Barycentric Interpolation Collocation Method For Two-membrances Problem And Viscoelastic Contact Problem With Long Memory

We introduces the barycentric interpolation collocation method(BRICM)in details,which is applied to two-membrances problem and quasistatic and dynamic viscoelastic contact problems with long memory involving normal compliance,damage and adhesion respectively.The main work is as follows:In chapter2,it presents two-membrances problem and its equivalent equation briefly.Then gives three kinds of barycentric interpolation shape functions and discusses the effect of the kinds of nodes,number of nodes and parameters by numerical examples.Finally,we apply this method into two-membrances problem,and illustrates the effective of the method by numerical examples in different dimensions and areas.In chapter 3,it gives mathematical description forms and detailed algorithm of BRICM for quasistatic viscoelastic contact problems with long memory involving normal compliance,damage and adhesion.Due to the damage and adhesion,the problems are transformed into coupled equations of displacement,damage and adhesion,so a decoupling algorithm of BRICM and time difference method is constructed to solve it.Numerical results show that the method has the advantage of high accuracy and easily programming.In chapter 4,it presents the mathematical model and algorithm framework of dynamic viscoelastic contact problems with long memory involving normal compliance,damage and adhesion.Similar to the case of quasistatic,the first step is decoupling,Newmark method and time difference method are used to decouple problems into three equations about displacement,damage and adhesion respectively,and BRICM is constructed to solve these problems.Finally,comparing with RBF-PS,numerical examples shows that BRICM is effective and easy to implement...