A simple estimator for stress errors dedicated to large elastic finite element simulations: Locally reinforced stress construction

Abstract

Purpose

This paper aims to deal with the verification of local quantities of interest obtained through linear elastic finite element analysis. A technique is presented for determining the most accurate error estimation. This technique enables one to address industrial‐size problems while keeping computing costs reasonable.

Design/methodology/approach

The concept of error in constitutive relation is used to assess the quality of the finite element solution. The key issue is the construction of admissible fields. The objective is to show that it is possible to build admissible fields using a new method. These fields are obtained by using a high‐quality construction over a limited zone while the construction is less refined and less expensive elsewhere.

Findings

Numerical tests are presented in order to illustrate a very satisfying presented methodology. It shows clearly how to take advantage of the method to treat large examples. They clearly show the interest of this new method to treat large examples.

Originality/value

The paper demonstrates clearly that verification of large finite element problem must have dedicated methods in order to be applicable.

Citation

Florentin, E., Guinard, S. and Pasquet, P. (2011), "A simple estimator for stress errors dedicated to large elastic finite element simulations: Locally reinforced stress construction", Engineering Computations, Vol. 28 No. 1, pp. 76-92. https://doi.org/10.1108/02644401111097037