各向异性柱体扭转的充分必要的边界积分方程

A NECESSARY AND SUFFICIENT FORMULATION FOR TORSION PROBLEMS OF ANISOTROPIC BODIES

本文列出了各向异性柱体扭转问题无量纲化后的有关方程和边界条件，推导和验证了基本解，并指出一些书中基本解列式有误［９－１１］．列出了充分必要的边界积分方程，进行了数值计算，并与习用的边界积分方程所得结果进行了比较．表明在退化值附近，习用的边界积分方程所得的边界剪应力会出现巨大的误差，扭转刚度的误差则要小得多，而充要的边界积分方程计算的结果则始终保持良好的精度，再次显示了它的优点．

The non-dimensionalized equations concerned and boundary conditions are presented for the torsion problem of anisotropic cylinders. The error of the fundamental solution cited in some books of boundary element is pointed out after examined the fundamental solution. Furthermore,a necessary and sufficient boundary integral equation is given for the problem and compared with the conventional boundary integral equation. Numerical results show that the error of the boundary shear stresses obtained by the conventional boundary integral equation might be great, where as the error of torsional stiffness is small. Meanwhile, the necessary and sufficient boundary integral equation always gives accurate results.