系统固有频率的特征方程。本文用子空间迭代法求解特征方程,并以开孔板、混合边界条件板和突变厚度板为例研究了方法的收敛性和计算精度。     

Thermal post-buckling analysis of imperfect laminated plates using a higher-order shear deformation theory

Thermal post-buckling analysis is presented for a simply supported, composite laminated plate subjected to uniform or non-uniform tent-like temperature loading. The initial geometrical imperfection of the plate is taken into account. The formulations are based on the Reddy's higher-order shear deformation plate theory, and include thermal effects. The analysis uses a mixed Galerkin-perturbation technique to determine thermal buckling loads and post-buckling equilibrium paths. Numerical examples cover the performances of perfect and imperfect, antisymmetrically angle-ply and symmetrically cross-ply laminated plates. The effects played by transverse shear deformation, thermal load ratio, plate aspect ratio, total number of plies, fiber orientation and initial geometrical imperfections are studied. Typical results are presented in dimensionless graphical form.     

A variational solution of coupled vibration for moderately thick floating plate seated on the sea floor with variable water depth

Based on Reissner's plate theory, a localized variational principle for the coupled vibrations of moderately thick floating plates seated on the sea floor with variable water depth is presented in this paper. It will be a powerful tool to formulate various approximate methods of moderately thick floating plates. By means of this variational principle a formula for calculating the natural frequencies of moderately thick floating plates is also obtained. A numerical example shows that high accuracy and computational time saving may be achieved in calculation.     

含基体横向损伤的黏弹性板的蠕变后屈曲分析

基于Schapery三维黏弹性损伤本构关系,引入沈为和Kachanov损伤演化方程,建立了基体横向损伤的纤维单一方向铺设黏弹性板的损伤模型;应用von Karman板理论,导出了考虑损伤效应的具初始挠度的纤维单一方向铺设黏弹性矩形板的非线性压屈平衡方程. 对未知变量在空间上采用差分法离散,时间上采用增量算法和Newton-Cotes积分法离散,控制方程被迭代求解. 算例中讨论了损伤以及有关参数对黏弹性复合材料板后屈曲行为的影响,且与已有文献的结果进行了比较. 数值结果表明：随着外载荷或者初始挠度的增大,板后屈曲趋于稳定时的挠度就愈大,损伤的影响愈明显;而随着长宽比的增大,板后屈曲趋于稳定时的挠度愈小,损伤的影响却随之增大.     

Nonlocal thermal buckling and postbuckling of functionally graded graphene nanoplatelet reinforced piezoelectric micro-plate

This paper analyzes the nonlocal thermal buckling and postbuckling behaviors of a multi-layered graphene nanoplatelet(GPL) reinforced piezoelectric micro-plate. The GPLs are supposed to disperse as a gradient pattern in the composite micro-plate along its thickness. The effective material properties are calculated by the Halpin-Tsai parallel model and mixture rule for the functionally graded GPL reinforced piezoelectric(FG-GRP) micro-plate. Governing equations for the nonlocal thermal buckling a...