A unified aggregation and relaxation approach for stress-constrained topology optimization

Abstract

Document VersionAbstract In this paper, we propose a unified aggregation and relaxation approach for topology optimization with stress constraints. Following this approach, we first reformulate the original optimization problem with a design-dependent set of constraints into an equivalent optimization problem with a fixed design-independent set of constraints. The next step is to perform constraint aggregation over the reformulated local constraints using a lower bound aggregation function. We demonstrate that this approach concurrently aggregates the constraints and relaxes the feasible domain, thereby making singular optima accessible. The main advantage is that no separate constraint relaxation techniques are necessary, which reduces the parameter dependence of the problem. Furthermore, there is a clear relationship between the original feasible domain and the perturbed feasible domain via this aggregation parameter.

Stress-based topology optimization of compliant mechanisms using nonlinear mechanics

“…It is important to underline the fact that this does not depend directly on density distribution. In this work the unified approach proposed by Verbart et al [40] was adopted to incorporate stress constraints in topology optimization. Assuming that the densities in SIMP represent a porous micro-structure, one can distinguish the stress at macroscopic (effective) versus microscopic levels [55].…”

“…To access singular optima classic of mathematical program with vanishing constraints, a relaxation method is adopted [40]. In particular, the relaxed constraint is defined as:…”

“…Essentially, two problems arise [36]: first, a large number of constraints must be considered, since unlike stiffness, stress is a local quantity; second, stress is highly nonlinear with respect to design variables. Recent advances show possibilities to overcome these difficulties [37][38][39][40][41][42]. There are few recent examples in the literature where the stress distribution is considered as a constraint in TO problems with geometrical nonlinearities (as for instance [39]).…”

A level set–based method for stress‐constrained multimaterial topology optimization of minimizing a global measure of stress

“…In such cases, however, convergence oscillation and numerical overflow may arise . Verbart et al propose a unified aggregation and relaxation approach, which concurrently aggregates stress constraints and relaxes the feasible domain, thereby making singular optima accessible. By combining the local and global stress methods, the regional or block aggregation technique is developed by París et al and Holmberg et al In this technique, the design domain is divided into several subregions.…”

Topology Optimization Considering Limit Analysis

“…However, the solutions available in the literature are, in general, obtained by constraining the elastic stress [5,6,7,8,9, 10], which may not fully consider structural safety. Therefore, a plastic design should be preferred over an elastic design when attempting to reach an optimal structural design [11,12,13].…”