Éléments finis pour le calcul à la rupture des structures de coque

National audienceLes approches statique et cinématique du calcul à la rupture dans le cadre d'une modélisation de type coque sont mises en oeuvre numériquement par la méthode des éléments finis. La formulation statique en efforts généralisés ou cinématique en vitesse virtuelle reposent sur la superposition d'un élément de membrane et d'un élément de plaque en flexion. L'écriture du critère de résistance généralisé par intégration du critère local dans l'épaisseur permet de formuler les problèmes d'optimisation dans le cadre de la programmation conique pour laquelle existent des solveurs performants tels que MOSEK

Limit design of axisymmetric shells with application to cellular cofferdams

This paper is devoted to the limit design of cellular cofferdams that are regarded as mixed structures where the backfill is modeled as a three-dimensional continuum, while the surrounding sheet pile wall is treated as a cylindrical shell. Dealing with this structure from a static point of view, it turns out that the problem under consideration requires the calculation of the ultimate load value of a circular cylindrical shell subjected to a linearly varying pressure distribution representing the thrust of the backfill material. Extending the results of previous works, a complete solution to this problem is developed for different boundary conditions. The corresponding results are discussed, notably the influence of the shell relative thickness. They are applied to the design of a single cellular cofferdam whose stability under gravity forces is examined, with the strength of the granular backfill material being described by a Mohr-Coulomb criterion

Bearing capacity of a foundation resting on a soil improved by a group of columns

A new design method for a foundation on a soil reinforced by columns is described. A lower bound of the bearing capacity is determined within the framework of the yield design theory. It takes into account the three-dimensional nature of the problem and is applicable to a wide range of geometries. A parametric study on the improvement of the bearing capacity as a function of the proportion of reinforcement, and on the strength characteristics, is presented. A complete analytical solution is given for the strength of a composite cell subjected to a triaxial loading, which provides an insight into the reinforcement mechanism

Stability analysis of homogenized stone column reinforced foundations using a numerical yield design approach

International audienceThis paper deals with the ultimate bearing capacity of soft clayey soils, rein-forced by stone columns, analyzed in the framework of the yield design theory. Since such geotechnical structures are almost impossible to analyze directly due to the strong heterogeneity of the reinforced soil, an alternative homogenization approach is advocated here. First, numerical lower and upper bound estimates for the macroscopic strength criterion of the stone column reinforced soil are approximated in a rigorous way with convex ellipsoidal sets, which makes the approximated criteria much easier to handle than the initial ones. Then, both static and kinematic approaches are carried out numerically on the homoge-nized problem using the above approximated macroscopic strength domains in an adapted finite element method. The whole numerical procedure is applied on one classical geotechnical problem: the ultimate bearing capacity of stone column reinforced foundations. The strength capacity of the structure is rigor-ously framed and the efficiency of the proposed numerical method is highlighted in terms of accuracy and calculation time

Bearing capacity of a foundation resting on a soil improved by a group of columns

A new design method for a foundation on a soil reinforced by columns is described. A lower bound of the bearing capacity is determined within the framework of the yield design theory. It takes into account the three-dimensional nature of the problem and is applicable to a wide range of geometries. A parametric study on the improvement of the bearing capacity as a function of the proportion of reinforcement, and on the strength characteristics, is presented. A complete analytical solution is given for the strength of a composite cell subjected to a triaxial loading, which provides an insight into the reinforcement mechanism

Application of mixed formulations of quasi-reversibility to solve ill-posed problems for heat and wave equations: the 1d case

International audienceIn this paper we address some ill-posed problems involving the heat or the wave equation in one dimension, in particular the backward heat equation and the heat/wave equation with lateral Cauchy data. The main objective is to introduce some variational mixed formulations of quasi-reversibility which enable us to solve these ill-posed problems by using some classical La-grange finite elements. The inverse obstacle problems with initial condition and lateral Cauchy data for heat/wave equation are also considered, by using an elementary level set method combined with the quasi-reversibility method. Some numerical experiments are presented to illustrate the feasibility for our strategy in all those situations. 1. Introduction. The method of quasi-reversibility has now a quite long history since the pioneering book of Latt es and Lions in 1967 [1]. The original idea of these authors was, starting from an ill-posed problem which satisfies the uniqueness property, to introduce a perturbation of such problem involving a small positive parameter ε. This perturbation has essentially two effects. Firstly the perturbation transforms the initial ill-posed problem into a well-posed one for any ε, secondly the solution to such problem converges to the solution (if it exists) to the initial ill-posed problem when ε tends to 0. Generally, the ill-posedness in the initial problem is due to unsuitable boundary conditions. As typical examples of linear ill-posed problems one may think of the backward heat equation, that is the initial condition is replaced by a final condition, or the heat or wave equations with lateral Cauchy data, that is the usual Dirichlet or Neumann boundary condition on the boundary of the domain is replaced by a pair of Dirichlet and Neumann boundary conditions on the same subpart of the boundary, no data being prescribed on the complementary part of the boundary

Renforcement des sols et des roches par inclusions : de la modélisation mécanique au calcul des ouvrages.

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Comportement élastique non linéaire macroscopique d'un matériau comportant un réseau de joints

S'appuyant sur la définition du comportement élastique en transformation finie d'un milieu multicouche à partir de son potentiel macroscopique, on aboutit par passage à la limite du modèle multicouche, à la formulation en transformation infinitésimale macroscopique d'une loi de comportement élastique non linéaire. Cette non-linéarité provient des grandes déformations que subit localement le matériau constitutif des joints dont on fait simultanément tendre l'épaisseur vers zéro. Ce modèle est appliqué aux massifs rocheux fracturés dont on fait clairement apparaître l'anisotropie élastique induite par la direction préférentielle des joints