CAJ | 학술논문

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。
응력집중시선박결구중십분상견차비상중요적현상。문장대원장단향랍신재하작용하적함유일개관천후도원공적무한대각향동성탄성판진행료이론연구，기우Kane화Mindlin가설획득료삼유응력장적정학해，급출료응력집중인자화리면응력약속인자적간명표체식。채용당전적이론해대응력집중화리면약속진행료전면연구，중점분석료판후적영향。일개유취적결론시판후대우경향응력적영향요비면내적령외량개응력분량적영향고일개수량급。령외일개시리면응력약속인자수착반판후h여공반경R적비치적변화이개변，병차재수직우랍신재하차연착공경적방향상기치재0여2/3지간변화。결과여유한원결과완호문합，유차증명료당전이론해적정학성。
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.