RBF-PS Method For The Elastic-plastic Torsion And Viscoelastic Dynamic Frictionless Contact Problem

The elasto-plastic torsion problem and viscoelastic dynamic frictionless contactproblem appear widely in the fields such as physics, mechanics, engineering, etc. Thestudy of such problems are ofen transformed into variational inequality. In this paper, wewill apply the radial basis function-Pseudospectral method(RBF-PS) and the coupling ofthe finite difference method and the PBF-PS method to the static and dynamicelastic-plastic torsion problems respectively. We also apply the RBF-PS method to theviscoelastic dynamic frictionless contact problem. The main work is as follows：1． The basic principle of Spectral and Pseudospectral Methods is introduced. And thenwe present the RBF-PS method and its application in the time-depedent differentialequations. Next, we give the choice method of the optimal parameter in the RBF-PSmethod and the processing techniques for the boundary conditions when the problemis defined on the rectangular area. Finally, numerical examples prove the validity ofthis method and reveal the effect of the choices of basis functions in Spectral andPseudospectral Methods and radial basis function in the RBF-PS method.2． First, we give the basic model of the static elastic-plastic problems and its ellipticvariational inequality. We construct the coupling algorithm of Uzawa method and theRBF-PS method. Next, we introduce the dynamic elastic-plastic problem and itsparabolic variational inequality. Using time difference method, the original problemreduces to a elliptic variational inequality. We present the coupling algorithm ofUzawa method and the RBF-PS method under the time iteration. Numerical resultsverify the validity of the proposed method, show that the method has the advantageof high accuracy, short computing time, easily programming, etc., it is a puremeshless method. 3． We apply the RBF-PS method to the viscoelastic dynamic frictionless contactproblem. Applying the time difference and spatical RBF-PS method, we construct thedecoupling RBF-PS method for this dynamic model. Numerical examples arepresented. Comparing the numerical results with the FEM method and the DQMmethod, it show the good efficiency and precision of our method.