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 w...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.展开更多
Fundamental theory presented in Part (I)[8] is used to analyze anisotropic plane stress problems. First we construct the generalized variational principle to enter Hamiltonian system and get Hamiltonian differential o...Fundamental theory presented in Part (I)[8] is used to analyze anisotropic plane stress problems. First we construct the generalized variational principle to enter Hamiltonian system and get Hamiltonian differential operator matrix; then we solve eigen problem; finally, we present the process of obtaining analytical solutions and semi-analytical solutions for anisotropic plane stress porblems on rectangular area.展开更多
基金This project is supported by National Natural Science Foundation of China for Post-Doctorate Research
文摘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.
文摘Fundamental theory presented in Part (I)[8] is used to analyze anisotropic plane stress problems. First we construct the generalized variational principle to enter Hamiltonian system and get Hamiltonian differential operator matrix; then we solve eigen problem; finally, we present the process of obtaining analytical solutions and semi-analytical solutions for anisotropic plane stress porblems on rectangular area.
