基于二次移动单元的边界点法解弹性力学问题

边界点法是一种结合基本解法和边界元法二者优点的新的边界型无网格数值方法.将边界点法推广到弹性力学问题的数值求解中,在边界点法原有的常数移动单元基础上，引入了二次移动单元，解决了后处理过程中由于近奇异性而产生的边界附近应力的计算精度问题以及薄壁构件的分析问题.用改进的边界点法对弹性力学平面问题的典型算例进行了分析，结果表明数值解与精确解吻合良好.

Boundary Point Method Based on Quadratic Moving Elements for Elasticity

The boundary point method(BPM)is a newly developed boundary-type meshless method with favorable features of both the method of fundamental solution(MFS)and the boundary element method (BEM).The present paper extends the BPM to the numerical analysis of linear elasticity.In order to improve accuracy of stresses near boundaries due to the near singularity in post-processing and in the analysis of thin-wall structures,quadratic moving elements are introduced into BPM in addition to the original constant moving elements.Numerical tests are carried out with benchmark examples in the two-dimensional elasticity.Good agreement is observed between the numerical results and the rigorous solutions.