复合材料力学的Hamilton体系和辛几何方法(Ⅰ)——一般原理*
Hamiltonian System and Simpletic Geometry in Mechanics of Composite Materials(Ⅰ)——Fundamental Theory
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摘要: 首次把用于动态体系的Hamilton系统引入到静力学中,建立了与原控制方程相对应的Hami-lton方程,可以对全状态向量分离变量,求出解析解和半解析解,特别适合于求解矩形域平面问题和柱形域空间问题.本文建立了一种求解偏微分方程的新方法,并对复合材料力学中的层合板的弯曲和平面应力问题的求解做了详细说明.
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关键词:
- Hamilton体系 /
- 辛几何 /
- 解析解 /
- 半解析解
Abstract: For the first time,Hamiltonian systemused in dynamics is introduced to formulate statics and Hamiltonian equation is derived corresponding to the original governing equation,which enables separation of variables to work and eigen function to be obtained for the boundary problem.Consequently,analytical and semi-analytical solutions can be got.The method is especially suitable to solve rectangular plane problem and spatial prism in elastic mechanics.The paper presents a new idea to solve partially differential equation in solid mechanics.The flexural problem and plane stress problem of laminated plate are studied in detail.-
Key words:
- Hamiltonian system /
- simpletic geometry /
- analytical solution /
- semi-analytical solution
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