Analytical structural mechanics and FEM
The analytical mechanics is traditionally given in the context of dynamics. However, the analogy theory between structural mechanics is established on the basis of analytical mechanics, which implies that the methodology of analytical mechanics applies both to structural mechanics and optimal control. This paper describes analytical mechanics in terms of structural mechanics, and is given the term analytical structural mechanics. As is well- known, a by conservative system can be described by the Hamilton system theory, and its characteristic is symplectic conservation, which determines the most important characteristic of a conservative system. The FEM was initiated in structural mechanics, and the symmetry of element stiffness matrix means symplectic conservation. Based on the statement that the element strain energy is a fiinction of the two end displacements, the typical statements of analytical mechanics, i.e. both the Lagrange bracket and Poisson bracket, are derived with mathematical analysis and then the canonical equations, the symplectic duality system, and canonical transformation etc. follow.
Wan-xie Zhong
State Key Lab of Structural Analysis for Industrial Equipment, Dalian University of Technology,Dalian 116023, China
国际会议
The 5th International Conference on Nonlinear Mechanics(第五届国际非线性力学会议)
上海
英文
110-122
2007-06-11（万方平台首次上网日期，不代表论文的发表时间）