2D topology optimization MATLAB codes for piezoelectric actuators and energy harvesters

Abstract

In this paper, two separate topology optimization MATLAB codes are proposed for a piezoelectric plate in actuation and energy harvesting. The codes are written for one-layer piezoelectric plate based on 2D finite element modeling. As such, all forces and displacements are confined in the plane of the piezoelectric plate. For the material interpolation scheme, the extension of solid isotropic material with penalization approach known as PEMAP-P (piezoelectric material with penalization and polarization) which considers the density and polarization direction as optimization variables is employed. The optimality criteria and method of moving asymptotes (MMA) are utilized as optimization algorithms to update the optimization variables in each iteration. To reduce the numerical instabilities during optimization iterations, finite element equations are normalized. The efficiencies of the codes are illustrated numerically by illustrating some basic examples of actuation and energy harvesting. It is straightforward to extend the codes for various problem formulations in actuation, energy harvesting and sensing. The finite element modeling, problem formulation and MATLAB codes are explained in detail to make them appropriate for newcomers and researchers in the field of topology optimization of piezoelectric material.

Multiphysics Topology Optimization Using Automatic Differentiation and Adjoint Method

“…With different output 'spring' stiffness, the actuator designs changed. The three generated designs are qualitatively similar to those presented in [24], indicating that the AD-based TO framework can generate designs similar to those with analytical sensitivity analysis. Again, the advantage of the current work is that the user only needs to define the forward FE analysis and the calculation of the objective function and constraints, and there is no need to analytically derive the density-space gradients used in TO.…”

“…Further, it is assumed that the voltage is uniform in the XY plane, and varies linearly in the Z direction. These assumptions follow from the work of Homayouni-Amlashi et al [24]. In the absence of any body force and externally applied traction, the strong form of the problem can be written as:…”

“…TO settings are identical to the previous example. The material properties used in this example were adopted from [24] and are presented in Table 1. The final, optimized geometries are shown in Fig.…”

Reliability-based topology optimization of piezoelectric smart structures with voltage uncertainty

“…Notice there exists a huge scale difference between mechanical stiffness matrix ( K uu ) and dielectric matrix ( K u ϕ ) in equation (6), which may generate numerical singularity in the finite element analysis. To avoid this problem and ensure the accuracy of displacement response, normalization method is adopted as the author’s previous work in Homayouni-Amlashi et al (2021). The normalization mechanical stiffness matrix and the normalization piezoelectric coupling matrix are expressed as follows…”

“…In this study, we propose an RBTO method of piezoelectric smart structures with multi-parameters optimization based on the author’s previous work (Homayouni-Amlashi et al, 2021). The proposed approach embeds reliability analysis into the entire topology optimization process, providing a proper design that meets reliability requirements.…”