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Intrinsic formulation of compatibility conditions in nonlinear shell theory. (English) Zbl 1210.74118

Summary: Using the polar decomposition \(RU\) of the deformation gradient of a shell midsurface and studying the variations of \(R\), we introduce new shell variables. These variables simplify remarkably the differential calculus over a surface. So, we obtain an explicit form of the compatibility conditions satisfied by the membrane strain tensor \(E\) and the curvature strain tensor \(K\). Moreover, these equations are decomposed into a first order differential system. To end the article we show how to obtain the deformed surface when the strain tensors are given.

MSC:

74K25 Shells
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