This paper formulates the concurrent optimization of structural topology and anisotropic materials for laminated composite structures by simultaneously optimizing laminate topology and fiber orientations. In this formulation and model, both constant-stiffness and variable-stiffness designs can be obtained. For constant-stiffness designs, ply orientation optimization is studied, and for variable-stiffness designs, element or patch (cluster) orientation optimization is considered, in which both geometry-based and fiber angle-based methods are developed for patch clustering. Analytical solutions to determine optimal material orientations are derived for patch or ply orientation in addition to element orientation. Moreover, out-of-plane loadings are involved, and hence shear deformations and transverse shear effects are taken into consideration. An extended moving iso-surface threshold (MIST) algorithm is proposed to implement the formulation and optimization model, with which the optimization of topology and element/patch/ply orientation is in a fully-coupled concurrent manner.
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