含有贯穿厚度圆孔的无限大板的精确三维应力解(英文)

Exact Three-dimensional Solutions of an Infinite Plate with a Though-the-thickness Circular Hole

应力集中是船舶结构中十分常见且非常重要的现象。文章对远场单向拉伸载荷作用下的含有一个贯穿厚度圆孔的无限大各向同性弹性板进行了理论研究,基于Kane和Mindlin假设获得了三维应力场的精确解,给出了应力集中因子和离面应力约束因子的简明表达式。采用当前的理论解对应力集中和离面约束进行了全面研究,重点分析了板厚的影响。一个有趣的结论是板厚对于径向应力的影响要比面内的另外两个应力分量的影响高一个数量级。另外一个是离面应力约束因子随着半板厚h与孔半径R的比值的变化而改变,并且在垂直于拉伸载荷且沿着孔径的方向上其值在0与2/3之间变化。结果与有限元结果完好吻合,由此证明了当前理论解的正确性。

Stress concentration is a common and very important phenomenon in ship structures. A the-oretical analysis is performed on an infinite isotropic elastic plate containing a through-the-thickness circular hole subjected to uni-axial tension at far field. The exact three-dimensional solutions for the stress field are obtained by using Kane and Mindlin’s assumption. The expressions of the stress con-centration factor and the out-of-plane stress constraint factor are found in a concise, explicit form. Based on the present theoretical solutions, a comprehensive analysis is performed on stress concen-tration and out-of-plane constraint and the emphasis was placed on the effects of the plate thick-ness. It is interesting to find that the influence of the plate thickness on the radial stress is one or-der higher than that on the other two in-plane stresses. Another important observation is that the out-of-plane stress constraint factor varies with ratio of the semi-thickness h to the radius R of the cir-cular hole and its values on the section passing through the hole diameter and perpendicular to the tension range from 0 to 2/3. Results are compared well with the FE results, and the validity of the pre-sent theoretical solutions is thus verified.