A Matlab code of topology optimization by imposing the implicit floating projection constraint

Abstract This paper presents a Matlab code to implement the three-field floating projection topology optimization (FPTO) method using the linear material interpolation scheme. The implicit floating projection constraint in the FPTO method numerically simulates 0/1 constraints of the design variables so that even a linear material interpolation scheme can be employed. By gradually tightening 0/1 constraints, more and more design variables are pushed to 0/1 until an optimized element-based design with a clear topology can be accurately represented by a smooth design. In general, the implicit floating projection constraint provides a numerical engine for topology optimization, which is fundamentally different from the existing topology optimization methods. The Matlab code in this paper describes the numerical implementation of such an implicit constraint and the extraction and evaluation of the smooth design in detail. Apart from the compliance minimization problem, the Matlab code can be equally applied to other extended topology optimization problems. The provided Matlab code enables the users to understand and test this newly-developed topology optimization method for their own topology optimization problems.