RBF-PS For The Viscoelastic Contact Problem With Long Memory

The radial basis function-Pseudospectral method(RBF-PS)is applied to the quasistatic and dynamic viscoelastic contact problems with long memory involving normal compliance,damage and adhesion respectively.The main work is as follows:The chapter 2 introduces the RBF-PS method briefly.Next,it discusses respectively the quasistatic and dynamic viscoelastic contact problems with long memory involving normal compliance.Then,it constructs the RBF-PS for the quasistatic problem.Coupling RBF-PS and Newmark method,it presents the algorithm for the dynamic problem.Finally,numerical examples show the validity of this method.In chapter 3,the damage is introduced.The quasistatic and dynamic viscoelastic contact problems with long memory involving normal compliance and damage are described respectively.Due to the damage,the problems are transformed into two coupled equations of displacement and damage,so a coupling algorithm of RBF-PS,Newmark method and time difference method is constructed to solve it.Numerical results verify the effectiveness of the proposed algorithm,show that the method has the advantage of high accuracy and easily programming.In chapter 4,adhesion,damage and normal compliance are added to the quasistatic and dynamic viscoelastic contact problems with long memory at the same time,and then the mathematical models are given.Next,Newmark method and time difference method are used to decouple problems into three equations about displacement,damage and adhesion respectively,and RBF-PS method is constructed to deal with this problem.Finally,numerical examples show that the RBF-PS is effective and easy to implement to deal with the viscoelastic contact problems with long memory involving normal compliance,damage and adhesion.