Limit analysis of plates and slabs using a meshless equilibrium formulation

Abstract

Published paperLe, Canh V., Gilbert, Matthew and Askes, Harm (2010) SUMMARYA meshless Element-Free Galerkin (EFG) equilibrium formulation is proposed to compute the limit loads which can be sustained by plates and slabs. In the formulation pure moment fields are approximated using a moving least squares technique, which means that the resulting fields are smooth over the entire problem domain. There is therefore no need to enforce continuity conditions at interfaces within the problem domain, which would be a key part of a comparable finite element formulation. The collocation method is used to enforce the strong form of the equilibrium equations and a stabilized conforming nodal integration scheme is introduced to eliminate numerical instability problems. The combination of the collocation method and the smoothing technique means that equilibrium only needs to be enforced at the nodes, and stable and accurate solutions can be obtained with minimal computational effort. The von Mises and Nielsen yield criteria which are used in the analysis of plates and slabs respectively are enforced by introducing second-order cone constraints, ensuring that the resulting optimization problem can be solved using efficient interior-point solvers. Finally, the efficacy of the procedure is demonstrated by applying it to various benchmark plate and slab problems.

Limit analysis of cracked structure by combination of extended finite element method with linear matching method

“…where r and  are local crack tip polar coordinates, taking account for the first term concerning with the SIF in crack tip asymptotic displacement fields (Le et al, 2010;Fries & Belytschko, 2010). Enriched nodes near a crack tip could be chosen by various ways.…”

“…Enriched nodes near a crack tip could be chosen by various ways. First, only elements containing a crack tip are completely enriched with singular functions (Le et al, 2010). With this technique, one or more layers of neighboring elements are added to the enriched region, so that its size is increased.…”

“…In order to overcome such a difficulty, some authors raised the mesh adaptive strategies of upper and lower bounds in limit analysis, where assess the convergence based on results of simultaneous upper and lower analysis, leading to the re-meshing for iterative computation (Ciria et al, 2008;Munoz et al, 2009). Some authors suggested the lower-bound limit analysis by using meshless element-free Galerkin (EFG) and non-linear programming that is unlike standard FEM (Chen et al, 2008;Le et al, 2009Le et al, , 2010. Nevertheless, it is widely accepted that XFEM is more effective for crack problem as compared with EFG.…”

Adaptive mesh-free lower bound limit analysis using non-linear programming

“…Chen et al [4] also applied the element-free Galerkin method to the lower bound shakedown analysis of structures under variable repeating loads. Le et al [5,6] used element-free Galerkin method to discretize the moment eld in the limit analysis of plates. Liu and Zhao [7] used the radial point interpolation method and nonlinear programming to develop a technique for upper bound limit analysis of solid structures.…”

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

“…It is known as the stabilized conforming nodal integration (SCNI) scheme. The SCNI scheme has been applied successfully to various problems, for instance, elastic analysis [12][13][14], plastic limit analysis [15], error estimation [16] and a stabilized mesh-free equilibrium model for limit analysis [17]. It is shown that, when the SCNI scheme is applied, the solutions obtained are accurate and stable, and locking problems can also be prevented.…”