A topology optimization algorithm for electroelasticity coupled problems

A problem of applying topology optimization to elastic deformable bodies exposed to coupled electric and mechanical fields has been studied. The main goal was to find the optimal distribution of electric and mechanical properties in the given area, taking into account restrictions on the final volume of the structure. A topology optimization algorithm was formulated and implemented (as program code in Python) for bodies under the action of the coupled electric and mechanical fields. The algorithm included solving the coupled electroelasticity problem using the finite element method, analyzing derivatives of the objective function, and optimizing by the dual procedure within the method of moving asymptotes. The algorithm was tested in numerical experiments on the optimization problem of a piezoelectric actuator exposed to uniform or linearly distributed electric fields. As a result, the distributions of mechanical and electrical properties were obtained for various values of the stiffness coefficient.