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.

In this paper, we propose a new method for topology optimization with local stress constraints. In this method, material in which a stress constraint is violated is considered as damaged. Since damaged material will contribute less to the overall performance of the structure, the optimizer will promote a design with a minimal amount of damaged material. We tested the method on several benchmark problems, and the results show that the method is a viable alternative for conventional stress-based approaches based on constraint relaxation followed by constraint aggregation.

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Document Version Peer reviewed versionLink back to DTU Orbit Citation (APA): Verbart, A., & Stolpe, M. (2018). A working-set approach for sizing optimization of frame-structures subjected to time-dependent constraints. Structural and Multidisciplinary Optimization, 58(4), 1367-1382. CITATION 1 READS 118 2 authors, including: Some of the authors of this publication are also working on these related projects: Structural optimization of offshore windturbine support structures View project Topology Optimization with Stress Constraints View project Alexander Verbart Ramboll 8 PUBLICATIONS 70 CITATIONS SEE PROFILE All content following this page was uploaded by Alexander Verbart on 03 September 2018. The user has requested enhancement of the downloaded file.Structural and Multidisciplinary Optimization: Post-print. The final publication is available via http://dx. AbstractIn this paper, we propose a working-set approach for sizing optimization of structures subjected to time-dependent loads. The optimization problems we consider have a very large number of constraints while relatively few design variables and degrees of freedom. Instead of solving the original problem directly, we solve a sequence of smaller sub-problems. The sub-problems consider only constraints in the working set, which is a small sub-set of all constraints. After each sub-problem, we compute all constraint function values for the current design and add critical constraints to the working set. The algorithm terminates once an optimal point to a sub-problem is found that satisfies all constraints of the original problem. We tested the approach on several reproducible problem instances and demonstrate that the approach finds optimal points to the original problem by only considering a very small fraction of all constraints. The proposed approach drastically reduces the memory storage requirements and computational expenses of the linear algebra in the optimization solver and the computational cost of the design sensitivity analysis. Consequently, the approach can efficiently solve large-scale optimization problems with several hundred millions of constraints.