Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



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.

References [Enhancements On Off] (What's this?)

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DOI: https://doi.org/10.1090/qam/1012271
Article copyright: © Copyright 1989 American Mathematical Society

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