摘要
以二维弹性力学自然边界积分方程法为基础建立了二维弹塑性问题的自然边界积分方程 .这种方法从位移导数边界积分方程出发 ,通过适当组合和分部积分 ,将全部和部分边界上张量转换为新的边界张量 ,从而构造出一种新的边界积分方程 .这种新边界积分方程相应的积分核函数在源点处表现为强奇异积分 ,并易于获得其Cauchy主值积分 .自然边界积分方程与位移边界积分方程联合使用可直接获取边界应力 ,大大提高了边界应力的计算精度 .数值结果证实了本文方法的有效性和正确性 .
Based on the natural boundary integral equation for two dimensional elasticity, a corresponding elasto plastic formulation is presented in this paper. The boundary displacements, traction and displacement derivatives are transformed into a set of new boundary variables in terms of tedious manipulation. It produces a new derivative: BIEs. Natural BIEs only contain the strongly singular integrals, which are easily evaluated, instead of the originally hypersingular integrals. They can be managed to obtain the same accurate boundary stresses as the displacement together with the displacement BIEs. Further application of natural BIEs to elasto plastic problems is presented. The numerical results demonstrate the efficiency and the correctness of the present formulation.
基金
国家自然科学基金资助项目 ( 10 2 72 0 3 9)
