A novel coupling algorithm for the electric field–structure interaction using a transformation method between solid and shell elements in a thin piezoelectric bimorph plate analysis

Abstract

Thin piezoelectric bimorph cantilever is increasingly employed throughout the field of actuator and sensor applications in the microelectromechanical system (MEMS). Generally for finite element analysis of piezoelectric bimorph cantilever, three–dimensional (3D) solid element can accurately takes into account a linear or quadratic distribution of electric potential over the thickness for various electric configurations of the actuator and sensor applications. As the MEMS structures usually are quite thin and undergo large deformations, shell elements are very well suited for the structural discretization. This paper is focused on the development of a novel coupled algorithm to analyze the electromechanical coupling in a piezoelectric bimorph actuator and sensor using the shell and solid elements to simulate the structural and electric fields, respectively. The electric force induced by the inverse piezoelectric effect is transformed from the solid elements to the shell elements as an equivalent external force and moment, and the resultant displacements are transformed from the shell elements to the solid elements to evaluate the direct piezoelectric effect. Two different approaches were developed to analyze the electric field–structure interaction. In the first approach, for each block Gauss–Seidel (BGS) iteration, multiple full Newton–Raphson (N–R) iterations are executed until the tolerance criteria are satisfied. In the second approach, the BGS and N–R loops are unified into a single loop. A piezoelectric bimorph actuator and sensor were analyzed for various electrical configurations to demonstrate the accuracy of the proposed method.