含一个无外力圆柱面带转动的三维杂交应力元简

根据一种修正的余能原理，建立了一类具有一个无外力圆柱表面及结点含转动自由度的8 结点新型三维杂交应力元. 单元边界位移场选择二次位移插值函数，且与相邻元协调；单元内假定应力场满足以柱坐标表示的平衡方程及圆柱面上无外力边界条件. 数值算例表明，这种特殊杂交应力元在相当粗的网格下即能十分准确地分析圆弧形槽口附近及曲梁的三维（及二维）的孔边应力分布.

SPECIAL HYBRID STRESS SOLID ELEMENT WITH DRILLING DEGREES OF FREEDOM AND A TRACTION-FREE CIRCULAR BOUNDARY

New 8-node special hybrid stress elements with drilling degrees of freedom have been developed based on the principle of minimum complementary energy. These elements are used jointly with conventional displacement elements for the analysis of stress concentrations around different holes and notches. The assumed stress fields in the elements satisfy the equilibrium equations, the traction-free boundary conditions and the compatibility equations. The examples of these special elements have been shown that these present special elements are far superior in predicting the stress concentration factors, the distributions of circumferential stresses and the normal stress when only very coarse meshes are used near holes and notches.