Abstract
Abstract A direct weight minimization subject to compliance constraints or plastic yielding constraints leads to a non‐convex variational problem. Both the theoretical and the numerical analysis are unsatisfactory: the minimum weight is not achieved by any design, and the approximate designs oscillate as the element mesh is refined. We look for equivalent ‘relaxed problems’ with the same minima. They come from allowing composite materials constructed in an optimal way from the original materials. The constructions are different for elasticity and plasticity, but surprisingly the final relaxed problems are in some cases the same.
Keywords
PlasticityElasticity (physics)Maxima and minimaMinificationFinite element methodMathematical optimizationRegular polygonMathematicsMinimum weightApplied mathematicsOptimal designStructural engineeringMathematical analysisMaterials scienceEngineeringGeometryCombinatoricsComposite material
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Publication Info
- Year
- 1986
- Type
- article
- Volume
- 22
- Issue
- 1
- Pages
- 183-188
- Citations
- 76
- Access
- Closed
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Cite This
Gilbert Strang,
Robert V. Kohn
(1986).
Optimal design in elasticity and plasticity.
International Journal for Numerical Methods in Engineering
, 22
(1)
, 183-188.
https://doi.org/10.1002/nme.1620220113
Identifiers
- DOI
- 10.1002/nme.1620220113