Length scale control for level set-based topology optimization through spread skeletons

Abstract This paper presents an efficient and easy-to-implement method for imposing feature size in level set-based topology optimization. A minimum length scale is enforced via a penalty based on a spread skeleton that captures the location of the skeleton and the required distance to it. The skeleton is constructed using first-order gradient information by solving a heat conduction problem and smoothing the resulting gradient with a PDE-based filter. Unlike other approaches, the method does not require to carry out integration over the skeleton, construct additional integration domains, or build an accurate distance from the skeleton. The work focuses on the generation of spread skeletons and the influence of the formulated penalty on optimization results. The design geometry is represented by a level set function, and structural responses are predicted using the extended finite element method. Optimization problems are solved using gradient-based algorithms, and the sensitivity analysis is performed with the adjoint approach. The ability of the proposed method to accurately control length scale is demonstrated with compliance minimization problems under a volume constraint. Similarly to other feature size control schemes, the developed geometric penalty tends to inhibit topological changes, especially in two dimensions, and results in a high dependence on the initial layout. An activation strategy that successively recruits regions of the design domain based on the spread skeleton value is used to avoid early convergence to suboptimal solutions. Numerical examples demonstrate the potential of the proposed framework to generate designs exhibiting both enhanced performance and a minimum length scale.