Description :

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 for 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 conservative system can be described with 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 function 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.

Biography:

Professor Zhong was elected as the member of Chinese Academy of Sciences in 1993. He is currently a professor of Engineering Mechanics and the Director of Research Institute of Engineering Mechanics, Dalian University of Technology, Dalian, China. Professor Zhong has been working over a wide range of engineering mechanics including general purpose structural analysis programs based on the multi-level sub-structural analysis technique; Group theory application in structural analysis; Parametric variational principle, parametric quadratic programming for elasto-plastic non-associative flow and Contact problems, etc.; dynamic programming method for the unfavorable loading of highway traffic based on influence function of bridge structure; analogy between computational structural mechanics and optimal control theory, etc.; precise integration method for ODEs; wave propagation along repetitive structure, wave guide problems; electomagnetic wave guide analysis via symplectic mathematics; gyroscopic system vibration; eigenvalue problems of Hamiltonian and symplectic matrices, the symplectic eigenvalue problems; Symplectic solution system for classical elasticity; duality system in applied mechanics and optimal control; symplectic mathematical method in applied mechanics.