A level set method with maximum design domain limits

Abstract

The design domains of practical structures are often limited and significantly affect the final optimal design of the structures. Structural boundaries under traction and prescribed displacements should be treated as a zero set in the level set methods. However, structural optimization methods based on level set movements do not consider these realistic requirements. To overcome the limitations of current level set methods and the stopping issue of structural boundary movements, this paper presents a new level set based optimization method for the optimal design of continuum structures with bounded design domains. A set of new normal velocities required by the level set movements is proposed. Optimization algorithms are developed and implemented with several robust and efficient numerical techniques. The difference of the proposed method and the existing level set method is given. The validity and effectiveness of the proposed method are demonstrated with one example.