Piecewise constant level set method for structural topology optimization

In this paper, a piecewise constant level set (PCLS) method is implemented to solve the structural shape and topology optimization problems. In this approach, by defining a piecewise density function over the whole design domain, the sensitivity of the objective function respect to the design variable, the level set surface, can be explicitly obtained. Thus the piecewise density function can be viewed as a bridge establishing the relationship between the implicit level set function and the performance function defined on the design domain. This proposed method keeps the advantages of the implicit level set represen-tation such as the interface can develop sharp corners, break apart, and merge together in a flexible manner. Because the piecewise constant level set method is implemented by an implicit iteration differ-ential scheme other than solving the Hamilton-Jacobi equation, it is free of the CFL condition and the reinitialization scheme. These favorable properties lead to a great time advantage over the conventional level set method. Some issues in numerical implementation are discussed and numerical examples of 2D structural topology optimization problem of minimum compliance design are given and combined with a comparative study and the efficiency, convergency and accuracy of the present method are highlighted. 2. Keywords: topology optimization, level set method, piecewise constant level set metho