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.
For the first time, Hamiltonian system used 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 semiana-lytical 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.
出处
《应用数学和力学》
CSCD
北大核心
1992年第11期971-975,共5页
Applied Mathematics and Mechanics
基金
国家博士后科学基金资助项目
关键词
辛几何
复合材料力学
哈密顿体系
Hamiltonian system, simpletic geometry, analytical solution, semi-analytical solution
