Hamiltonian system and simpletic geometry in mechanics of composite materials (I) — Fundamental theory
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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 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 wordsHamiltonian system simpletic geometry analytical solution semi-analytical solution
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