中文摘要：

对有限球法（MFS）的基本原理、形函数的构造方法进行阐述.当施加边界条件时,对边界点做了特殊布置,大幅简化了边界条件;选择积分方案时,选择了精度和稳定性都比较高的分段高斯-勒让德积分法,克服了分段中点积分法则带来的稳定性差的问题,并且对该方法中每个积分球划分的份数和每个子区域积分点数的选择给出了建议.通过受轴向拉力杆问题和带孔悬臂柱问题两个数值算例,对有限球法得到的结果和解析解或有限元法得到的结果进行比较,印证了有限球法的有效性.

英文摘要：

The basic principles of finite spheres method and construction method of interpolation function were elaborated.When the boundary conditions imposed,a special arrangement of the nodes on the boundary spheres was performed,which greatly simplifies the scheme.When integration program was considered,piecewise Gauss Legendre quadrature rule was selected,which has relative high precision and stability,overcoming the poor stability problem when using piecewise midpoint quadrature rule.In addition,a suggestion of the partition of each integral sphere and the number of points for each sub region in the integral method was given.Finally,two numerical examples were analyzed,i.e.the problem of a bar with axial tension and perforated cantilever plate problem.The results obtained by the method of finite spheres and results of analytical solution or obtained by the finite element method were compared,showing the effectiveness of the method of finite spheres.