Combination of topology optimization and optimal control method

This paper presents the combination of topology optimization and optimal control method to find the optimal match between the material topology and control. In the presented method, the material topology is determined using the SIMP (Solid Isotropic Material with Penalization) method, which has been popularly used in topology optimization. In the SIMP method, the design variable is relaxed and bounded in the interval [ 0 , 1 ] , and the evolution of the design variable is usually implemented by the method of moving asymptotes (MMA), which can be used to deal with optimization problem with multiple integral constraints and bound constraint of the design variable. In the combination of topology optimization and optimal control method, the control variable appears along with the design variable. In order to evolve the control variable and design variable using MMA simultaneously, the control variable is regularized using a bound constraint and the corresponding bound constraint is projected onto the interval [ 0 , 1 ] , which is the same as the bound constraint of the design variable. The optimization problem is analyzed using the adjoint method to obtain the adjoint sensitivity. During the optimization procedure, the design and control variables are filtered by the Helmholtz filters to ensure the smoothness of the distribution. To ensure the minimum scale length and remove the gray area in the material topology, the filtered design variable is projected by the threshold method. The feasibility and robustness of the combination of these two methods are demonstrated by several test problems, including heat transfer, fluid flow and compliance minimization.