船体结构非圆孔口问题的复变函数解  

The complex variable function solution for curvilinear hole problems of ship

作　　者：宋竞正[1] 李鸿 何蕴增[2] 欧贵宝[2] 

机构地区：[1]哈尔滨工程大学船舶工程学院,黑龙江哈尔滨150001 [2]哈尔滨工程大学建筑工程学院,黑龙江哈尔滨150001

出　　处：《哈尔滨工程大学学报》2004年第5期558-562,共5页Journal of Harbin Engineering University

摘　　要：针对船体焊接结构上甲板大开口边缘,舱壁开口边缘的应力集中现象严重影响船体强度这一问题,根据弹性力学基本理论,引入保角变换技术,以无限大平板一般形状孔口为算例,给出了适合数值计算的复变函数解法.并且按照这一方法编制了相应的计算程序,具体计算了船体结构和工程中常见的曲线孔口———六角形孔和腰圆孔在均匀拉伸和纯弯曲两种情况下的孔边最大应力、应力分布及腰圆孔长宽比对应力集中问题的影响,并对比了板宽变化对孔口应力的影响.实算结果与有关文献及边界元法的计算结果十分吻合.Stress concentration at the edge of deck openings and cabin openings decreases the strength of ship structures. A numerical method to solve the complex variable function for stress concentration on an infinite plate where there are curvilinear holes is described.Based on the general laws of elastic mechanics and using the conformal mapping technique,computer programs were made to calculate the stress concentration of curvilinear holes (hexagonal form and oval form) that are often used in ship structures and engineering. The maximum of the stresses and the distribution of the stresses under axial loading and pure bending were calculated. Furthermore, the variation of factor of stress concentration with value of c/b for oblate holes was considered. At the same time, solutions were compared with the numerical results of boundary unit method and related articles. Calculations show that this method can be used as a simple and useful method to analyze the characters of stress distribution around the curvilinear holes in an infinite plate.

关 键 词：应力集中 曲线孔口 复变函数 保角变换 

分 类 号：O343[理学—固体力学]