An improved time domain meshfree method for analysis of quasi-static and dynamic inhomogeneous viscoelastic problems

Abstract

An improved meshfree radial point interpolation method (RPIM) is formulated for quasi-static and dynamic analyses of 2D inhomogeneous viscoelastic solids. The presented improved RPIM is formulated in time domain, in which, there is no need for the viscoelastic material to obey the correspondence principle and therefore, all kinds of inhomogeneous viscoelastic materials can be analyzed by the method. The domain integrals, appeared in the proposed RPIM, are computed by the Cartesian transformation method (CTM), which is a truly meshfree integration technique. In the implementation of the CTM no background mesh is required and the domain integrals are computed accurately and efficiently. The accuracy of the method is studied by presenting several numerical examples. The results are compared with available analytic or numerical solutions and very good agreement is observed in all cases.