Error estimation for adaptive computations on shell structures

Abstract

The finite element discretization of a shell structure introduces two kinds of errors: the error in the functional approximation and the error in the geometry approximation. The first is associated with the finite dimensional interpolation space and is present in any finite element computation. The latter is associated with the piecewise polynomial approximation of a curved surface and is much more relevant in shell problems than in any other standard 2D or 3D computation. In this work, a residual type error estimator introduced for standard finite element analysis is generalized to shell problems. This allows easily to account for the real original geometry of the problem in the error estimation procedure and precludes the necessity of comparing generalized stress components between non coplanar elements. That is, the main drawbacks of flux projection error estimators are avoided.