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陈莘莘 刘应华 岑章志. 极限下限分析的正交基无网格伽辽金法[J]. 力学学报, 2007, 23(5): 633-640. DOI:10.6052/0459-1879-2007-5-2006-567
引用本文: 陈莘莘 刘应华 岑章志. 极限下限分析的正交基无网格伽辽金法[J]. 力学学报, 2007, 23(5): 633-640.DOI:10.6052/0459-1879-2007-5-2006-567
Shenshen Chen, Yinghua Liu, Zhangzhi Cen. Lower bound limit analysis by using the element-free galerkin method with orthogonal basis[J]. Chinese Journal of Theoretical and Applied Mechanics, 2007, 23(5): 633-640. DOI:10.6052/0459-1879-2007-5-2006-567
Citation: Shenshen Chen, Yinghua Liu, Zhangzhi Cen. Lower bound limit analysis by using the element-free galerkin method with orthogonal basis[J].Chinese Journal of Theoretical and Applied Mechanics, 2007, 23(5): 633-640.DOI:10.6052/0459-1879-2007-5-2006-567

极限下限分析的正交基无网格伽辽金法

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

  • 摘要:基于极限分析的下限定理,建立了用正交基无单元Galerkin法进行理想弹塑性结构极限分析的整套求解算法.下限分析所需的虚拟弹性应力场可由正交基无单元Galerkin法直接得到,所需的自平衡应力场由一组带有待定系数的自平衡应力场基矢量的线性组合进行模拟.这些自平衡应力场基矢量可由弹塑性增量分析中的平衡迭代得到.通过对自平衡应力场子空间的不断修正,整个问题的求解将化为一系列非线性数学规划子问题,并通过复合形法进行求解.算例表明该方法有效地克服了维数障碍问题,使计算效率得到了充分的提高,是切实可行的.

    Abstract: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.

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