A meshless local natural neighbour interpolation method for analysis of two-dimensional piezoelectric structures

A novel meshless method applied to solve two-dimensional piezoelectric structures is presented and discussed in this paper. It is called meshless local natural neighbour interpolation (MLNNI) method, which is derived from the generalized meshless local Petrov–Galerkin (MLPG) method as a special case. In the present method, nodal points are spread on the analysed domain and each node is surrounded by a polygonal sub-domain, which can be conveniently constructed with Delaunay tessellations. The spatial variation of the displacements and the electric potential are interpolated by the natural neighbour interpolation. As the shape functions so constructed possess the delta function property, the essential boundary conditions can be imposed by directly substituting the corresponding terms in the system of equations. Furthermore, the usage of three-node triangular FEM shape functions as test functions reduces the order of integrands involved in domain integrals. Numerical examples are presented at the end to demonstrate the applicability and accuracy of the present approach in analysing two-dimensional piezoelectric structures.