NDLI: Γ-convergence for incompressible elastic plates

Content Provider	Springer Nature Link
Author	Dolzmann, Georg Conti, Sergio
Copyright Year	2008
Abstract	We derive a two-dimensional model for elastic plates as a Γ-limit of three-dimensional nonlinear elasticity with the constraint of incompressibility. The resulting model describes plate bending, and is determined from the isochoric elastic moduli of the three-dimensional problem. Without the constraint of incompressibility, a plate theory was first derived by Friesecke et al. (Comm Pure Appl Math 55:1461–1506, 2002). We extend their result to the case of p growth at infinity with p ϵ [1, 2), and to the case of incompressible materials. The main difficulty is the construction of a recovery sequence which satisfies the nonlinear constraint pointwise. One main ingredient is the density of smooth isometries in W 2,2 isometries, which was obtained by Pakzad (J Differ Geom 66:47–69, 2004) for convex domains and by Hornung (Comptes Rendus Mathematique 346:189–192, 2008) for piecewise C 1 domains.
Ending Page	551
Page Count	21
Starting Page	531
File Format	PDF
ISSN	09442669
e-ISSN	14320835
Journal	Calculus of Variations and Partial Differential Equations
Issue Number	4
Volume Number	34
Language	English
Publisher	Springer-Verlag
Publisher Date	2008-07-18
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Methods involving semicontinuity and convergence; relaxation Calculus of Variations and Optimal Control; Optimization Systems Theory, Control Mathematical and Computational Physics Analysis Plates
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Analysis

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