Matlab codes for 3D topology optimization of multi-material piezoelectric actuators and energy harvesters

This paper presents two MATLAB codes for topology optimization of multi-material piezoelectric actuators and energy harvesters. These codes provide the extensions of the previously published 2D topology optimization codes for piezoelectric actuators and energy harvesters (Struct Multidisc Optim 63 (2), 983–1014) with two major contributions: (1) extension to the third dimension, (2) combination of piezoelectric (active) and non-piezoelectric (passive) materials in the design domain. The codes are written in the most flexible form to be compatible with different optimization problems and practical case studies of piezoelectricity that exist in the literature. The codes address unique challenges that emerge by introducing the third dimension to non-isotropic piezoelectric materials including the polarization direction and definition of electrodes. The finite element discretization has been done with two different types of 3D hexahedral elements: (1) 8-node trilinear elements, (2) 20 node quadratic elements. The users are free to choose between these element types for the finite element model of the structure based on having preferences for accuracy or computation time. A new method of indexing the elements, nodes, and degrees of freedom is introduced to facilitate the definition of loads, boundary conditions, electrodes, etc. The inclusion of piezoelectric material and non-piezoelectric material in the design domain is by default. In comparison to previously published 2D codes, the codes in this paper benefit from the latest advancements in optimization algorithms, filtering methods, and speed-up techniques. The codes are independent and hence can be run without calling any external code. Different parts of the codes are explained in detail to make them comprehensive for newcomers in the field of topology optimization of piezoelectric structures.