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

Hung Nguyen-Xuan,Chien Hoang Thai,Jeremy Bleyer,Phu Vinh Nguyen

doi:10.1186/s40540-014-0012-5

Abstract

This paper presents a simple and effective formulation based on a rotation-free isogeometric approach for the assessment of collapse limit loads of plastic thin plates in bending. The formulation relies on the kinematic (or upper bound) theorem and namely B-splines or non-uniform rational B-splines (NURBS), resulting in both exactly geometric representation and high-order approximations. Only one deflection variable (without rotational degrees of freedom) is used for each control point. This allows us to design the resulting optimization problem with a minimum size that is very useful to solve large-scale plate problems. The optimization formulation of limit analysis is transformed into the form of a second-order cone programming problem so that it can be solved using highly efficient interior-point solvers. Several numerical examples are given to demonstrate reliability and effectiveness of the present method in comparison with other published methods.

Highlights

This paper presents a simple and effective formulation based on a rotation-free isogeometric approach for the assessment of collapse limit loads of plastic thin plates in bending
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]
Results and discussion we examine the performance of the present approach through the limit analysis of beams and plates

Summary

Introduction

This paper presents a simple and effective formulation based on a rotation-free isogeometric approach for the assessment of collapse limit loads of plastic thin plates in bending. 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 it will be used in our study

Methods

Results

Conclusion