A Meshless Radial Basis Function Based on Partition of Unity Method for Piezoelectric Structures

Abstract

A meshless radial basis function based on partition of unity method (RBF-PUM) is proposed to analyse static problems of piezoelectric structures. The methods of radial basis functions (RBFs) possess some merits: the shape functions have high order continuity;h-adaptivity is simpler than mesh-based methods; the shape functions are easily implemented in high dimensional space. The partition of unity method (PUM) easily constructs local approximation. The character of local approximate space can be varied and regarded asp-adaptivity. Considering the good properties of the two methods, the RBFs are used for local approximation and the local supported weight functions are used in the partition of unity method. The system equations of the RBF-PUM are derived using the variational principle. The field variables are approximated using the RBF-PUM shape functions which inherit all the advantages of the RBF shape functions such as the delta function property. The boundary conditions can be implemented easily. Numerical examples of piezoelectric structures are investigated to illustrate the efficiency of the proposed method and the obtained results are compared with analytical solutions and available numerical solutions. The behaviors of some parameters that probably influenced numerical results are also studied in detail.