Interpolating Element-free Galerkin Method For Several Kinds Of Variational Inequality Problems

This paper introduces interpolating element-free Galerkin Method(IEFG)in detail,and constructs the IEFG method for the frictionless contact problems with normal compliance involving viscoelastic material with long memory and a kind of evolutionary variational inequality(EVI)with second order,numerical examples are also presented.Finally,this method is extended to a more complex problem of variational-hemivariational inequality problems with both normal compliance and unilateral constraint.The main contents in this paper are as follows:Moving least squares(MLS)and interpolating Moving least squares(IMLS)are introduced first in the second chapter.It describes the concrete procedure of IEFG method using a kind of boundary value problems.Combine with Uzawa dual algorithm,it constructs IEFG numerical framework for the second kind of variational inequality problems.Then this method is applied to the elastoplastic torsion problem in mechanics,the numerical examples show its feasibility and accuracy.The third chapter deals with the frictionless contact problems with normal compliance involving viscoelastic material with long memory.it presents the mathematical description of this problem and its equivalent variational inequality form.Using the compound trapezoid formula to deal with long memory item and IEFG,we also provide the numerical algorithm for the frictionless contact problems.Several numerical experiments including inverted concave,M-shaped and other irregular regions are concerned,the influence of each parameter on the result is still discussed.The fourth chapter introduces a kind of evolutionary variational inequality with second order,the equivalent equation form and dual IEFG fully discrete scheme are given,numerical examples are realized.We put forward the frictionless elastic contact problems with normal compliance and unilateral constraint and its formulation of variational-hemivariational inequalities in the fifth chapter.We construct the penalized IEFG numerical scheme for the variational-hemivariational inequality.Effectiveness of the method is verified by numerical examples,and the influence of penalty parameter is also discussed.