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We present several applications for 2D or axisymmetric elasticity problems of a method to control the quality of a finite element computation, and to optimize the choice of meshes. The method used, which is very general, is based (i) on the concept of error in constitutive relation and (ii) on explicit techniques to construct admissible fields. Illustrative examples are shown for several 2D or axisymmetric elements (3 or 6 node triangles, 4 or 8 node quadrilaterals). They have been achieved with our code ESTEREF, a post‐processor of error computation and mesh optimization which can be interfaced with any finite element code.

The purpose of this paper is to acquire strict upper and lower bounds on quantities of slender beams on Winkler foundation in finite element analysis.

It leans on the dual analysis wherein the constitutive relation error (CRE) is used to perform goal-oriented error estimation. Due to the coupling of the displacement field and the stress field in the equilibrium equations of the beam, the prolongation condition for the stress field which is the key ingredient of CRE estimation is not directly applicable. To circumvent this difficulty, an approximate problem and the solution thereof are introduced, enabling the CRE estimation to proceed. It is shown that the strict bounding property for CRE estimation is preserved and strict bounds of quantities of the beam are obtainable thereafter.

Numerical examples are presented to validate the strict upper and lower bounds for quantities of beams on elastic foundation by dual analysis.

This paper deals with one-dimensional (1D) beams on Winkler foundation. Nevertheless, the present work can be naturally extended to analysis of shells and 2D and 3D reaction-diffusion problems for future research.

CRE estimation is extended to analysis of beams on elastic foundation by a decoupling strategy; strict upper bounds of global energy norm error for beams on elastic foundation are obtained; strict bounds of quantities for beams on elastic foundation are also obtained; unified representation and corresponding dual analysis of various quantities of the beam are presented; rigorous derivation of admissible stresses for beams is given.

In this paper we present a new method of mesh optimization which automatically accounts for steep gradients. With this method, the user needs no previous knowledge of the problem. The method is based on the concept of error in the constitutive relation, coupled with an h‐version remeshing procedure. The steep gradient regions are detected by using the local errors, which are taken into account using the finite energy element. Consequently the procedure can be extended to all estimators of discretization errors. It is implemented in our code ESTEREF, a post‐processor of error computation and mesh optimization that can be used with any finite element code. Numerous examples show the capabilities of the proposed method.

Presents a modular method for obtaining either a quick or a precise calculation for three‐dimensional structure assemblies with local non‐linearities, such as unilateral contact with friction, or technological components, such as prestressed bolt joints. An iterative method, including a domain‐decomposition technique, is proposed to solve such quasi‐static problems in small perturbations. Two types of entities are introduced: sub‐structures and interfaces. A local and a global stage are successively carried out by an iterative algorithm until convergence. The linear problem in the global stage is solved by a FEM (3D case) or by another approach using Trefftz functions (2D axisymmetrical case). Applications developed with AÉROSPATIALE‐Les Mureaux are presented and concern the study of structure joints with different types of flanges.

A new approach called the “variational theory of complex rays” (VTCR) is developed for calculating the vibrations of weakly damped elastic structures in the medium‐frequency range. Here, the emphasis is put on the most fundamental aspects. The effective quantities (elastic energy, vibration intensity, etc.) are evaluated after solving a small system of equations which does not derive from a finite element discretization of the structure. Numerical examples related to plates show the appeal and the possibilities of the VTCR.

In this paper, we discuss the application of the constitutive relation error (CRE) to model updating and validation in the context of uncertain measurements. First, a parallel is drawn between the CRE method and a general theory for inverse problems proposed by Tarantola. Then, an extension of the classical CRE method considering uncertain measurements is proposed. It is shown that the proposed mechanics‐based approach for model validation is very effective in filtering noise in the experimental data. The method is applied to an industrial structure, the SYLDA5, which is a satellite support for Ariane5. The results demonstrate the robustness of the method in actual industrial situations.

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.

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.

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.

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

An extension of the concept of error on constitutive relation is proposed to the case of Mindlin plate finite element computations. The error of the performed analysis is estimated from the incompatibility in relation with the constitutive equation of admissible fields calculated from the finite element results. In a first stage, loads and moments densities leading to the equilibrium of each element are computed on the element edges as the sums of densities derived from the finite element solution and of densities with a resultant equal to zero on each element edge. Then strictly statically admissible stress resultants are calculated within each element. Both of the two stages allow an optimization for the statically admissible field in order to get a more accurate error. The calculations are local which is very interesting especially in case of complex structure analyses with a large number of degrees of freedom for which adaptivity is an important feature. A set of examples shows the efficiency of the proposed estimator and the good adaptation of the error on constitutive law method to Mindlin plate analysis.

This paper deals with numerical techniques dedicated to the predictive calculation of complex structures undergoing medium‐frequency vibrations. This field presents challenging difficulties. The first difficulty is the development of an efficient computational method because with the traditional finite element method (FEM), as the frequency increases, it becomes more expensive to control the pollution error. The second difficulty is the availability of sufficiently realistic joint models to take into account damping phenomena because in vibration problems dissipation controls the magnitude of the response directly.

We use the Variational Theory of Complex Rays (VTCR), an approach which effectively avoids the difficulties encountered with traditional FE techniques. Using two‐scale shape functions which verify the dynamic equation and the constitutive relation within each substructure, the VTCR can be viewed as a means of expressing the power balance at the different interfaces between substructures in variational form. New joint models which include heterogeneous mass, stiffness and damping are introduced to deal with the second difficulty.

This paper focuses on a new, substructured version of the VTCR which enables us to separate the realistically modeled substructures from the less accurate joints. The equations of the substructures are enforced exactly, whereas the interface equations are verified approximately through the minimization of an L² residual. We show that this new formulation gives good results compared to the traditional VTCR or the FEM.

Although the examples presented in this paper are very simple, this new formulation shoult encounter no difficulties when dealing with more complex assemblies composed of several plates, beams, shells,…

This new, substructured VTCR approach provides more flexibility in the improvement of joint models, for example by carrying out experimental measurements on real structures.

The purpose of this paper is to propose a virtual testing strategy in order to predict damping due to the joints which are present in the ARIANE 5 launcher.

Since engineering finite element codes do not give satisfactory results, either because they are too slow or because they cannot calculate dissipation accurately, a new computational tool is introduced based on the LArge Time INcrement (LATIN) method in its multiscale version.

The capabilities of the new strategy are illustrated on one of the joints of ARIANE 5. The damping predicted virtually is compared to experimental results, and the approach appears promising.

The tool which has been developed gives access to calculations which were previously unaffordable with standard computational codes, which may improve the design process of launchers. The code is transferred into ASTRIUM‐ST, where it is being used to build a database of dissipations in the joints of the ARIANE 5 launcher.