Multiscale isogeometric optimization for cellular structure with multiple prototypes

This paper presents a multiscale concurrent isogeometric design method for the cellular structure composed of the multiple prototype microstructures. Based on the unified-skeleton modeling scheme, the graded microstructures obtained from a same prototype have similar topology and good connectivity between each other. For the different prototypes, the configurations are rearranged and added the thin-wall material in common interfaces. Thus, the geometric features as well as the structural skeletons can have a smooth transition. Through combining the numerical homogenization method with the interpolation technique, the effective properties of graded microstructures can be estimated efficiently. For the multiscale scheme, the allocation of microstructures is optimized by a material distribution-based method while the configurations of prototypes are designed by the isogeometric parameterized level set method. The proposed method inherits the high accuracy and high efficiency of isogeometric analysis and the smooth boundaries and distinct interfaces of level set method. The cellular structure can be freely customized with favorable connectivity