Isogeometric Analysis (IGA)-Based Topology Optimization for 3D Flexoelectric Structures

This paper presents isogeometric analysis (IGA)-based topology optimization for electrical performance of three-dimensional (3D) flexoelectric structures. IGA is employed to provide C1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${C}<^>{1}$$\end{document} continuity in shape function, which is required in treating high-order electromechanical coupling equations. To improve the computational efficiency in treating 3D problems, the redundant degrees of freedom removal technique is introduced. Regularization treatments are also implemented to avoid the numerical singularity induced by flexoelectricity. Both virtual loads and strain energy constraints are taken into consideration to prevent unexpected structural disconnection. Numerical examples and experiments on optimized structures demonstrate that the flexoelectric performance can be effectively improved using the proposed approach.