A Weighted Control Scheme for Topology Optimization

The SIMP and RAMP approaches are widely used to solve the discretized topology optimization problems with continuous design variables. Based on these two methods, this paper proposes a weighted control scheme for the purpose of taking advantage of the high efficiency of SIMP and the high stability of RAMP. The scheme is established by introducing a weighted factor and, it allows the designer to switch between SIMP and RAMP optionally. The negative feedback control technique is introduced to the proposed scheme to determine the proper value of weighted factor. With the proposed method, a desired target is firstly set by the designer to indicate the final goal. The topology optimization problem is solved by the weighted scheme to obtain process variable. The process variables and the desired target value together constitute the input matrix of the proposed scheme. Next, the error is estimated by subtract the process variable from desired target value. A correction is then applied by error-based regulator according to the error information. Finally, the desired value of weighted factor is achieved by eliminating the error to a permissible range. The weighted control scheme is verified by the heat conduction topology optimization problem. (paper)