Displaying similar documents to “A phase-field model for compliance shape optimization in nonlinear elasticity”

A phase-field model for compliance shape optimization in nonlinear elasticity

Patrick Penzler, Martin Rumpf, Benedikt Wirth (2012)

ESAIM: Control, Optimisation and Calculus of Variations

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Shape optimization of mechanical devices is investigated in the context of large, geometrically strongly nonlinear deformations and nonlinear hyperelastic constitutive laws. A weighted sum of the structure compliance, its weight, and its surface area are minimized. The resulting nonlinear elastic optimization problem differs significantly from classical shape optimization in linearized elasticity. Indeed, there exist different definitions for the compliance: the change in potential energy...

A phase-field model for compliance shape optimization in nonlinear elasticity

Patrick Penzler, Martin Rumpf, Benedikt Wirth (2012)

ESAIM: Control, Optimisation and Calculus of Variations

Similarity:

Shape optimization of mechanical devices is investigated in the context of large, geometrically strongly nonlinear deformations and nonlinear hyperelastic constitutive laws. A weighted sum of the structure compliance, its weight, and its surface area are minimized. The resulting nonlinear elastic optimization problem differs significantly from classical shape optimization in linearized elasticity. Indeed, there exist different definitions for the compliance: the change in potential energy...

Geometrically nonlinear shape-memory polycrystals made from a two-variant material

Robert V. Kohn, Barbara Niethammer (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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Bhattacharya and Kohn have used small-strain (geometrically linear) elasticity to analyze the recoverable strains of shape-memory polycrystals. The adequacy of small-strain theory is open to question, however, since some shape-memory materials recover as much as percent strain. This paper provides the first progress toward an analogous geometrically nonlinear theory. We consider a model problem, involving polycrystals made from a two-variant elastic material in two space dimensions....