Optimal design in elasticity and plasticity

Gilbert Strang, Robert V. Kohn

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)183-188
Number of pages6
JournalInternational Journal for Numerical Methods in Engineering
Issue number1
StatePublished - Jan 1986

ASJC Scopus subject areas

  • Numerical Analysis
  • General Engineering
  • Applied Mathematics


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