MATLAB implementations of velocity field level set method for topology optimization: an 80-line code for 2D and a 100-line code for 3D problems

This paper presents MATLAB implementations of the velocity field level set method for topology optimization. An 80-line code and a 100-line code are provided for 2D and 3D static compliance minimization problems, respectively. The velocity field level set method inherits the implicit topology and shape representation of the standard level set method but advances the design boundaries with a velocity field constructed from the velocity design variables and basis functions. Therefore, it can achieve structural designs with relatively clear and smooth material boundaries. Moreover, it allows general mathematical programming algorithms to be conveniently employed to handle more constraints when solving the optimization problem. In the presented codes, the method of moving asymptotes is used as the optimizer. For simplification, the presented MATLAB code is in a basic version. Some modifications and extensions are given in the examples to show the validity and efficiency of the codes. Further adaption of the current codes can also be made to fulfill various requirements.