Error estimation for adaptive computations on shell structures

Author (s): Díez, P., and Huerta, A.
Journal: European Journal of Finite Elements (Revue Européenne des éléments finis)

Volume: 9, Issue 1, 2 i 3,/2000
Pages: 49 – 66
Date: 2000


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 it 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
the shells framework, formerly the quality control of the finite element solution
has been carried out using flux projection a posteriori error estimators. This
technique exhibits two main drawbacks: 1) the flux smoothing averages stress components
over different elements that may have different physical meaning if the tangent
planes are different and 2) the error estimation process uses only the approximate
solution and hence, the discretized forces and the computational mesh: the data
describing the real geometry and load is therefore not accounted for. In this
work, a residual type error estimator introduced for standard 2D finite element
analysis is generalized to shell problems. This allows to easily 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. This estimator is based on approximating a reference error associated
with a refined reference mesh. In order to build up the residual error equation
the computed solution must be represented (projected) on the reference mesh. The
use of thin shell finite elements requires a proper formulation in order to preclude
shear locking. Following an idea of Donea and Lamain, the interpolation of the
rotations is not unique and requires a particular technique to transfer the information
from the computational mesh to the reference mesh. This technique is also developed
in this work and may be used in any adaptive evolution problem where the solution
must be transferred from one mesh to another.



Author = {Huerta, A., and D{\'\i}ez, P.},
Title = {Error estimation for adaptive computations on shell structures}}
FJournal = {Revue europ{\'e}enne des {\'e}l{\'e}ments finis},
Journal = {Journal = {Rev.Europ{\'e}ene  {\'E}l{\'e}m. Finis},
Pages = {49--66},
Volume = {9},
Number = {1,2,3},
Year = {2000}}