Topology optimization provides useful mathematical tools for the design of optimal (e.g., minimizing the compliance) structures for assigned loads and boundary conditions, and under suitable constraints (e.g., a given fraction of the initial volume). The SIMP (Solid Isotropic Material with Penalization) method represents one of the most investigated approaches for topology optimization. It belongs to the family of density-based methods, where an auxiliary (unknown) scalar field (the density), taking values between zero (void) and one (material), is adopted to describe the final layout of the optimized structure. SIMP exhibits many drawbacks, among which the non-uniqueness of the optimal structure and issues related to the adopted discretization for the optimization problem (e.g., checkerboard, greyscale, and staircase effects). In this talk, we present the new algorithm SIMPATY (SIMP+AdaptiviTY) which enriches the basic SIMP method with anisotropic mesh adaptivity to alleviate some of the above-mentioned issues.
After introducing the mathematical background, we provide a detailed description of the SIMPATY algorithm and we verify its performance on benchmarks as well as on more challenging structure configurations.