地基极限承载力的无网格分析

Analysis of the Ultimate Bearing Capacity of Subgrade by Element-Free Galerkin Method

在无网格伽辽金法的基础上,利用应力应变增量形式表征了基于Drucker-Prager屈服准则的土体弹塑性本构关系;在小变形假设的前提下,实现了基于增量本构关系的弹塑性分析的无网格伽辽金法;采用罚参数修正了能量变分方程式,方便地实现了无网格伽辽金法的本质边界条件;并采用Newton-Raphson增量迭代法计算地基土体的极限荷载,其分析结果与静载试验结果吻合较好,验证了本文方法的合理性,进一步拓展了无网格伽辽金法的应用范围.同时与有限元计算结果作了对比研究,体现了无网格法的优越性.

On the basis of the dement-free Galerkin method （EFGM）, the element-free Galerkin method for elasto-plastic analyses was proposed, based on the incremented constitutive equations and the small deformation hypothesis. In this proposed method, the increments of stress and strain were used to characterize the elasto-plastic constitutive relationship of the soil based on the Drucker-Prager yield criterion, and the penalty parameters were adopted to revise the energy variation equations to easily realize the essential boundary conditions in the EFGM, and the modified Newton-Raphson iteration method was used in computation. In this paper, EFGM was used to calculate the ultimate bearing capacity of the subgrade. The good accordance between the results of this method and field plate load tests has shown that the method in,this paper is rational and valid. The application domain of EFGM has been expanded. The results of EFGM and finite element method （FEM） were also compared, which showed the advantages of EFGM.