Philippe Le Grognec

An enriched 1D finite element for the buckling analysis of sandwich beam-columns

Sandwich constructions have been widely used during the last few decades in various practical applications, especially thanks to the attractive compromise between a lightweight and high mechanical properties. Nevertheless, despite the advances achieved to date, buckling still remains a major failure mode for sandwich materials which often fatally leads to collapse. Recently, one of the authors derived closed-form analytical solutions for the buckling analysis of sandwich beam-columns under compression or pure bending. These solutions are based on a specific hybrid formulation where the faces are represented by Euler–Bernoulli beams and the core layer is described as a 2D continuous medium. When considering more complex loadings or non-trivial boundary conditions, closed-form solutions are no more available and one must resort to numerical models. Instead of using a 2D computationally expensive model, the present paper aims at developing an original enriched beam finite element. It is based on the previous analytical formulation, insofar as the skin layers are modeled by Timoshenko beams whereas the displacement fields in the core layer are described by means of hyperbolic functions, in accordance with the modal displacement fields obtained analytically. By using this 1D finite element, linearized buckling analyses are performed for various loading cases, whose results are confronted to either analytical or numerical reference solutions, for validation purposes.

General formulation for local integration in standard elastoplasticity with an arbitrary hardening model

Abstract This paper describes a general method for deriving the plastic corrections and the consistent tangent modulus for a wide range of arbitrary non-linear hardening models within the framework of standard small strains elastoplasticity. The features of the proposed formulation are: (i) the local solution is obtained through an iterative procedure. The plastic corrections are given in closed forms exhibiting one scalar function denoted by Galg and three fourth-order tensors D alg , G alg , L alg , which are shown to be the algorithmic discrete counterparts of usual theoretical continuum quantities, (ii) the consistent tangent modulus has a symmetrical expression involving the same quantities. Finite element computations are performed using a particular non-linear kinematic hardening model and allow to exhibit the ratcheting phenomenon usually observed on mechanical components subjected to cyclic loadings.

Etude numérique et semi-analytique de la nocivité de défauts dans les coques sphériques

Dans ce travail, on s’intéresse à la nocivité des défauts rencontrés dans les équipements sous pression sphériques, dont le comportement en présence de fissures est encore peu connu. La méthode des éléments finis permet d’évaluer la nocivité d’un défaut en fonction de sa taille et des caractéristiques géométriques de la pièce, dans l’hypothèse d’un comportement élastique. Ensuite, grâce au principe de superposition, on peut développer le champ des contraintes au voisinage du défaut sous une forme polynomiale et tabuler ainsi les résultats en fonction d’un éventail de configurations, tout en couvrant la plupart des cas réels de chargement. Enfin, l’utilisation d’approches semi-analytiques de type A16 ou R6 permet d’obtenir de manière efficace une mesure approchée de la nocivité des défauts en plasticité.

Plastic Bifurcation of Thin-Walled Members: Thin Shell Elements vs. GBT-Based Beam Elements

In this paper, one compares plastic bifurcation results concerning thin-walled members made of non-linear elastic-plastic materials, which are obtained by means of two independent approaches, namely (i) a Total Lagrangian thin shell finite element formulation, developed by the second author, and (ii) a computationally efficient beam formulation based on Generalised Beam Theory (GBT), developed by the remaining two authors it is worth mentioning that the latter neglects the effect of pre-buckling deflections. Initially, one addresses the fundamental concepts, procedures and underlying assumptions involved in the application of the above two formulations, focusing on the similarities and differences existing between them. Then, one presents and thoroughly discusses a set of numerical results, determined through analyses based on the two alternative approaches and concerning (i) aluminium lipped channel and (ii) stainless steel rectangular hollow section (RHS) thin-walled columns (i.e., uniformly compressed members). In the first case, a very good correlation was found between the results (bifurcation loads/stresses and buckling mode shapes) yielded by the two formulations (e.g., see Fig. 1). In the second case, a non negligible discrepancy was observed, as the bifurcation loads provided by the shell formulation consistently lay below the GBT values and the differences, due to the combined influence of relevant pre-buckling deflection and a high imperfectionsensitivity, reached 19% however, the RHS buckling mode shapes exhibited again an excellent agreement. Open image in new window Figure 1 Plastic distortional buckling mode shapes of a lipped channel column of length L=55cm (sheel FEA and GBT).