We present an efficient Matlab implementation of topology optimization for volume-constrained compliance minimization problems on unstructured polygonal finite element meshes considering multiple, anisotropic materials. As part of the PolyTop family of educational topology optimization codes, PolyAnisoMat extends the multi-material code, PolyMat, to handle anisotropic materials that are characterized by homogenized mechanical properties. In addition to material selection design variables that determine which candidate material exists at each design point, PolyAnisoMat includes relative density and orientation design variables that determine local porosity and orientation, respectively, of the materials. By fitting the components of each material’s stiffness elasticity tensor as a function of its relative density and orientation prior to optimization, recalculation of the element stiffness matrices in each optimization iteration is reduced to a dot product operation that avoids repeated numerical integration operations and significantly enhances computational efficiency. The material interpolation schemes used in PolyTop and PolyMat to avoid intermediate values of the material selection design variables and prevent material mixing are extended to account for the spatially varying relative density and orientation. To efficiently handle many materials and many volume constraints, the Zhang–Paulino–Ramos Jr. update scheme is used to update the material selection and relative density design variables, while steepest descent with modular arithmetic is used to update the orientation design variables that do not contribute to the volume constraints. Several numerical examples highlight PolyAnisoMat’s computational efficiency, capacity to handle many anisotropic materials with variable relative density and orientation, and ability to arrive at “good” local optima.
