2D topology optimization MATLAB codes for piezoelectric actuators and energy harvesters
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EDUCATIONAL PAPER
2D topology optimization MATLAB codes for piezoelectric actuators and energy harvesters Abbas Homayouni-Amlashi1,2
· Thomas Schlinquer2 · Abdenbi Mohand-Ousaid2 · Micky Rakotondrabe1
Received: 19 May 2020 / Revised: 8 August 2020 / Accepted: 14 August 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
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. Keywords Topology optimization · MATLAB code · Piezoelectric actuator · Piezoelectric energy harvester
1 Introduction Topology optimization (TO) is a methodology to distribute the material within a design domain in an optimal way while there is no prior knowledge about the final layout of the material (Bendsoe 2013). This main specification of TO provides a great degree of freedom in terms of designing innovative structures to satisfy predefined
Responsible Editor: Palaniappan Ramu Electronic supplementary material The online version of this article (https://doi.org/10.1007/s00158-020-02726-w) contains supplementary material, which is available to authorized users. Abbas Homayouni-Amlashi
[email protected] 1
Laboratoire G´enie de Production, Nationale School of Engineering in Tarbes (ENIT), Toulouse INP, University of Toulouse, 47, Avenue d’Azereix, Tarbes, France
2
CNRS, FEMTO-ST Institute, Universit´e Bourgogne Franche-Comt´e, Besanc¸on, 25000, France
engineering goals. Historically, minimization of mechanical deformation of a structure under application of different loading conditions was a classical engineering goal (Schmit 1960). Aiming for this goal, the work of Bendsoe and Kikuchi (1988) paves the way for a methodology known today as topology optimization. The general idea of this methodology is the combination of finite element method and op
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