Damage approach: A new method for topology optimization with local stress constraints

Verbart, Alexander; Langelaar, Matthijs; Keulen, Fred van

doi:10.1007/s00158-015-1318-9

Cited by 61 publications

(24 citation statements)

References 27 publications

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“…This phenomenon was not observed for simple compliance minimization under mesh refinement for which the densities in void regions converged to a value closer to zero (≈ 3 · 10 −5 ). However, it was also observed using other approaches for stress-constrained topology optimization; e.g., the damage approach (Verbart et al, 2015) and the conventional approach of constraint relaxation followed by aggregation. For example, Figure 15 shows a result obtained by considering qp-relaxed stresses aggregated into a single P -norm constraint (Le et al, 2009).…”

Section: Effect Of Mesh Refinementmentioning

confidence: 91%

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

Verbart

Langelaar

Keulen

2016

Struct Multidisc Optim

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104

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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.

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Section: Effect Of Mesh Refinementmentioning

confidence: 91%

“…Examples of aggregation functions that have been applied in literature are the Kreisselmeier-Steinhauser function (KS-function hereafter) (Kreisselmeier, 1979;Yang and Chen, 1996), and the P -norm (Duysinx and Sigmund, 1998). Recently, the authors have proposed an alternative solution (Verbart et al, 2015).…”

Section: Introductionmentioning

confidence: 99%

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

Verbart

Langelaar

Keulen

2016

Struct Multidisc Optim

Self Cite

104

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“…The value of λ is determined by whether the local stress constraints are satisfied. The material in which a stress constraint is violated is considered as damaged, and then, the corresponding local structural performance is penalized. The stress penalty factor α is used to control the penalization weight, which is of vital importance for controlling the local stress level because it makes the stresses that are larger than the allowable stresses play a prominent role during the optimization.…”

Section: Topology Description and Optimization Modelsmentioning

confidence: 99%

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

Chu

Xiao

Gao

et al. 2018

Numerical Meth Engineering

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Summary In multimaterial topology optimization of minimizing a global measure of stress, the maximum stresses in different materials may not satisfy the strength design requirements simultaneously if stress constraints for different materials are not considered. In this paper, a level set–based method is presented to handle the stress‐constrained multimaterial topology optimization of minimizing a global stress measure. Specifically, a multimaterial level set model is adopted to describe the structural topology, and a stress interpolation scheme is introduced for stress evaluation. Then, a stress penalty‐based topology optimization model is presented. Meanwhile, an adaptive adjusting scheme of the stress penalty factor is employed to improve the control of the local stress level. To solve the stress‐constrained multimaterial topology optimization problem minimizing the global measure of stress, the parametric level set method is employed, and the sensitivity analysis is carried out. Numerical examples are provided to demonstrate the effectiveness of the presented method. Results indicate that multimaterial structures with optimized global stress can be gained, and stress constraints for different materials can be satisfied simultaneously.

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“…Bruggi and Duysinx too have considered discretisations in the order of 10 000 FE's. Other recent developments include the level set method by Emmendoerfer and Fancello and the so‐called ‘damage approach’ by Verbart et al .…”

Section: Introductionmentioning

confidence: 99%

Local stress‐constrained and slope‐constrained SAND topology optimisation

Munro

Groenwold

2016

Numerical Meth Engineering

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Summary We study the alternative ‘simultaneous analysis and design’ (SAND) formulation of the local stress‐constrained and slope‐constrained topology design problem. It is demonstrated that a standard trust‐region Lagrange–Newton sequential quadratic programming‐type algorithm—based, in this case, on strictly convex and separable approximate subproblems—may converge to singular optima of the local stress‐constrained problem without having to resort to relaxation or perturbation techniques. Moreover, because of the negation of the sensitivity analyses—in SAND, the density and displacement variables are independent—and the immense sparsity of the SAND problem, solutions to large‐scale problem instances may be obtained in a reasonable amount of computation time. Copyright © 2016 John Wiley & Sons, Ltd.

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Damage approach: A new method for topology optimization with local stress constraints

Cited by 61 publications

References 27 publications

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

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

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

Local stress‐constrained and slope‐constrained SAND topology optimisation

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