变宽度板在拉伸和弯曲作用下的三维应力集中

根据一种修正的余能原理，建立了具有一个无外力圆柱面的三维杂交应力元，元内假定应力场满足三维柱坐标表示的平衡方程及无外力圆柱面上的外力边界条件；当元退化为二维时，也满足协调条件。单元位移场选择与相邻单元协调。数值算例表明这种特殊杂交应力元在相当粗的网格下，能十分有效地分析变宽度薄／厚板在拉伸与弯曲作用下的三维(及二维)应力集中。

Three-Dimensional Stress Concentration in Fillets under Tension and Bending

A kind of 12-node solid finite element with one traction-free cylindrical surface is developed based on the modified complementary energy principle. Cylindrical coordinates are used so that the assumed stresses satisfy the equilibrium equate as well as the traction-free condition over the cylindrical boundary. In the limiting case of two-dimensional problem of plane stress, the assumed stresses also satisfy the compatibility conditions. The two-dimensional and three-dimensional stress concentration of thin and thick fillets under tension and pure bending are analysed by using the present special hybrid stress elements. The results indicate that the present special solid finite elements are far superior in predicting the distributions of the circumferential stresses and the stress concentration factors for a series of fillets.