On the performance of non‐conforming finite elements for the upper bound limit analysis of plates

Abstract

This is a preprint version of an article accepted for publication in International Journal for Numerical Methods in Engineering Copyright © 2012 John Wiley & Sons, Ltd.International audienceIn this paper, the upper bound limit analysis of thin plates in bending is addressed using various types of triangular finite elements for the generation of velocity fields and second order cone programming (SOCP) for the minimization problem. Three different C1-discontinuous finite elements are considered : the quadratic 6 node Lagrange triangle (T6), an enhanced T6 element with a cubic bubble function at centroid (T6b) and the cubic Hermite triangle (H3). Through numerical examples involving Johansen and von Mises yield criteria, it is shown that cubic elements (H3) give far better results in terms of convergence rate and precision than fully conforming elements found in the literature, especially for problems involving clamped boundaries

Locking‐free discontinuous finite elements for the upper bound yield design of thick plates

“…Contrary to what was obtained in [10], this element actually converges to the exact thin plate limit load when refining the mesh, confirming the results of [32]. The results presented in [10] have indeed been improved by fixing an error present in the initial numerical code which yielded a very poor convergence rate. Moreover, theoretical Γ−convergence results for this quadratic thin plate element are currently investigated.…”

“…In this context, the plate is assumed to be infinitely resistant to membrane forces, so that the in-plane membrane strains must be equal to zero. See [10,19] for more details.…”

“…It has been shown that discontinuous elements can give good estimates of the true collapse load with a relatively coarse mesh. Recently, Bleyer et al [10] have proposed various types of discontinuous finite elements for plate bending, where the transversal velocity is continuous but its derivative (the rotation field) is not. The method can provide more accurate upper bound solutions compared with other element-based formulations for kinematic limit analysis of thin plate problems.…”

Upper bound limit analysis of plates using a rotation-free isogeometric approach

“…Nowadays, limit analysis has become a well-known tool for assessing the safety load factor of engineering structures as an efficient direct method. Due to limitation of analytical methods, various numerical approaches such as finite element methods (FEM) [1][2][3][4][5][6], meshfree methods [7,8], and natural element method [9], just to mention a few, have therefore been developed.…”

“…However, most of the yield criteria for plates can be formed as an intersection of cones for which the limit analysis problem can be solved efficiently by the primal-dual interior point method [10,11] implemented in the MOSEK software package [12]. This algorithm was proved to be a very effective optimization tool for the limit analysis of structures [4,6,7,[13][14][15][16], and therefore it will be used in our study.…”