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A design methodology based on a combination of isogeometric analysis (IGA), level set and
point wise density mapping techniques for topology optimization of piezoelectric/flexoelectric
materials will be presented [1-3]. The fourth order partial differential equations
(PDEs) of flexoelectricity, which require at least C1 continuous approximations, are
discretized using polynomial/rational splines over hierarchical T-meshes (PHT/RHT-splines)
[4-7]. The point wise density mapping technique with consistent derivatives is directly used in
the weak form of the governing equations. The boundary of the design domain is implicitly
represented by a level set function. The accuracy of the IGA model is confirmed through
numerical examples including a cantilever beam under a point load and a truncated pyramid
under compression with different electrical boundary conditions. Finally, we provide
numerical examples demonstrating the significant enhancement in electromechanical coupling
coefficient that can be obtained using topology optimization.