一类新的具有无外力圆柱表面的杂交应力元

New Hybrid Solid Element with Tractiion-Free Cylindrical Surface

根据Hellinger-Reissner原理,建立了进一步改进的具有一个无外力圆柱表面三维杂交应力元。元内假定应力场满足以柱坐标表示的平衡方程,及圆柱面上的无外力边界条件。当退化为二维时,也满足协调方程。数值算例表明,当分析带圆弧的槽孔板、块时,在稀疏的有限元网格下,这类单元即可提供较以前各类特殊元、一般假定位移元及一般假定应力元远为准确的三维及二维应力分布。

A new type of 12-node 3-dimensional assumed stress hybrid finite elements with a traction-free cylindrical surface are developed based on the Hellinger-Reissner principle. Six new expressions of stress components are derived with five stress functions. The assumed stress field satisfies the equilibrium equations in the element as well as the traction-free conditions over the cylindrical surface. In case of plane problems, the assumed stress field also satisfies the compatibility conditions. The special elements are a-dopted in conjunction with conventional elements to analyze a number of problems consisting of thick or thin plates with holes or notches under tension or bending. Excellent results are obtained compared with the exact solutions or with the other independent solutions when only the very coarse element meshes are assembled near the cutouts.