A geometric deformation constrained level set method for structural shape and topology optimization

In this paper, a geometric deformation constrained level set method is presented as an effective approach for structural shape and topology optimization. A level set method is used to capture the motion of the free boundary of a structure. Furthermore, the geometric deformation of the free boundary is constrained to preserve the structural connectivity and/or topology during the level set evolution. An image-processing-based structural connectivity and topology preserving approach is proposed. A connected components labeling technique based on the 4-neighborhood connectivity measure and a binary image is used for the present region identification. The corresponding binary image after an exploratory move of the free boundary at each time predicted by an explicit upwind finite difference scheme is first identified. Once a violation on structural connectivity and/or topology is encountered, removed components crucial to preserve the structural connectivity and/or topology are further identified and recovered to make the actual move properly connected. The geometric deformation is thus constrained and the structural connectivity and/or topology can be well maintained. Structural disconnectivity as well as topological changes during the evolution can be prevented. Shape optimization may be allowed for and topology optimization may become more robust. A bi-sectioning algorithm is used to handle the volume constraint and the fluctuations of the total volume can be eliminated. The present method may be structural connectivity and/or topology preserving and volume conservative to generate monolithic feasible designs. The effectiveness of the present method is illustrated with numerical examples in minimum compliance design and compliant mechanism design.