HAMILTONIAN SYSTEM AND SIMPLETIC GEOMETRY IN MECHANICS OF COMPOSITE MATERIALS (Ⅰ)——FUNDAMENTAL THEORY  

作　　者：钟万勰 欧阳华江 

机构地区：[1]Dalian University of Technology, Dalian,Dalian University of Technology, Dalian

出　　处：《Applied Mathematics and Mechanics(English Edition)》1992年第11期1017-1022,共6页应用数学和力学（英文版）

基　　金：This project is supported by National Natural Science Foundation of China for Post-Doctorate Research

摘　　要：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.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.

关 键 词：Hamiltonian system simpletic geometry analytical solution semi-analytical solution 

分 类 号：O3，O1[理学—力学]