Analysis Of Dynamic Contact Problems By Parametric Variational Principle And Finite Element Method

The structural nonlinear dynamic analysis is very important in industry area, it comprehensively exists in aeronautics, space, mechanics and architectonics. With the demand of the improvement in industry and the development of the computer science, the more effective method is needed in nonlinear dynamic analysis area. The parametric quadratic programming method based on the Parametric Variational Principle is an available and acceptable approach. Using this method, the border value problem in mechanics is transformed to the system determined by control condition, and many problems can be solve, which is unsolved by the classical Variational Principle. When consider the nonlinear problem, the classical iteration process is avoided, the accuracy and the stability of the results are more advisable.This thesis is focused on the dynamic contact problem, we apply the approach, which is combined the parametric quadratic programming method and the Newmark integration method, to analyzes the dynamic contact.Firstly, extending the application of the Parametric Variational Principle method to the structural dynamic elastic-plastic response analysis, the parametric quadratic programming based on the parametric minimum potential energy principle is delived and the gradient dependent model of the dynamic strain softening analysis is presented. According to the combination of the parametric quadratic programming method and the Newmark integration method, a general method for the structural dynamic elastic-plastic response analysis is presented, and using this method to analyze the dynamic strain softening problem and giving a numerical example.Secondly, based on the former discussion, the dynamic contact is emphasized researched. The general description of the contact problem is introduced; the constitutive law and the parametric minimum potential energy principle are presented. According to the combination of the parametric quadratic programming method and the Newmark integration method, a general approach for the structural dynamic contact problem is presented. The detailed theory and algorithms are also presented, one-dimension and two-dimension numerical examples of the dynamic contact are given to demonstrate the validity of this algorithm.