# Airy-based equilibrium mesh-free method for static limit analysis of plane problems

## This paper presents a numerical procedure for lower bound limit analysis of plane problems governed by von Mises yield criterion. The stress fields are calculated based on the Airy function which is approximated using the moving least squares technique. | Vietnam Journal of Mechanics, VAST, Vol. 38, No. 3 (2016), pp. 167 – 179 DOI: AIRY-BASED EQUILIBRIUM MESH-FREE METHOD FOR STATIC LIMIT ANALYSIS OF PLANE PROBLEMS Canh V. Le1,∗ , Phuc L. H. Ho2 , Hoa T. Nguyen3 1 International University, Vietnam National University - Ho Chi Minh City, Vietnam 2 Ho Chi Minh City University of Technology and Education, Vietnam 3 Ho Chi Minh City Open University, Vietnam ∗ E-mail: lvcanh@ Received March 16, 2015 Abstract. This paper presents a numerical procedure for lower bound limit analysis of plane problems governed by von Mises yield criterion. The stress fields are calculated based on the Airy function which is approximated using the moving least squares technique. With the use of the Airy-based equilibrium mesh-free method, equilibrium equations are ensured to be automatically satisfied a priori, and the size of the resulting optimization problem is reduced significantly. Various plane strain and plane stress with arbitrary geometries and boundary conditions are examined to illustrate the performance of the proposed procedure. Keywords: Limit analysis, equilibrium mesh-free method, second-order cone programming, Airy function. 1. INTRODUCTION The estimation of the load required to cause collapse of a body or structure plays an important role in design and assessment the safety of many engineering components and structures. If a suitable approximation for the stress field is used, and the static theorem is applied, a lower-bound on the exact limit load can be obtained. In the framework of equilibrium limit analysis formulation, the assumed stress fields are expressed in terms of spatial coordinates and parameters that are usually associated with nodal stress values. These approximated fields are required to satisfy equilibrium conditions over the problem domain. The equilibrium equations are frequently treated in one of two ways in numerical procedures: (i) equilibrium is enforced at .

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