One fundamental aspect of the modelling of shells is the geometry of the submanifold which describes the mean surface. Recent developments in the use of oriented boundary distance functions have led to a completely intrinsic differential calculus on submanifolds. This makes it possible to develop new intrinsic models of shells and express classical models in terms of intrinsic differential operators. It reduces the complexity of the models and yields equations which are (mathematically more tractable. Our techniques naturally extend to nonlinear equations and other rheological laws.
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