Effect of design parameterization and relaxation on model responses in topology optimization with stress constraints

Alexander Verbart, Nico Van Dijk, Laura Del Tin, Matthijs Langelaar, Fred van Keulen

Research output: Chapter in Book/Report/Conference proceedingArticle in proceedingsResearchpeer-review

Abstract

Extensive research has been done on the handling of stress constraints in topology optimization. One of the main difficulties when dealing with stress constraints is the so-called singularity phenomenon. Constraint relaxation techniques are commonly applied to avoid the presence of singular optima. In this paper, we focus on the handling of stress constraints for density-based topology optimization, where the design is parameterized by the well-known SIMP model. We investigate the nature of the stress response and the effect of design parameterization, stress
relaxation and analysis discretization on the model response. For this purpose, an elementary numerical example is presented which represents a situation as may occur in density-based continuum topology optimization. The results show clearly the intrinsic difficulties that may be encountered when dealing with stress constraints in density-based topology optimization. We find that artificial local optima may arise and
that penalization increases non-convexity, causing optimizers to converge to suboptimal designs. Finally, it is shown that the global solution of the relaxed problem may not converge to the global solution of the original problem, which agrees with the results reported in truss optimization. The results give an insight in the limitations and difficulties of the present ways of dealing with stress constraints in density-based
topology optimization.
Original languageEnglish
Title of host publicationProceedings of 9 th World Congress on Structural and Multidisciplinary Optimization
Number of pages14
Publication date2011
Publication statusPublished - 2011
Externally publishedYes
Event9th World Congress on Structural and Multidisciplinary Optimization - Shizuoka, Japan
Duration: 13 Jun 201117 Jun 2011
Conference number: 9

Conference

Conference9th World Congress on Structural and Multidisciplinary Optimization
Number9
CountryJapan
CityShizuoka
Period13/06/201117/06/2011

Keywords

  • Topology optimization
  • Stress constraints
  • Singular optima
  • Regularization
  • qp-approach

Cite this

Verbart, A., Van Dijk, N., Del Tin, L., Langelaar, M., & Keulen, F. V. (2011). Effect of design parameterization and relaxation on model responses in topology optimization with stress constraints. In Proceedings of 9 th World Congress on Structural and Multidisciplinary Optimization
Verbart, Alexander ; Van Dijk, Nico ; Del Tin, Laura ; Langelaar, Matthijs ; Keulen, Fred van. / Effect of design parameterization and relaxation on model responses in topology optimization with stress constraints. Proceedings of 9 th World Congress on Structural and Multidisciplinary Optimization. 2011.
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Verbart, A, Van Dijk, N, Del Tin, L, Langelaar, M & Keulen, FV 2011, Effect of design parameterization and relaxation on model responses in topology optimization with stress constraints. in Proceedings of 9 th World Congress on Structural and Multidisciplinary Optimization. 9th World Congress on Structural and Multidisciplinary Optimization, Shizuoka, Japan, 13/06/2011.

Effect of design parameterization and relaxation on model responses in topology optimization with stress constraints. / Verbart, Alexander; Van Dijk, Nico; Del Tin, Laura; Langelaar, Matthijs; Keulen, Fred van.

Proceedings of 9 th World Congress on Structural and Multidisciplinary Optimization. 2011.

Research output: Chapter in Book/Report/Conference proceedingArticle in proceedingsResearchpeer-review

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PY - 2011

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N2 - Extensive research has been done on the handling of stress constraints in topology optimization. One of the main difficulties when dealing with stress constraints is the so-called singularity phenomenon. Constraint relaxation techniques are commonly applied to avoid the presence of singular optima. In this paper, we focus on the handling of stress constraints for density-based topology optimization, where the design is parameterized by the well-known SIMP model. We investigate the nature of the stress response and the effect of design parameterization, stressrelaxation and analysis discretization on the model response. For this purpose, an elementary numerical example is presented which represents a situation as may occur in density-based continuum topology optimization. The results show clearly the intrinsic difficulties that may be encountered when dealing with stress constraints in density-based topology optimization. We find that artificial local optima may arise andthat penalization increases non-convexity, causing optimizers to converge to suboptimal designs. Finally, it is shown that the global solution of the relaxed problem may not converge to the global solution of the original problem, which agrees with the results reported in truss optimization. The results give an insight in the limitations and difficulties of the present ways of dealing with stress constraints in density-basedtopology optimization.

AB - Extensive research has been done on the handling of stress constraints in topology optimization. One of the main difficulties when dealing with stress constraints is the so-called singularity phenomenon. Constraint relaxation techniques are commonly applied to avoid the presence of singular optima. In this paper, we focus on the handling of stress constraints for density-based topology optimization, where the design is parameterized by the well-known SIMP model. We investigate the nature of the stress response and the effect of design parameterization, stressrelaxation and analysis discretization on the model response. For this purpose, an elementary numerical example is presented which represents a situation as may occur in density-based continuum topology optimization. The results show clearly the intrinsic difficulties that may be encountered when dealing with stress constraints in density-based topology optimization. We find that artificial local optima may arise andthat penalization increases non-convexity, causing optimizers to converge to suboptimal designs. Finally, it is shown that the global solution of the relaxed problem may not converge to the global solution of the original problem, which agrees with the results reported in truss optimization. The results give an insight in the limitations and difficulties of the present ways of dealing with stress constraints in density-basedtopology optimization.

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Verbart A, Van Dijk N, Del Tin L, Langelaar M, Keulen FV. Effect of design parameterization and relaxation on model responses in topology optimization with stress constraints. In Proceedings of 9 th World Congress on Structural and Multidisciplinary Optimization. 2011