Multiscale topology optimization of structures by using isogeometrical level set approach

This study aims to optimize topology of structures at macro and micro scales, simultaneously, by using a level set method in an isogeometric analysis (IGA) framework. To achieve this, equilibrium and homogenization equations in the model are solved by IGA method. The level set functions are defined over a grid in parameter space of associating b-splines of the IGA model. Therefore, control net of the model and level set grid are separated and there is no need to refine the control net for having smooth boundaries. Sensitivity analyses for both scales are performed to calculate the velocity of boundary points and the level set functions are updated by solving reaction-diffusion equations. Finally, several 2D and 3D examples with different geometry and boundary conditions are provided to show performance and efficiency of the method. Obtained results show good agreement with examples in literature in terms of both topology and final value of objective function. Also, by using IGA level set method, smooth boundaries are achieved in the final topology of micro and macro structures.