Geometric nonlinearity: potential energy, complementary energy, and the gap function

Authors:
Yang Gao and Gilbert Strang

Journal:
Quart. Appl. Math. **47** (1989), 487-504

MSC:
Primary 73C50; Secondary 49H05, 73B99, 73G05

DOI:
https://doi.org/10.1090/qam/1012271

MathSciNet review:
MR1012271

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Abstract: Dual minimum principles for displacements and stresses are well established for linear variational problems and also for nonlinear (and monotone) constitutive laws. This paper studies the problem of geometric nonlinearity. By introducing a *gap function*, we recover complementary variational principles in the equilibrium problems of mathematical physics. When the gap function is nonnegative those become minimum principles. The theory is based on convex analysis, and the applications made here are to nonlinear mechanics.

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Additional Information

DOI:
https://doi.org/10.1090/qam/1012271

Article copyright:
© Copyright 1989
American Mathematical Society