考虑横向剪切效应时圆柱型正交各向异性球面扁壳在横向载荷作用下的非线性压屈

本文应用参考文献所介绍的修正迭代法探讨了横向载荷作用下,圆柱型正交各向异性圆底球面扁壳的非线性稳定同题,得出了这一同题的解析解。在求解过程中,本文放弃了经典板壳理论的Kirchhoff假定,从而考虑了横向剪应变对于弯曲变形的影响, 计算结果表明:本文的分析方法和结论是正确的;对于正交各向异性复合材料板壳而言,横向剪切效应是值得注意的。     

复合载荷作用下波纹扁壳的非线性振动

应用轴对称旋转扁壳的非线性大挠度动力学方程，研究了波纹扁壳在复合载荷作用下的非线性受迫振动问题。采用格林函数方法，将扁壳的非线性偏微分方程组化为非线性积分微分方程组。再使用展开法求出格林函数，即将格林函数展开为特征函数的级数形式，积分微分方程就成为具有退化核的形式，从而容易得到关于时间的非线性常微分方程组。针对单模态振形，得到了谐和激励作用下的幅频响应。作为算例，研究了正弦波纹扁球壳的非线性受迫振动现象。得到的解答可供波纹壳的设计参考。     

纤维增强复合材料迭层圆柱壳的几何非线性分析

本文从非线性弹性理论出发,在小应变、中等小转动的前提下,全面考虑了变形对于平衡方程的影响,导出了和传统理论不同的壳体非线性理论;并用摄动法和伽略金法分别求解了四边不可动固支正交各向异性复合材料迭层园桂壳块以及考虑横向剪切的四边可动简支园桂形扁壳的非线性弯曲问题。计算表明:变形较大时,变形对所有平衡方程的影响都是值得注意的。      

层壳考虑横向剪切效应的自由振动分析

本文采用一个分层的剪切变形理论分析层壳的自由振动。假定层壳各层横向剪切应变彼此线性相关,从而未知函数个数与一阶剪切变形理论相同,但控制微分方程的阶数为十二阶,且不含剪切修正因子。文中计算了一个短圆柱壳与两种扁壳的自由振动频率,数值结果与经典层合理论、一阶剪切变形理论及其他剪切变形理论的计算结果进行了比较。      

工程中板壳结构的一种实用计算方法

本文采用—维B3样条插值─—半离散法，建立了正交各向异性板壳结构位移和内力的统一计算式。编制的程序适用于两对这简支另两对边任意支承的正交各向异性矩形双曲扁壳、圆柱形扁壳和板；适用于集中、均布、线性荷载或其组合。算例表明该方法能有效地解决板壳的计算。     

正交各向异性扁球壳的非线性振动

本文以正交各向异性扁球壳非线性动力方程为基础,提出以简单多项式作为振型函数,采用Galefkin技术,导出了带有平方项的Duffing型方程。并分别用摄动法和数值积分法求出其解。研究了扁球壳的拱高、正交各向异性系数、边界条件和中心集中质量对系统非线性动力特性的影响,给出了扁球壳由非线性振动硬特性向软特性过渡的临界拱高H_(cr)和对应于最大软特性的最大拱高H_M。     

用加权残数法分析正交异性扁薄壳体的大变形问题

本文用加权残数法对正交异性扁薄壳体的大变形问题进行了计算分析，首先，本文推导了正交异性扁薄壳体出中曲面挠度Ｗ和应力函数Φ表示的微分方程，其次，本文用加权残数法中的离散最小二乘法编写了计算程序，对四种支承情况下的正交异性扁薄壳体在均布荷载下的变形问题进行了计算，最后，本文进行了其中一种情况的验证试验，结果与计算吻合。     

含有流动液体的复合材料管道的振动

本文讨论了含有流动液体与复合材料管道的耦合振动问题,其方法是引入位移函数,将文献[1]中关于考虑沿厚度方向的剪切变形及转动惯量的正交各向异性园柱层壳的五个微分方程式转化成一个微分方程式,在此基础上,借助于文献[2]中动水压力公式,研究了无限长度复合材料管道在平均流速为U时的振动问题,作了数值计算,得到了一些有意义的结果。     

土中浅埋层合扁球壳的非线性动力响应

本文建立了考虑横向剪切影响、纤维增强对称正交铺设层合扁球壳的非线性动力方程。应用一维波阻法分析了土与结构的相互作用,对冲击波作用下土中浅埋周边弹性支承层合扁球壳的非线性动力响应问题进行了探讨。数值计算中考虑了各种材料参数及横向剪切变形对动力响应的影响。      

轴向冲击下环向加筋复合材料圆柱壳的非线性动力响应

采用半解析的方法，建立离散加筋圆柱壳模型，基于复合材料多层扁壳大挠度的剪切变形理论，利用Hamilton原理导出环向加筋复合材料圆柱壳的非线性运动控制方程；用Galerkin方法对空间变量进行离散，将位移和载荷展开为双级数，得到有关时间的常微分方程组，最后采用R-Kutta方法数值求解．通过算例，讨论了加筋肋骨几何参数、铺层角度、辅层方式、铺层层数等因素对动力响应的影响。     

The fundamental solutions of orthotropic shallow shells

Summary A set of partial differential equations governing orthotropic shallow shells with arbitrary quadratic midsurface is reduced into an eight order partial differential equation with one function as unknown. By use of the method of plane wave decomposition this partial differential equation is transformed into an ordinary differential equation. The fundamental solutions for orthotropic shallow shells are presented in the form of a definite integral. The calculation of the fundamental solutions is discussed in detail.     

Methods of Fundamental Solutions in the Mechanics of Thin-Walled Structures

We present the foundations of the method of fundamental solutions in the mechanics of thin-walled structures and consider basic procedures of modeling that enable one to reduce mechanical problems to systems of partial differential equations with Dirac -functions on the right-hand sides. A method used for the construction of fundamental solutions is described. As examples, we consider the problem of action of point heat sources in a spherical orthotropic shell and the force problem for orthotropic shells with holes. The results of numerical calculations are presented in the form of plots.     

复合材料层合扁锥壳的冲击屈曲

研究了计及横向剪切的对称铺设正交异性复合材料层合扁锥壳在三角脉冲载荷作用下的非线性动力屈曲问题；通过在复合材料层合扁锥壳非线性稳定性的基本方程中增加横向转动惯量项并引入三角脉冲冲击力，得到了层合扁锥壳的冲击控制方程，采用Galerkin方法得到以顶点挠度表达的冲击响应方程，并用Runge—Kutta方法进行数值求解，应用B—R准则确定冲击屈曲的临界荷载；讨论了壳体几何参数、物理参数和边界条件对复合材料层合扁锥壳冲击屈曲的影响。     

Boundary value problems in thin shallow shells of arbitrary plan form

Summary This paper is concerned with a general method of analysis of boundary-value problems in thin shallow shells of arbitrary plan form. Two specific shell configurations are considered. General solutions to the governing partial differential equations are obtained in complex form, containing a sufficient number of arbitrary elements to satisfy the four boundary conditions permitted by classical thin shell theory. An algorithm for the determination of these arbitrary elements from a general form of boundary condition is presented. The method of solution is based on I.N.Vekua's theory of elliptic partial differential equations.Part 1 of the paper is devoted to shallow spherical shells. An example calculation is given for a circular planform shell, for which a closed form of solution may be obtained. The computed results show close agreement with the exact solution.Part 2 of the paper deals with shallow circular cylindrical shells, including the calculation of a shell the planform of which is a square with rounded corners. Graphs of deflection and stress function are given.     

各向异性薄扁壳的积分方程法

利用薄板和平面问题的基本解建立壳体的积分方程再采用数值方法求解,这种分析方法同其他方法相比较,具有显著的优点[1]。本文应用此法求解各向异性材料的薄扁壳,分析过程非常简单而且计算精度也很高。      

复合材料浅球壳模态分析与结构优化设计

复合材料层合壳体在航空、航天、工程结构中得到了广泛应用.结合复合材料层合浅球壳的结构特点,基于有限元分析软件ANSYS,采用层合壳单元建立有限元模型,分析了几种壳体参数对浅球壳自振频率的影响,并采用函数逼近法和梯度寻优法相结合的方法对壳体参数进行优化设计,给出了壳体参数的最优组合,使壳体的一阶自振频率为最大,改善了壳体的动态特性,为复合材料层合浅球壳的结构设计提供了有价值的理论依据,也为进一步进行结构动力学分析奠定基础.     

正交异性扁薄球壳的非线性轴对称振动

给出了一种研究圆柱正交异性扁薄球壳非线性轴对称自由振动的新的时间模态方法。首先,使用变分法导出了决定振动频率的一对代数-微分方程。然后,利用作者提出的改进的修正迭代法求得了渐进解。这使此种壳体的非线性振动的进展获得扩充研究。     

Application of the two-dimensional Hermitian finite difference method to linear shear deformation theory of plates and arbitrarily curved shells

Summary Starting from the linear, partial differential equations of thin shell theory including the effect of transverse shear deformation a matrix formulation is presented in which all kinematic and dynamic variables appear as differential quotients of first order.The transformation of the local field equations into an algebraic form by appropriate two-dimensional finite-difference operators leads to an unsymmetrical banded algebraic equation system from which all variables requested are directly evaluated.The constitutive equations take into consideration a symmetrically layered cross section consisting of tangentially isotropic and transversally orthotropic material. Because of the kinematic assumptions of a first approximation shell theory the deformation of the cross section can be seized in an integral sense only.Since the basic equations are formulated in tensor notation with the procedure presented shells of arbitrary curvature may be analyzed, of which surface is given as an analytic continuously differentiable function. The algorithm pointed out shows good convergence attributes. Its efficiency is demonstrated by two examples of which analytical solutions are known.