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

Applied Mathematics and Mechanics (English Edition) ›› 1992, Vol. 13 ›› Issue (11): 1017-1022.

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

钟万勰, 欧阳华江

Dalian University of Technology, Dalian

收稿日期:1991-07-01 出版日期:1992-11-18 发布日期:1992-11-18
基金资助:
This project is supported by National Natural Science Foundation of China for Post-Doctorate Research

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

Zhong Wan-xie, Ouyang Hua-jiang

Dalian University of Technology, Dalian

Received:1991-07-01 Online:1992-11-18 Published:1992-11-18
Supported by:
This project is supported by National Natural Science Foundation of China for Post-Doctorate Research

摘要/Abstract

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.

关键词: Hamiltonian system, simpletic geometry, analytical solution, semi-analytical solution

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

钟万勰;欧阳华江. HAMILTONIAN SYSTEM AND SIMPLETIC GEOMETRY IN MECHANICS OF COMPOSITE MATERIALS(Ⅰ)——FUNDAMENTAL THEORY[J]. Applied Mathematics and Mechanics (English Edition), 1992, 13(11): 1017-1022.

Zhong Wan-xie;Ouyang Hua-jiang. HAMILTONIAN SYSTEM AND SIMPLETIC GEOMETRY IN MECHANICS OF COMPOSITE MATERIALS(Ⅰ)——FUNDAMENTAL THEORY[J]. Applied Mathematics and Mechanics (English Edition), 1992, 13(11): 1017-1022.

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

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

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