Efficient hybrid topology and shape optimization combining implicit and explicit design representations

This paper presents an interactive hybrid topology optimization method that (1) employs density for topology optimization and (2) in a seamless fashion uses a Deformable Simplicial Complex for shape optimization. Omitting hole insertions during the shape optimization allows us to utilize adaptive mesh coarsening, which reduces the mesh size with up to seven times. The result is a combined method which can reduce computation time up to ten times in comparison with pure Lagrangian methods, while still producing adaptive meshes of good quality for analysis and design. Given the robustness of the method, we are able to perform topology optimization by explicit meshing and shape optimization on a mobile device at frame rates that allow for real-time user interaction. The resulting “TopOpt Shape” app is available in the App Store for iOS devices.