Dynamic Elastoplastic Softening Analysis Of Parametric Variational Principle And Finite Element Method

In this thesis, the applications of the parametric variational principle and the parametric quadratic programming method in the structural dynamic elastic- plastic response analysis and the dynamic strain softening problem are studied. Firstly, according to the combination of the parametric quadratic programming method and the Newmark method, a general method for the structural dynamic elastic-plastic response analysis is presented. The parametric minimum potential energy principle and the corresponding parametric quadratic programming algorithm are thus derived. Secondly, based on the combination of the parametric quadratic method and the precise integration method, a new algorithm for structural dynamic elastic- plastic response analysis is put forward. The precise integration method, which is widely used in the linear problems, is furthermore adopted for the solution of dynamic nonlinear equations, and the algorithm for the solution of dynamic elastic-plastic problems is derived. Finally, the result mesh sensitivity problem in the dynamic strain softening analysis is discussed and the gradient dependent model is proposed to overcome this difficulty. In order to solve the dynamic localization problem, a new method that is based on the parametric variational principle and the gradient dependent model is presented. One dimension and two dimension examples are shown to demonstrate the validity and the efficiency of the theory and algorithm presented in the thesis.