复合载荷下环形薄板的热屈曲*

基于von K×rm×n薄板大挠度方程,本文研究了经受非均匀轴对称温度场的环形薄板在多种边界条件下的热屈曲问题.采用分析与计算相结合的方法着重讨论了热屈曲的线性化问题,获得了反映环板失稳特征的稳定边界.     

薄板热力耦合的屈曲分析

基于Rayleigh-Ritz理论,采用有限元方法,推导了薄板在热力耦合载荷作用下屈曲临界载荷的表达式.假设力载荷与热载荷同时加载,采用MATLAB编译环境编写的有限元程序求解薄板结构在热力耦合载荷作用下的屈曲临界载荷.在做屈曲分析时,热载荷以温度场的形式施加到节点上.采用非均匀温度场加载,分析了力载荷分量与热载荷分量对薄板结构失稳的影响.研究结果表明,随着给定温度载荷、力载荷的增加或者降低,临界载荷随之增加或者降低,它们几乎呈线性变化.     

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。     

简支矩形复合材料薄板压缩屈曲后的极限强度

本文通过283块简支矩形玻璃钢薄板的压缩屈曲后极限强度的试验,证明了复合材料薄板在屈曲失稳后仍能继续承载,以玻璃钢为例,可以超过临界载荷的十几倍。文中对薄板的极限强度进行了大挠度和小挠度理论分析,结合复合材料的能量强度理论,最后得出有关极限强度计算公式的C参数曲线,对于45°方向的薄板与试验结果较符合,对于经纬向薄板当β<0.11时比试验结果略大。文中给出的C参数可供产品设计时参考。     

非轴对称面内边界力作用下环形板的屈曲和过屈曲

本文基于[1,2]中提出的开孔薄板大挠度的一般理论和[4]中建立的分析开孔薄板屈曲和过屈曲性态的有限单元法,讨论了在边界上受面内非轴对称法向压力作用下环形板的屈曲和过屈曲.     

矩形薄板的屈曲状态*

本文根据薄板的广义变分原理,用有限元法对单向受压矩形板的屈曲状态进行了讨论,并用延续算法获得了在不同边界条件下的屈曲状态.     

轴向均布载荷和约束对石油钻采管柱失稳长度的影响

以石油行业中的直井管柱为研究对象,建立了管柱在轴向均布载荷作用下的屈曲力学模型,概括了三种轴向均布载荷的分布特征.采用特征值屈曲有限元法,提出了分段计算管柱失稳长度的迭代流程.在正反三角形分布载荷作用下,其失稳长度小于三角形分布载荷作用下的失稳长度,前者的最大挠度靠近中和点;在梯形分布载荷作用下,给出了失稳长度随该段及其以上受压段的无量纲曲线.不同的位移约束条件也对管柱失稳长度有较大影响,工程应用中应区分不同的约束条件,方可得出实际的失稳长度.     

高阶剪切变形板理论Karman型方程及在热后屈曲分析中的应用

本文基于Ｒｅｄｄｙ高阶剪切变形板理论导出Ｋａｒｍａｎ型非线性大挠度方程并用于层合板热后屈曲分析，分析中计及板初始几何缺陷和热效应。给出了四边简支，对称正交铺设层合板在均匀或非均匀抛物型热分布作用下的后屈曲分析。采用摄动－Ｇａｌｅｒｋｉｎ混合法确定板的热屈曲载荷与热后屈曲平衡路径。同时讨论了横向剪切变形。采用摄动－Ｇａｌｅｒｋｉｎ混合法确定板的热屈曲载荷与热后屈曲平衡路径。同时讨论了横向剪切变形，板     

高阶剪切变形板理论K■rm■n型方程及在热后屈曲分析中的应用

本文基于Reddy高阶剪切变形板理论导出Karman型非线性大挠度方程并用于层合板热后屈曲分析．分析中计及板初始几何缺陷和热效应．给出了四边简支．对称正交铺设层合板在均匀或非均匀抛物型热分布作用下的后屈曲分析．采用摄动-Galerkin混合法确定板的热屈曲载荷与热后屈曲平衡路径．同时讨论了横向剪切变形，板长宽比，铺层数以及初始几何缺陷等各种参数变化的影响．     

环形和圆形薄板屈曲后性态的非线性分析*

本文应用改进的多重尺度法,研究环形和圆形薄板屈曲后的性态.求出其渐近解和极限荷载以及指出薄板屈曲后其皱纹和弯曲刚度间的关系.     

Buckling analysis of a ring under the action of internal pressure in a cylindrical shell

Buckling analysis of a thin cylindrical shell stiffened by rings with T-shaped cross section under the action of uniform internal pressure in the shell is performed. An annular plate stiffened over the outer edge by a circular beam is used as the ring model. The classical ring model, which is a beam with a T-shaped cross section, is inappropriate in this problem, since in the case of the loss of stability, buckling deformations are localized on the ring surface. The beam model does not allow one to find the critical pressure that corresponds to such a loss of stability. In the first approximation, the problem of the loss of stability of the annular plate connected with the shell is reduced to solving the boundary value problem for finding eigenvalues of the annular plate bending equation. Approximate formulas for determining critical pressure are obtained under the assumption that the plate width is much smaller than its inner radius. The results found using the Rayleigh method and the shooting method differ slightly from each other. It has been demonstrated that the critical pressure for rings with rectangular cross section is higher than that for rings with a T-shaped cross section.     

The extended Melnikov method for non-autonomous nonlinear dynamical systems and application to multi-pulse chaotic dynamics of a buckled thin plate

The extended Melnikov method, which was used to solve autonomous perturbed Hamiltonian systems, is improved to deal with high-dimensional non-autonomous nonlinear dynamical systems. The multi-pulse Shilnikov type chaotic dynamics of a parametrically and externally excited, simply supported rectangular thin plate is studied by using the extended Melnikov method. A two-degree-of-freedom non-autonomous nonlinear system of the rectangular thin plate is derived by the von Karman type equation and the Galerkin approach. The case of buckling is considered for the rectangular thin plate. The extended Melnikov method is directly applied to the non-autonomous governing equations of motion to investigate multi-pulse Shilnikov type chaotic motions of the buckled rectangular thin plate for the first time. The results obtained here indicate that multi-pulse chaotic motions can occur in the parametrically and externally excited, simply supported buckled rectangular thin plate.     

Thermal buckling analysis of point-supported laminated composite plates in unilateral contact

This paper deals with the thermal buckling analysis of point-supported thin laminated composite plates. The analysis is performed for rhombic and rectangular plates and two cases of bilateral and unilateral buckling. In the unilateral buckling, it is assumed that the plate is in contact with a rigid surface and lateral deflection is forced to be only in one direction. The element-free Galerkin (EFG) method is employed to discretize equilibrium equations. Point supports are modeled in the form of distinct restrained circular surfaces through developing a numerical procedure based on the Lagrange multiplier technique. The unilateral behavior of the plate is incorporated in the analysis by using the penalty method and the Heaviside contact function. The final system of nonlinear algebraic equations is solved iteratively. Two types of point support arrangements are considered and the effect of different parameters such as number of point supports, plate aspect ratio and lamination scheme on the buckling coefficient of composite plates is investigated.     

Bifurcation problems for discrete variational inequalities

The buckling of a beam or a plate which is subject to obstacles is typical for the variational inequalities that are considered here. Birfurcation is known to occur from the first eigenvalue of the linearized problem. For a discretization the bifurcation point and the bifurcating branches may be obtained by solving a constrained optimization problem. An algorithm is proposed and its convergence is proved. The buckling of a clamped beam subject to point obstacles is considered in the continuous case and some numerical results for this problem are presented.     

Buckling of an annular plate under tensile point loading

In this paper, we address the stability of an elastic thin annular plate stretched by two point loads that are located on the outer boundary. A roller support is considered on the outer boundary while the inner edge of the plate is free. Muskhelishvili’s theory of complex potentials has been applied to obtain a solution of the plane problem in the form of a power series. The buckling problem has been solved using the Rayleigh–Ritz method, based on the energy criterion. The critical Euler force and the respective buckling mode have been computed. Dependence between the critical force and the relative orifice size has been illustrated. Analysis of the results has shown that a symmetric buckling mode takes place for a sufficiently large hole, with the greatest deflection observed around the hole along the force line. However, an antisymmetric buckling mode occurs for relatively small holes, with the greatest deflection being along a line that is orthogonal to the force line.     

Nonlinear bending and buckling for strain gradient elastic beams

Nonlinear bending of strain gradient elastic thin beams is studied adopting Bernoulli–Euler principle. Simple nonlinear strain gradient elastic theory with surface energy is employed. In fact linear constitutive relations for strain gradient elastic theory with nonlinear strains are adopted. The governing beam equations with its boundary conditions are derived through a variational method. New terms are considered, already introduced for linear cases, indicating the importance of the cross-section area, in addition to moment of inertia in bending of thin beams. Those terms strongly increase the stiffness of the thin beam. The non-linear theory is applied to buckling problems of thin beams, especially in the study of the postbuckling behaviour.     

On the mixed finite element approximation for the buckling of plates

We consider the mixed finite element method for the buckling problem of the thin plate by using piecewise linear polynomials. We give error estimates for the approximate eigenvalues and the eigenfunctions.     

Elastic stability of all edges simply supported,stepped and stiffened rectangular plate under Biaxial loading

In this paper using finite difference method the lower bound buckling load for simply supported (a) stepped and stiffened rectangular thin plate (b) linear and non-linear variation of thickness (c) uniformly distributed compressive forces in both directions (d) uniformly distributed compressive force in y direction and non-uniform distribution of compressive force in x-direction is discussed. The thin plate is divided into 900 rectangular meshes. The partial derivatives are approximated using central difference formula. Eight hundred and forty one equations are formed and using the program developed and the least eigenvalue is obtained. The buckling coefficients are calculated for different types of stepped and non prismatic plates and the results are presented in tables and graphs for ready use by designers. Buckling factors for some cases are presented in the form of three separate tables and compared with the values obtained by Xiang, Wei and Wang. The results are in close agreement.     

Size dependent buckling analysis of functionally graded micro beams based on modified couple stress theory

Buckling analysis of functionally graded micro beams based on modified couple stress theory is presented. Three different beam theories, i.e. classical, first and third order shear deformation beam theories, are considered to study the effect of shear deformations. To present a profound insight on the effect of boundary conditions, beams with hinged-hinged, clamped–clamped and clamped–hinged ends are studied. Governing equations and boundary conditions are derived using principle of minimum potential energy. Afterwards, generalized differential quadrature (GDQ) method is applied to solve the obtained differential equations. Some numerical results are presented to study the effects of material length scale parameter, beam thickness, Poisson ratio and power index of material distribution on size dependent buckling load. It is observed that buckling loads predicted by modified couple stress theory deviates significantly from classical ones, especially for thin beams. It is shown that size dependency of FG micro beams differs from isotropic homogeneous micro beams as it is a function of power index of material distribution. In addition, the general trend of buckling load with respect to Poisson ratio predicted by the present model differs from classical one.