Alternating active-phase algorithm for multimaterial topology optimization problems: a 115-line MATLAB implementation

A new algorithm for the solution of multimaterial topology optimization problems is introduced in the present study. The presented method is based on the splitting of a multiphase topology optimization problem into a series of binary phase topology optimization sub-problems which are solved partially, in a sequential manner, using a traditional binary phase topology optimization solver; internal solver. The coupling between these incomplete solutions is ensured using an outer iteration strategy based on the block coordinate descend method. The presented algorithm provides a general framework to extend the traditional binary phase topology optimization solvers for the solution of multiphase topology optimization problems. Interesting features of the presented algorithm are: generality, simplicity and the ease of implementation. The presented algorithm is used to solve multimaterial minimum structural and thermal compliance topology optimization problems based on the classical optimality criteria method. Details of MATLAB implementation are presented and the complete program listings are provided as the Supplementary Materials. The success and performance of the presented method are studied through several two dimensional numerical examples.