Integrated topology optimization with embedded movable holes based on combined description by material density and level sets

This paper presents a novel topology description model for topology optimization problems with embedded movable holes, combining the ability of the level set model for accurate geometrical description of the prescribed hole shapes, and the high efficiency of the material density-based method. By this means, any arbitrary hole shapes can be represented accurately and smoothly, while the topological changes can be easily handled by the material distribution model. An explicit mathematical expression is defined to obtain the actual structural layout by combing both models. Moreover, an effective model for the non-overlap constraint is proposed in a unified and systematic manner to avoid the overlaps between the holes and between each hole and the design domain boundary. Therein, the non-overlap constraint for all the embedded holes is imposed as a single explicit integral constraint over the design domain, thus avoiding the difficulties in the overlap detection of multiple arbitrary-shaped geometries. Such a non-overlap constraint is accurate and differentiable, facilitating an analytical design sensitivity analysis. Numerical examples are given to demonstrate the effectiveness and efficiency of the present method.