A meshless local natural neighbour interpolation method to modeling of functionally graded viscoelastic materials

A meshless local natural neighbour interpolation (MLNNI) method applied to solve two-dimensional quasi-static and transient dynamic problems in continuously heterogeneous and linear viscoelastic media is presented and discussed in this article. The analysis is performed using the correspondence principle and the Laplace transform technique. In the present method, nodal points are spread on the analyzed domain and each node is surrounded by a polygonal sub-domain. The trial functions are constructed by the natural neighbour interpolation and the three-node triangular FEM shape functions are taken as test functions. The natural neighbour interpolants are strictly linear between adjacent nodes on the boundary of the convex hull. As a result, the essential boundary conditions can be imposed by directly substituting the corresponding terms in the system of equations. To get the viscoelastic solution in the time domain, the inverse Laplace transform algorithm of Stehfest is employed. Some numerical examples are given at the end to demonstrate the availability and accuracy of the present method.