Convolution finite element method for analysis of piezoelectric materials

A new finite element scheme is proposed to analyze the elastodynamics of materials having interactions between electrical and mechanical fields. Based on coupled constitutive equations and the alternative field equations, a new form of weighted residual in terms of the convolution product is established. Next, the Galerkin formulation is utilized with a particular form of spatial-temporal shape functions. High precision for arbitrary time intervals can be attained by reducing the integral forms to a set of algebraic equations. To show the accuracy of the proposed method, several examples, including elastodynamics of 1d and 2d piezoelectric materials under various initial and boundary conditions are presented. The present contribution introduces a new solution procedure for the analysis and design of active materials.(c) 2022 Elsevier B.V. All rights reserved.