A novel local radial basis function collocation method for multi-dimensional piezoelectric problems
Journal
Journal of Intelligent Material Systems and Structures
Date Issued
2021
Author(s)
Abstract
The local radial basis function collocation method (LRBFCM), a strong-form formulation of the meshless numerical method, is proposed for solving piezoelectric medium problems. The proposed numerical algorithm is based on the local Kansa method using variable shape parameter. We introduce a novel technique for the determination of shape parameter in the LRBFCM, which leads to greater accuracy, and simplicity. The implemented algorithm is first verified with a 2D Poisson equation. Then, we employed LRBFCM in a numerical simulation for 2D and 3D piezoelectric problems involving mutual coupling of the electric field and elastodynamic equations for mechanical field. The presented meshless method is verified using corresponding results obtained from the finite element method and moving least squares meshless local Petrov–Galerkin method. In particular, the 2D piezoelectric problem is verified with an exact solution. ? The Author(s) 2021.
Subjects
Local radial basis function collocation method
multiquadrics
piezoelectric materials
shape parameter
strong-form formulation
Functions
Galerkin methods
Heat conduction
Image segmentation
Least squares approximations
Numerical methods
Piezoelectric materials
Piezoelectricity
Radial basis function networks
Local radial base function collocation method
Local radial basis function
Meshless numerical method
Multi dimensional
Multiquadrics
Piezoelectric problems
Radial basis function collocation method
Shape parameters
Strong form
Strong-form formulation
Poisson equation
Type
journal article