Barycentric Interpolation Collocation Method Of Quasistatic Frictionless Contact Problem For Viscoelastic Materials With Long Memory

The meshfree barycentric interpolation method was introduced in details in this paper.Barycentric Lagrange interpolation collocation method(BLIM)and high-order barycentric rational interpolation collocation method(HBRIM)are applied to the problem of elastic-plastic torsion and quasistatic frictionless contact problem for viscoelastic materials with long memory.The main work is as follows:In chapter 2,the approximation method of meshfree barycentric interpolation is given in details,and barycentric interpolation collocation method is applied for solving a kind of second order elliptic partial differential equations.Many numerical examples are given in this chapter.In the given examples,we discussed the effect of the number of nodes,node types and shape parameters on the solution.Finally,we constructed the barycentric interpolation method for the classic elastic-plastic torsion problem in computational mechanics and realized the numerical examples.In chapter 3,we mainly focus on Volterra integral equations and Volterra differential-integral equations.A new discrete scheme for Volterra intergral equations is given and we applied this scheme into the numerical examples.Comparing the new discrete scheme with traditional discrete scheme for Volterra intergral equations,we find this new scheme is efficent.In chapter 4,we studied the quasistatic frictionless contact problem for viscoelastic materials with long memory.Combined with the new scheme in chapter 3to treat the viscoelastic term with long memory,it presents in details barycentric interpolation collocation method of quasistatic frictionless contact problem for viscoelastic materials with long memory.Finally,we realized many numerical examples and found the effectiveness of this method.Numerical results showed that barycantric interpolation collocation method has the advantages of easy to implement and high precision.