Mathematical Elasticity: Three-dimensional elasticity, Volume 1
This volume is a thorough introduction to contemporary research in elasticity, and may be used as a working textbook at the graduate level for courses in pure or applied mathematics or in continuum mechanics. It provides a thorough description (with emphasis on the nonlinear aspects) of the two competing mathematical models of three-dimensional elasticity, together with a mathematical analysis of these models. The book is as self-contained as possible.
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Geometrical and other preliminaries
The equations of equilibrium and the principle
The boundary value problems of threedimensional
A(tr applied body force applied forces applied surface force arbitrary assume assumption Ball boundary condition boundary value problem Cauchy stress tensor Cauchy stress vector Ciarlet condition of place constitutive equation continuous converges convex function defined definition deformed configuration denote density differentiable displacement-traction problem domain elastic material equivalent Exercise existence results F G M3 given Green's formula Hence hyperelastic material implicit function theorem implies inequality injective isotropic lower semi-continuous Lp(fl M3 x M3 mapping matrix minimizer nonlinear normed vector space notation open set open subset orthogonal matrix p(dfl p(fl partial derivatives Piola-Kirchhoff stress tensor polyconvex proof of Theorem pure displacement problem pure traction problem reference configuration relation Remark response function satisfies Sect sequence set fl Show smooth Sobolev space solution St Venant-Kirchhoff material stored energy function strain tensor symmetric tensor field topology vector field Vi/r