Level Set Based Topology Optimization with Stress Constraints and Consistent Sensitivity Analysis

Alexander Verbart, Matthijs Langelaar, Nico Van Dijk, Fred van Keulen

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Abstract

For aeronautical applications of topology optimization, it is of importance to develop topology optimization techniques, that can handle stress constraints in an efficient and accurate manner. The development of such topology optimization techniques is a challenging task due to the local nature of the stress constraints, their highly non-linear behaviour with respect to the design variables and the so-called singularity phenomenon. An accurate sensitivity analysis is essential for these type of problems with multiple constraints. In this paper, we propose a methodology of dealing with stress constraints in a level set based framework. In this framework, the level set function nodal values are related to element densities by an exact Heaviside projection. Stress relaxation and constraint aggregation techniques are used to deal with the singularity phenomenon and the local nature of the stress, respectively. A constrained optimization problem is then solved, in which the design variables (the level set nodal values) are updated in the projected steepest-descent direction, which is determined using a consistent sensitivity analysis.We demonstrate the effectiveness of this technique on two numerical examples. The results show that the level set method with a consistent sensitivity analysis allows for the treatment of multiple constraints by using constrained optimization techniques.
Original languageEnglish
Title of host publication53rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference
Number of pages15
Publication date2012
ISBN (Print)978-1-60086-937-2
DOIs
Publication statusPublished - 2012
Externally publishedYes
Event53rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference - Honolulu, HI, United States
Duration: 23 Apr 201226 Apr 2012
Conference number: 53

Conference

Conference53rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference
Number53
CountryUnited States
CityHonolulu, HI
Period23/04/201226/04/2012

Cite this

Verbart, A., Langelaar, M., Van Dijk, N., & van Keulen, F. (2012). Level Set Based Topology Optimization with Stress Constraints and Consistent Sensitivity Analysis. In 53rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference https://doi.org/10.2514/6.2012-1358