RETRACTED ARTICLE: A limit analysis of Mindlin plates using the cell-based smoothed triangular element CS-MIN3 and second-order cone programming (SOCP)

Nguyen-Thoi Trung,Phung-Van Phuc,Le Van Canh

doi:10.1186/2196-1166-1-6

Abstract

The paper presents a numerical procedure for kinematic limit analysis of Mindlin plate governed by von Mises criterion. The cell-based smoothed three-node Mindlin plate element (CS-MIN3) is combined with a second-order cone optimization programming (SOCP) to determine the upper bound limit load of the Mindlin plates. In the CS-MIN3, each triangular element will be divided into three sub-triangles, and in each sub-triangle, the gradient matrices of MIN3 is used to compute the strain rates. Then the gradient smoothing technique on whole the triangular element is used to smooth the strain rates on these three sub-triangles. The limit analysis problem of Mindlin plates is formulated by minimizing the dissipation power subjected to a set of constraints of boundary conditions and unitary external work. For Mindlin plates, the dissipation power is computed on both the middle plane and thickness of the plate. This minimization problem then can be transformed into a form suitable for the optimum solution using the SOCP. The numerical results of some benchmark problems show that the proposal procedure can provide the reliable upper bound collapse multipliers for both thick and thin plates.

Highlights

The paper presents a numerical procedure for kinematic limit analysis of Mindlin plate governed by von Mises criterion
The limit analysis problem of Mindlin plates is formulated by minimizing the dissipation power subjected to a set of constraints of boundary conditions and unitary external work
For Mindlin plates, the dissipation power is computed on both the middle plane and the thickness of the plate

Summary

Introduction

The paper presents a numerical procedure for kinematic limit analysis of Mindlin plate governed by von Mises criterion. Limit analysis is a branch of plasticity analysis and plays an important role in determining the limit loads of a structure. The fundamental theorems of limit analysis ignore the evolutive elastoplastic computations but focus to determine the upper or lower bound loads which cause the plastic collapse of structures. Using analytical methods and different yield criteria such as the maximum principal stress criterion, Tresca criterion, and von Mises criterion, many scholars derived the analytical solutions for the limit loads of plates. Some early works for the limit loads of plates can be mentioned such as those by Hodge and Belytschko [7] and Nguyen [8]. Due to the lack of efficient optimization algorithms and the limit of the computing power, the numerical limit analysis of plates seems to be ignored for a certain times

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