Lower bound limit analysis by using the element-free galerkin method with orthogonal basis

The limit analysis of structures is a very usefulin plasticity, which can determine the load-carrying capacityof structures and provide a theoretical foundation necessary forengineering design. The elasto-plastic incremental analysis is moregeneral and yields more information often at higher computational effort.But, in many practical engineering problems, only limit loads and collapsemodes are important, and the stress and strain field histories are notrequired. In order to avoid the complicated computations ofelasto-plastic incremental analysis, the limit analysis is an appealing directmethod for determining the load-carrying capacity.Based on the lower bound theorem of limit analysis, a solution procedure forlimit analysis of structures made of elasto-perfectly plastic material ispresented firstly making use of element free Galerkin (EFG) method withorthogonal basis. The numerical implementation is very simple and convenientbecause it is only necessary to construct an array of nodes in the domainunder consideration. In addition, the orthogonal basis functions areconstructed in the moving least squares (MLS) approximation so that the matrixinversion at each quadrature point is avoided. The elastic stress field forlower bound limit analysis can be computed directly by using the EFG methodwith orthogonal basis. The self-equilibrium stress field is expressed bylinear combination of several self-equilibrium stress basis vectors withparameters to be determined. These self-equilibrium stress basis vectors aredetermined by an equilibrium iteration procedure during the elasto-plasticincremental analysis. Through modifying the self-equilibrium stress subspacecontinuously, the whole solution process of the problem is reduced toseveral sub-problems of nonlinear programming. The complex method is used tosolve these nonlinear programming sub-problems and determine the maximalload amplifier. Numerical examples show that the present method overcomesthe dimension obstacle and improves the computational efficiency of the limitanalysis.