Shape optimization by homotopy methods with special application to membrane structures

Research output: Contribution to conferencePaperpeer-review

9 Scopus citations

Abstract

The shape optimization of three dimensional membrane and plane stress structures with respect to the minimization of weight or volume is the subject of the contribution. A homotopy method is developed which is derived from the mechanical analogy of homogenous stress fields and minimal surfaces, and from the pull back relation between Cauchy and second Piola Kirchhoff stresses. The method guarantees a positive definite approximation of the Hessian matrix and is insensitive to any scaling. In particularly, it is robust with respect to optimization parameters which do not contribute to the second derivatives of the problem and would otherwise generate singular Hessian matrices. It is, therefore, easy to apply which is demonstrated by several examples, with concentration on the form finding of membrane structures in 3D. In the context of a plane stress problem the behavior of the technique in an adaptive optimization scheme is demonstrated. Extensions to further objectives and constraints as well as to further structures as e.g. free form shells are subject of actual research.

Original languageEnglish
Pages122-130
Number of pages9
DOIs
StatePublished - 1996
Externally publishedYes
Event6th AIAA/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimization, 1996 - Bellevue, United States
Duration: 4 Sep 19966 Sep 1996

Conference

Conference6th AIAA/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimization, 1996
Country/TerritoryUnited States
CityBellevue
Period4/09/966/09/96

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