A parameter space approach for isogeometrical level set topology optimization

In this article, a new isogeometrical level set topology optimization is introduced. In previous studies, the level set function is approximated by b-splines basis functions and the control net is updated during the optimization process. Since control points are not basically on the level set surface, a discrepancy between zero level of function that represents boundaries of the structure, and zero level of its control netis appeared. In this article, the idea is solving level set equation (LSE) over the parameter space of b-splines basis functions defined in the IGA model. Afterwards, the updated level set function is mapped into the physical space. The level set function is approximated over a grid defined in parameter space which is constantly a unit square. By doing so, control net of the IGA model and the grid for solving LSE are separated. Two well-known radial basis functions (RBF) and reaction-diffusion (RD) based methods are employed to solve the LSE. The proposed method is applied to minimize the mean compliance when certain amount of material is used and also for weight minimization subject to local stress constraints. Several numerical examples are presented to demonstrate performance and accuracy of the proposed method.