Finite element method coupled with TLBO for shape control optimization of piezoelectric bimorph in COMSOL Multiphysics

Abstract

Finite element methods (FEMs) are more advantageous for analyzing complex geometry and structures than analytical methods. Local search optimization techniques are suitable for the unimodal problem because final result depends on the starting point. On the other hand, to optimize the parameters of multi-minima/maxima problems, global optimization-based FEM is used. Unfortunately, global optimization solvers are not present in, COMSOL Multiphysics, a versatile tool for solving varieties of problems using FEM. Teaching–learning-based optimization (TLBO) is a global optimization technique and does not require any algorithm-specific parameter. In this paper, FEM is coupled with TLBO algorithms in COMSOL Multiphysics for solving the global optimization problem. The TLBO algorithm is implemented in COMSOL Multiphysics using the JAVA application programming interface and tested with the standard benchmark functions. The solutions of the standard benchmark problem in COMSOL Multiphysics are in close agreement with the results presented in literature. Furthermore, the optimization procedure thus established is used for the optimization of actuator voltage for piezoelectric bimorphs to achieve the desired shapes. The FEM-based TLBO method is compared with two optimization methods present in COMSOL Multiphysics for a shape control problem; (i) method of moving asymptotes (MMA) and (ii) Bound Optimization BY Quadratic Approximation (BOBYQA). The root mean square error shows that the FEM-based TLBO algorithm converges to a global minimum and gives the same result (19.3 nm) at multiple runs, whereas MMA and BOBYQA trapped in local minimum and gave different results for different starting points.