复合材料力学的Hamilton体系和辛几何方法(Ⅱ)--平面问题

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Hamiltonian System and Simpletic Geometry in Mechanics of Composite Materials(Ⅱ)--Plane Stress Problem

摘要: 把在本文第(Ⅰ)部分^[8]中讲述的基本原理和方法用于求解各向异性平面问题.先建立可进入Hamilton体系的广义变分原理,求出Hamilton微分算子矩阵,再求解横向本征解,可得到矩形域各向异性线性弹性平面问题的级数解和半解析解.
- 各向异性 /
- 线弹性力学 /
- Hamilton矩阵 /
- 解析解 /
- 半解析解/辛几何
Abstract: The fundamental theory presented in part(I)^[8] is used to analyze anisotropic plane stress problems.First we construct the generalized variational principle to enter Hamiltonian system and get Hamiltonian differential operator matrix;then we solve eigen problem;finally,we present the process of obtaining analytical solutions and semi-analytical solutions for anisotropic plane stress porblems on rectangular area.
- anisotropy /
- linear theory of elasticity /
- Hamiltonian matrix /
- analytical solution /
- semi-analytical solution/simpletic geometry

[1]	钟万勰,分离变量法与哈密尔顿体系,计算结构力学及其应用,8(3)(1991).
[2]	钟万勰,条形域平面弹性问题与哈密尔顿体系,大连理工大学学步良,31(4)(1991).
[3]	Arnold,V.I.,Mathematical Methods of Classical Mechanics,Springer-Verlag.New York Inc.(1978).
[4]	列赫尼茨基,c,г.,《各向异性板》胡海昌译,科学出版社,北京(1963).
[5]	徐芝伦,《弹性力学》人民教育出版社,北京(1979).
[6]	秦孟兆,辛几何及计算哈密顿力学,力学与实践,12(6)(1990).
[7]	Zhong,Wan-xie and Zhong Xiang-xiang,Computational structural mechanics,optimal control and semi-analytical method for PDE,Computer and Structures,37,6(1990).
[8]	钟万勰、欧阳华江,复合材料力学的Hamilton体系和辛几何方法(Ⅰ)——一般原理,应用数学和力学.13(11)(1992).