均布压力下正交异性圆锥扁壳的后屈曲分析

基于Ｋａｒｍａｎ型大挠度方程,用修正迭代法分析了均布压力下夹支正交异性圆锥扁壳的几何非线性的后屈曲行为,给出二阶近似的荷载挠度特征关系式及临界荷载,给出了三种正交异性参数对应数值结果,分析了正交异性参数对壳体变形和屈曲荷载的影响。     

弹性扁壳的广义变分原理及扁壳理论的某些问题

本文导出了一个以应力函数及挠度为变量函数的弹性扁壳的广义变分原理。在这个变分原理中,扁壳全部基本方程都是Euler方程,全部边界条件都是自然边界条件。 应用这个变分原理,我們討論了以下問題: 1.用应力函数及挠度表示几何边界条件的問題; 2.多連通扁壳的位移单位条件問題。 文内还导出了大挠度情形的广义变分原理。     

正弦波纹扁球壳的非线性强迫振动

波纹壳是传感器弹性元件的一类重要形式,也是精密仪器仪表弹性元件中的一类重要形式。由于波纹壳形状复杂、参数众多、厚度薄,对其进行非线性分析非常重要同时也是十分困难的。本文考虑一种在传感器弹性元件中有重要应用价值的正弦波纹浅球壳体,将这种壳体视为结构上的圆柱正交异性扁球壳,根据Andryewa的思想,分别得到了正弦波纹壳径向、环向在拉伸、弯曲下的等价的四个各向异性参数;建立了正弦波纹扁球壳的非线性强迫振动微分方程;得到了正弦波纹扁球壳非线性强迫振动的共振周期解及幅频特性曲线。     

均匀内压作用下双模量简支扁壳的非线性弯曲

双模量扁壳在均匀内压作用下,会形成拉压弹性模量不同的各向同性拉伸区和压缩区,把双模量扁壳看成两种材料组成的层合扁壳,采用板壳理论求得了双模量扁壳在均匀内压作用下中性面位置;推导出了双模量扁壳挠度与均匀内压的关系式,并把该方法的计算结果与有限元方法计算结果进行了比较,验证了该计算方法的可靠性。算例分析表明,当拉压弹性模量相差较大时,将双模量材料当作单模量材料计算,其误差绝对值最小值为24.4%,误差绝对值最大值为35.38%。因此,均匀内压作用下双模量简支扁壳的大挠度弯曲计算必须考虑双模量材料拉压弹性模量不同的特性。     

环筋园柱壳静水压力作用下整体弹性屈曲

一、前言环筋园柱壳在静水压力作用下弹性整体失稳问题已有较多人进行了研究。一般以材料的正交各向异性壳来处理,并采用扁壳假定,例如Bodner把环筋壳折合为单层正交异性壳,即不能考虑环筋的偏心影响,同时也不知道扁壳近似将带来多大的误差。Singer等      

考虑横向剪切变形矩形底中厚扁壳的屈曲研究

基于考虑横向剪切变形直角坐标下矩形中厚扁壳的几何方程、本构关系、平衡方程,建立了关于三个中面位移和两个中面转角为独立变量的矩形中厚扁壳小挠度屈曲的基本微分方程。该方程可退化为矩形中厚板屈曲的基本微分方程,从而说明本文推导过程的正确性及一般性。文中矩形中厚扁壳小挠度屈曲的基本微分方程是一组耦合的变系数二阶偏微分方程,对常曲率扁壳使用双重三角级数并将其作为广义坐标对该方程组进行解耦,进一步建立中厚扁壳小挠度屈曲的特征方程,并得到了简支矩形中厚壳屈曲的临界荷载表达式,最后获得了其屈曲的临界荷载曲线及其相应的临界荷载值。该临界荷载曲线及其相应的临界荷载值可以退化为矩形中厚板的临界荷载曲线及临界荷载值。结果表明：本文提出的算法求解过程简便,矩形中厚扁壳临界荷载收敛较快。     

预制带肋底板混凝土双向叠合板等效各向同性板的弹性计算方法

结合预制带肋底板混凝土双向叠合板(简称双向叠合板)的正交构造异性特征,分析了当前实际工程设计中存在的问题。直接从双向叠合板的挠曲面基本微分方程出发,依据正交各向异性板理论,推导了双向叠合板与各向同性板挠度和内力的等效关系。由此等效关系,引入等效跨度比,修正双向叠合板的预制底板板肋平行、垂直方向边长,将其等效为相应的各向同性板来计算。最后,列举一边固支三边简支边界条件的双向叠合板算例,利用已有的各向同性板弹性计算系数表,直接按照等效跨度比进行插值计算,将所得结果同按照挠度和弯矩计算式计算结果进行比较。结果表明:计算结果吻合良好,各项弹性计算系数均满足双向叠合板与各向同性板挠度和内力的等效关系,说明本文提出的弹性计算方法是正确的。     

正交异性圆柱壳受局部外压的临界力

以往计算正交异性圆柱壳的临界力,多从微分方程组出发,编写较长的计算程序,化费很多机时才能得到结果。本文应用Cheng提出的准确四阶控制方程,把问题归化为解无限行列式的特征值。对于全部受外压,周向波数较多的壳导出了一个临界力公式。1.部分长度承受均布外压壳的临界力(图1) 文献[2]建立了正交异性圆柱壳准确的控制方程(本文使用的符号与[2]相同)     

复合材料层合开顶扁球壳的非线性动态屈曲

研究了复合材料层合开顶扁球壳的非线性动态屈曲问题。建立了对称层合圆柱正交异性开顶扁球壳考虑横向剪切的非线性振动微分方程,根据突变理论建立了该壳体动态屈曲的突变模型,得到了动态屈曲的临界方程。     

均布压力作用下圆底扁锥壳的大挠度问题

1.引言圆底扁锥壳是工程中的常见壳型结构,与扁球壳相比,对圆底扁锥壳的大挠度理论和实验研究都不多,仅有少数文献进行过研究,文献[1]和[2]用的是伽辽金方法,文献[3]用摄动法,文献[4]用修正迭代法,它们分别在壳体几何参数λ不大的范围内确定了失稳临界载荷。由于这些方法本身存在的困难,所得解答当λ稍大时就不准确了。本文利用牛顿-样条函数方法对均布压力作用下圆底扁锥壳(图1)的非线性弯曲和稳定性进行研究,获得一些有意义的结果。2.基本方程及其求解考虑均布压力作用下圆底扁锥壳的轴对称非线性方程:     

The R-function method used to solve nonlinear bending problems for orthotropic shallow shells on an elastic foundation

The paper proposes a method to solve geometrically nonlinear bending problems for thin orthotropic shallow shells and plates interacting with a Winkler–Pasternak foundation under transverse loading. This method is based on Ritz’s variational method and the R-function method. The developed algorithm and software are used to solve a number of test problems and to study complex-shaped shells. The effect of the shape of shells, the boundary conditions, the stiffness of the foundation, and the load distribution on the behavior of isotropic and orthotropic shells undergoing geometrically nonlinear bending is studied     

AN ANALYTICAL SOLUTION TO LARGE DEFLECTION EQUATIONS OF SIMPLY－SUPPORTED RECTANGULAR HYPERBOLOIDAL SHALLOW SHELLS OF ORTHOTROPIC COMPOSITES

ＡＮＡＮＡＬＹＴＩＣＡＬＳＯＬＵＴＩＯＮＴＯＬＡＲＧＥＤＥＦＬＥＣＴＩＯＮＥＱＵＡＴＩＯＮＳＯＦＳＩＭＰＬＹ－ＳＵＰＰＯＲＴＥＤＲＥＣＴＡＮＧＵＬＡＲＨＹＰＥＲＢＯＬＯＩＤＡＬＳＨＡＬＬＯＷＳＨＥＬＬＳＯＦＯＲＴＨＯＴＲＯＰＩＣＣＯＭＰＯＳＩＴＥＳＤ...     

NONLINEAR THEORY OF MULTILAYER SANDWICH SHELLS AND ITS APPLICATION (Ⅱ)──FUNDAMENTAL EQUATIONS FOR ORTHOTROPIC SHALLOW SHELLS

This paper applied the simplified theory for multilayer sandwich shells undergoing moderate/small rotations in Ref. [1] to shallow shells. The equilibrium equations and boundary conditions of large deflection of orthotropic and the special case, isotropic shells, are presented.     

Thermoelastic bending of locally heated orthotropic shells

The thermoelastic bending of locally heated orthotropic shells is studied using the classical theory of thermoelasticity of thin shallow orthotropic shells and the method of fundamental solutions. Linear distribution of temperature over thickness and the Newton’s law of cooling are assumed. Numerical analysis is carried out for orthotropic shells of arbitrary Gaussian curvature made of a strongly anisotropic material. The behavior of thermal forces and moments near the zone of local heating is studied for two areas of thermal effect: along a coordinate axis and along a circle of unit radius. Generalized conclusions are drawn __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 3, pp. 80–85, March 2007.     

Local Symmetry Group in the General Theory of Elastic Shells

We establish the local symmetry group of the dynamically and kinematically exact theory of elastic shells. The group consists of an ordered triple of tensors which make the shell strain energy density invariant under change of the reference placement. Definitions of the fluid shell, the solid shell, and the membrane shell are introduced in terms of members of the symmetry group. Within solid shells we discuss in more detail the isotropic, hemitropic, and orthotropic shells and corresponding invariant properties of the strain energy density. For the physically linear shells, when the density becomes a quadratic function of the shell strain and bending tensors, reduced representations of the density are established for orthotropic, cubic-symmetric, and isotropic shells. The reduced representations contain much less independent material constants to be found from experiments.     

Local boundary integral equations for orthotropic shallow shells

A meshless local Petrov–Galerkin (MLPG) formulation is presented for bending problems of shear deformable shallow shells with orthotropic material properties. Shear deformation of shells described by the Reissner theory is considered. Analyses of shells under static and dynamic loads are given here. For transient elastodynamic case the Laplace-transform is used to eliminate the time dependence of the field variables. A weak formulation with a unit test function transforms the set of governing equations into local integral equations on local subdomains in the plane domain of the shell. Nodal points are randomly spread in that domain and each node is surrounded by a circular subdomain to which local integral equations are applied. The meshless approximation based on the moving least-squares (MLS) method is employed for the implementation. Unknown Laplace-transformed quantities are computed from the local boundary integral equations. The time-dependent values are obtained by the Stehfest’s inversion technique.     

Nonlinear Bending Theory of Diagonal Square Pyramid Reticulated Shallow Shells

ＩｎｔｒｏｄｕｃｔｉｏｎＤｏｕｂｌｅ＿ｄｅｃｋｒｅｔｉｃｕｌａｔｅｄｓｈｅｌｌｓａｓａｍａｉｎｆｏｒｍｏｆｌａｒｇｅｓｐａｃｅｓｔｒｕｃｔｕｒｅｓ,ａｒｅｗｉｄｅｌｙｕｓｅｄｉｎｃｉｖｉｌｅｎｇｉｎｅｅｒｉｎｇａｎｄｍａｎｙｏｔｈｅｒｆｉｅｌｄｓ[1,2 ].Ｏｎｅｏｆｔｈｅｍｉｓｔｈｅｄｉａｇｏｎａｌｓｑｕａｒｅｐｙｒａｍｉｄｒｅｔｉｃｕｌａｔｅｄｓｈａｌｌｏｗｓｈｅｌｌ.Ｔｈｅｓｈｅｌｌｃｏｎｓｉｓｔｓｏｆｒｅｖｅｒｓｅｓｑｕａｒｅｐｙｒａｍｉｄｓｗｈｏｓｅｖｅｒｔｅｘｅｓａｒｅｌｉｎｋｅｄｂｙｌｏ…     

Free vibrations of shallow orthotropic shells with variable thickness and rectangular planform

The free vibrations of shallow doubly curved orthotropic shells with rectangular planform and varying thickness is solved using a refined formulation and the spline-approximation method. Various boundary conditions are considered. The effect of the curvature of the mid-surface on the spectrum of natural frequencies is examined. The natural frequencies and modes of orthotropic shells of constant and varying thickness are compared and analyzed     

On the non-classical mathematical models of coupled problems of thermo-elasticity for multi-layer shallow shells with initial imperfections

Mathematical modeling of evolutionary states of non-homogeneous multi-layer shallow shells with orthotropic initial imperfections belongs to one of the most important and necessary steps while constructing numerous technical devices, as well as aviation and ship structural members. In first part of the paper fundamental hypotheses are formulated which allow us to derive Hamilton–Ostrogradsky equations. The latter yield equations governing shell behavior within the applied hypotheses and modified Pelekh–Sheremetev conditions. The aim of second part of the paper is to formulate fundamental hypotheses in order to construct coupled boundary problems of thermo-elasticity which are used in non-classical mathematical models for multi-layer shallow shells with initial imperfections. In addition, a coupled problem for multi-layer shell taking into account a 3D heat transfer equation is formulated. Third part of the paper introduces necessary phase spaces for the second boundary value problem for evolutionary equations, defining the coupled problem of thermo-elasticity for a simply supported shallow shell. The theorem regarding uniqueness of the mentioned boundary value problem is proved. It is also proved that the approximate solution regarding the second boundary value problem defining condition for the thermo-mechanical evolution for rectangular shallow homogeneous and isotropic shells can be found using the Bubnov–Galerkin method.     

Stressed state of a composite cylindrical shell with an elliptical hole

The results of investigations of the stress-strained state (SSS) of isotropic cylindrical shells with an elliptical hole are represented in monograph [4]. The modified method of expansion in terms of minor parameter [3] is suggested for calculation of orthotropic shells. The method does not consider, however, lateral shear strains introducing a significant contribution in SSS of composite shells. The procedure for solving problems of SSS calculation near curvilinear holes in shells of arbitrary shape with variable geometrical and physical characteristics is suggested in [1] on the basis of variational-difference method (VDM). Here the relations of the linear theory of anisotropic inhomogeneous shells and the hypothesis of a straight line are taken as the initial ones for all the packet of laminated composite shell as a whole. In the present work we present the numerical results obtained according to the procedure given in [1] for an orthotropic cylindrical shell with an elliptical hole loaded by the axial force and complaint for the lateral shear.S. P. Timoshenko Institute of Mechanics, Ukrainian Academy of Sciences, Kiev. Translated from Prikladnaya Mekhanika, Vol. 29, No. 11, pp. 57–62, November, 1993.