Elastoplastic topology optimization of cyclically loaded structures via direct methods for shakedown

For the first time, the lower bound shakedown theorem is integrated into a level set–based topology optimization framework to identify lightweight elastoplastic designs. Shakedown is a cyclic elastoplastic behavior in which, upon cycling beyond the elastic limit, the accumulation of plastic strain a...

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Bibliographic Details
Published inStructural and multidisciplinary optimization Vol. 64; no. 1; pp. 189 - 217
Main Authors Boissier, Mathilde, Deaton, Joshua D., Beran, Philip A., Vermaak, Natasha
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.07.2021
Springer Nature B.V
Springer Verlag
Subjects
Computational Mathematics and Numerical Analysis
Design
Elastic deformation
Elastic limit
Elastic recovery
Elasticity
Elastoplasticity
Engineering
Engineering Design
Lower bounds
Mathematics
Mechanics
Numerical Analysis
Optimization
Optimization and Control
Partial differential equations
Physics
Plastic deformation
Research Paper
Strain
Theoretical and Applied Mechanics
Topology optimization
Weight reduction
Direct method
Elastoplastic
Shakedown
Level set method
Shape optimization
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Summary:For the first time, the lower bound shakedown theorem is integrated into a level set–based topology optimization framework to identify lightweight elastoplastic designs. Shakedown is a cyclic elastoplastic behavior in which, upon cycling beyond the elastic limit, the accumulation of plastic strain arrests and purely elastic behavior is recovered. In contrast to most elastoplastic topology optimization, the use of a lower bound shakedown limit allows elastoplastic shakedown limits to be rigorously estimated using only the elastic solution. Under small deformation assumptions, this amounts to solving one simple partial differential equation, avoiding the non-linearity associated with plasticity, and thus simplifying the resolution process. Numerical results are provided for several benchmark examples. The results highlight the design performance enhancements attributed to allowing elastoplastic shakedown to occur instead of designing to first yield. In particular, up to 10% reduction in weight is found for the simple structures considered.
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ISSN:1615-147X
1615-1488
DOI:10.1007/s00158-021-02875-6