Eric Florentin

Evaluation of the local quality of stresses in 3D finite element analysis

This article deals with the local quality on stresses produced during finite element analysis in 3D linear elasticity. We use an estimation technique based on the concept of error in constitutive relation, which yields excellent estimates of the local errors without requiring the approximate calculation of Green functions.

A simple estimator for stress errors dedicated to large elastic finite element simulations

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....

Error bounds on outputs of interest for linear stochastic problems.

This work deals with outputs of interest for linear elastic F.E. analysis in the presence of uncertainties (material, loads...). The objective of this paper is precisely to develop tools for the assessment of linear stochastic models. Our approach relies on an extension of the constitutive relation error method, which is a very effective verification tool in the deterministic case. In order to obtain bounds of outputs of interest, one must solve an adjoint problem. In order to do that, one must build for the direct and adjoint problems an associated admissible displacement-stress pair. Then, bounds corresponding to a given level of certainty can be calculated. Theses bounds take into account the errors due to the finite element discretization as well as the errors due to the stochastic approximation method.

Accuracy and Robustness Analysis of Geometric Finite Element Model Updating Approach for Material Parameters Identification in Transient Dynamic

We study the accuracy and the robustness of the Geometrical Finite Element Model Updating method proposed in Touzeau et al. [Touzeau, C., Magnain, B., Emile, B., Laurent, H. and Florentin, E. (2016) “Identification in transient dynamic using a geometry-based cost function in finite element model updating method,” Finite Elements Anal. Des. 122, 49–60]. In this work, the method is applied to transient dynamic in finite transformations to identify mechanical material parameters. A stochastic approach is performed to determine accuracy and robustness. The method is illustrated on numerical test cases and compared to a classical FEMU method. Uncertainties on the loading are taken into account in the identification using an original approach.