Modeling of magneto-electro-elastic problems by a meshless local natural neighbor interpolation method

This paper presents a novel numerical procedure based on the meshless local natural neighbor interpolation (MLNNI) method for modeling two-dimensional magneto-electro-elastic solids. As a special case of the generalized meshless local Petrov-Galerkin (MLPG) method, the MLNNI method satisfies the weak form equations locally in polygonal sub-domains which surround each node. The natural neighbor interpolation is used to approximate the unknown fields in numerical simulations and thus only a set of scattered nodes are utilized to represent the problem domain. The usage of three-node triangular FEM shape functions as test functions results in the reduction of the order of integrands in domain integrals. As the constructed shape functions possess a point interpolation property, the essential boundary conditions can be imposed directly without the need of introducing special techniques. Numerical examples for magneto-electro-elastic problems are presented to demonstrate the solutions of the present MLNNI method with other available solutions.