Robust Topology Optimization for Compliant Mechanisms Considering Uncertainty of Applied Loads

Abstract

In this study, a robust topology optimization method is proposed for compliant mechanisms, where the effect that variation of the input load direction has on the output displacement is considered. Variations are evaluated through a sensitivity-based robust optimization approach, with the variance evaluated using first-order derivatives. The robust objective function is defined as a combination of maximizing the output deformation under the mean input load and minimizing variation in the output deformation as the input load is varied, where variance due to changes in load can be obtained through mutual compliance and the presence of a pseudo load. For the topology optimization, a modified homogenization design method using the continuous approximation assumption of material distribution is adopted. The validity of the proposed method is confirmed with two compliant mechanism design problems. The effect that varying the input load direction has upon the obtained configurations is investigated by comparing these with deterministic optimum topology design results.

Length scale and manufacturability in density-based topology optimization

“…A large number of research papers are devoted to the exploitation of uncertainties like random inputs or imperfections in boundary conditions, e.g., [83], [98], [43] and [162]. It should be emphasized that the the focus here is on manufacturability and length scale of the the optimized designs, therefore, a detailed review on topology optimization under other types of uncertainties is omitted here.…”

Level Set-Based Topology Optimization for the Design of Light-Trapping Structures

“…We also note that the fact that this problem has several local optima implies that manufacturing errors on the light trapping structure significantly affect the performance of the light trapping structure. Although we did not consider such manufacturing tolerance here, the presented method can be extended to consider it by being combined with the robust topology optimization method [12]. and y direction, and = 1.0×10 7 in z direction, so that a uniform cross-section constraint is imposed in z direction.…”

Minmax topology optimization

“…Robust topology optimization (RTO) is similar to RBTO, wherein response functions are replaced by the sum of their mean values and their weighted variances, cf. [10];…”

“…[11]. Other robust design alternatives are available, like the sensitivity-based formulations in [10,12]. An overview of still other robust design approaches such as the Taguchi method, physical programming approach, and robust design with an axiomatic approach are discussed in [13].…”