基于m法的横向受荷桩无网格伽辽金分析

基于横向受荷桩m法控制微分方程的等效积分弱形式,对桩挠度函数采用移动最小二乘近似函数进行插值,采用罚因子法施加本质边界条件,进一步研究无网格伽辽金法(EFGM)在层状地基中横向受荷桩问题中的应用。利用MATLAB语言编制出相应的无网格计算程序对单层地基横向受荷桩进行计算,算例结果与幂级数解吻合良好,同时讨论了无网格伽辽金方法中的权函数和积分方案对计算结果的影响。最后,双层地基横向受荷桩的算例表明,无网格伽辽金方法适用于分析层状地基中的横向受荷桩,其具有不需要划分单元,前后处理方便,计算精度高的优点。

Analysis of Lateral Loaded Piles by Element-free Galerkin Method Based on Elastic Foundation Coefficient "m" Method

The Element-Free Galerkin Method(EFGM) was extended for application of lateral loaded piles in layered foundation using the moving least-square approximation to interpolate deflection variables based on the equivalent integral weak form of the governing differential equation according to the elastic foundation coefficient "m" method of lateral loaded piles.The penalty factor was used to impose the essential boundary condition.An EFGM calculation program was developed for calculation of the lateral loaded piles in single-layered foundation.Results of EFGM are in accord with power series solution.The influences of the different weight functions and integral methods on the accuracy were also investigated.An example of lateral loaded piles in double-layered foundation was given,whose results show that lateral loaded piles in layered foundation can be successfully analyzed by EFGM.The presented method is no need to make element division,its preprocess and post-process are easy,and high accuracy can be achieved.