Upper and lower bound limit analysis of plates using FEM and second-order cone programming

Abstract

Published paperLe, C.V., Nguyen-Xuan, H. and Nguyen-Dang, H. (2010) in which the pressure is equilibrated by corner loads only, ensuring that exact equilibrium relations associated with a uniform pressure can be obtained. Once the displacement or moment fields are approximated and the bound theorems applied, limit analysis becomes a problem of optimization. In this paper, the optimization problems are formulated in the form of a standard second-order cone programming which can be solved using highly efficient interior point solvers.The procedures are tested by applying it to several benchmark plate problems and are found good agreement between the present upper and lower bound solutions and results in the literature.Key words: Limit analysis, upper and lower bounds, displacement and equilibrium models, criterion of mean, second order cone programming

RETRACTED ARTICLE: A limit analysis of Mindlin plates using the cell-based smoothed triangular element CS-MIN3 and second-order cone programming (SOCP)

“…For the Kirchhoff plates, we can list the works by Christiansen and Larsen [28], Turco and Caracciolo [29], Corradi and Vena [30], Corradi and Panzeri [31], Tran et al [32], Le et al [33][34][35], and Zhou et al [36]. For the Mindlin plates, we can list the works by Capsoni and Corradi [37] and Capsoni and Vicente da Silva [38].…”

A cell‐based smoothed finite element method for kinematic limit analysis

“…In fact, most commonly used yield criteria can be cast in the form of conic constraints, and optimization problems involving such constraints can be solved using highly efficient primal-dual interiorpoint solvers [41]. Consequently, several numerical limit analysis procedures which involve the use of cone programming techniques have been reported recently [5,15,[42][43][44].…”

Topology Optimization Considering Limit Analysis

“…Moreover, the solution is proved to be global and independent of initial steps [46,50]. Therefore, secondorder cone programming has been widely adopted on limit analysis in order to provide solutions efficiently and permit the experimentation on more complex numerical examples [31,51,52,53].…”

“…Alternatively, a linear interpolation of the stress field may be used. In this case, 31) in which ϕ i is the shape function corresponding to the i th node of the element, the same used in the velocity interpolation [35,36]; and, for instance, σ i xx is σ xx at the element i th node.…”

“…Limit analysis is based on set of fundamental collapse theorems of plasticity [19,20], and it is applicable for a great variety of problems such as plane stress and plane strain [21,22,23,24]; trusses [25]; frames [26,27,28,29]; bending plates [30,31,32]; and three dimensional models [33,34]. Finite element discretization is adopted in most of these works [35,36,37], but it has been shown [38] that the element-free Galerkin approach [39] and the boundary element approach [40,41] are also possible.…”