Numerical study of a relaxed variational problem from optimal design

Jonathan Goodman, Robert Kohn, Luis Reyna

Research output: Contribution to journalArticle

Abstract

We revisit a well-known problem of optimal design, the placement of two elastic materials in the cross-section of a rod for maximum torsional rigidity. Another interpretation is the arrangement of two viscous fluids in a pipe for maximum flux under Poiseuille flow. The existence theory allows mixing on a microscopic scale, producing composite materials, and solving a relaxed version of the original design problem. This paper demonstrates that relaxation is as important for calculation as it is for existence. We minimize a discretized version of the relaxed problem using Newton's method; each quadratic approximation is solved by a multigrid method. This allows for greater resolution than previously published calculations, which were based on gradient flow.

Original languageEnglish (US)
Pages (from-to)107-127
Number of pages21
JournalComputer Methods in Applied Mechanics and Engineering
Volume57
Issue number1
DOIs
StatePublished - 1986

Fingerprint

multigrid methods
Newton methods
viscous fluids
Newton-Raphson method
laminar flow
rigidity
Rigidity
rods
Pipe
Fluxes
gradients
composite materials
Fluids
cross sections
Composite materials
approximation
Optimal design

ASJC Scopus subject areas

  • Computer Science Applications
  • Computational Mechanics

Cite this

Numerical study of a relaxed variational problem from optimal design. / Goodman, Jonathan; Kohn, Robert; Reyna, Luis.

In: Computer Methods in Applied Mechanics and Engineering, Vol. 57, No. 1, 1986, p. 107-127.

Research output: Contribution to journalArticle

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