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

SoK: Design Tools for Side-Channel-Aware Implementations

Side-channel attacks that leak sensitive information through a computing device's interaction with its physical environment have proven to be a severe threat to devices' security, particularly when adversaries have unfettered physical access to the device. Traditional approaches for leakage detection measure the physical properties of the device. Hence, they cannot be used during the design process and fail to provide root cause analysis. An alternative approach that is gaining traction is to automate leakage detection by modeling the device. The demand to understand the scope, benefits, and limitations of the proposed tools intensifies with the increase in the number of proposals. In this SoK, we classify approaches to automated leakage detection based on the model's source of truth. We classify the existing tools on two main parameters: whether the model includes measurements from a concrete device and the abstraction level of the device specification used for constructing the model. We survey the proposed tools to determine the current knowledge level across the domain and identify open problems. In particular, we highlight the absence of evaluation methodologies and metrics that would compare proposals' effectiveness from across the domain. We believe that our results help practitioners who want to use automated leakage detection and researchers interested in advancing the knowledge and improving automated leakage detection

Speeding up Simplification of Polygonal Curves using Nested Approximations

We develop a multiresolution approach to the problem of polygonal curve approximation. We show theoretically and experimentally that, if the simplification algorithm A used between any two successive levels of resolution satisfies some conditions, the multiresolution algorithm MR will have a complexity lower than the complexity of A. In particular, we show that if A has a O(N2/K) complexity (the complexity of a reduced search dynamic solution approach), where N and K are respectively the initial and the final number of segments, the complexity of MR is in O(N).We experimentally compare the outcomes of MR with those of the optimal "full search" dynamic programming solution and of classical merge and split approaches. The experimental evaluations confirm the theoretical derivations and show that the proposed approach evaluated on 2D coastal maps either shows a lower complexity or provides polygonal approximations closer to the initial curves.Comment: 12 pages + figure

Homogenization and seismic assessment : review and recent trends

The mechanics of masonry structures has been for long underdeveloped in comparison with other fields of knowledge. Presently, non-linear analysis is a popular field in masonry research and advanced computer codes are available for researchers and practitioners. The chapter presents a discussion of masonry behaviour and clarifies how to obtain the non-linear data required by the computations. The chapter also addresses different homogenisation techniques available in the literature in the linear and rigid-plastic case, aiming at defining a catalogue and at discussing the advantages and disadvantages of the different approaches. Special attention is given to stress assumed models based either on a polynomial expansion of the micro-stress field or in the discretization of the unit cell by means of a few constant stress finite elements CST with joints reduced to interfaces. Finally, the aspects of seismic assessment are presented and case studies involving the use of macro-block analysis, static (pushover) analysis and time integration analysis are discussed.(undefined

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