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The von Karman theory for incompressible elastic shells

Friday, May 20, 2011 - 9:30am - 10:00am
Lind 305
Hui Li (University of Minnesota, Twin Cities)
We rigorously derive the von Karman shell theory (and the resulting von Karman equations) for incompressible materials. Our approach is variational and starts from the general nonlinear 3-dimensional elastic energy functional. Our only assumption is that the midsurface of the shell enjoys the following approximation property: C3 first order infinitesimal isometries are dense in the space of all W^{2, 2} infinitesimal isometries. The class of surfaces with this property includes: flat surfaces, convex surfaces, developable surfaces and rotationally invariant surfaces.