Porous structure design through Blinn transformation-based level set method

This paper presents a novel porous structure modeling and shape optimization method. Specifically, the porous structure is simplified into a truss network, and the connecting node positions are optimized to achieve the optimal stiffness. Simultaneously, the porosity distribution is tailored by adding local geometry control constraints. Then, as a following step, the truss elements are restored back into the explicit form, described by the parametric level set functions; and by conducting the Blinn transformation, the optimized truss structure is transformed into a continuum lattice model with smooth transitions at the internal joints. Finally, the maximum stress level at the joints is optimized through parametric level set shape optimization. In summary, this method is effective in building heterogeneous porous structures with tailored porosity distribution, and more importantly, both the stiffness and the stress level can be effectively optimized, which is an outstanding characteristic compared to the majority of the existing porous structure modeling and optimization methods. Effectiveness of the proposed method is proved through a few numerical case studies.