Stress Concentration Factor Expression for a Tension Strip With an Eccentric Elliptical Hole[J]. Applied Mathematics and Mechanics, 2012, 33(1): 113-124. doi: 10.3879/j.issn.1000-0887.2012.01.009
 Citation: Stress Concentration Factor Expression for a Tension Strip With an Eccentric Elliptical Hole[J]. Applied Mathematics and Mechanics, 2012, 33(1): 113-124.

# Stress Concentration Factor Expression for a Tension Strip With an Eccentric Elliptical Hole

##### doi: 10.3879/j.issn.1000-0887.2012.01.009
• Rev Recd Date: 2011-10-15
• Publish Date: 2012-01-15
• First, an explicit stress concentration factor expression for a tension finite-width strip with a central elliptical hole was formulated by using a semi-analytical and semi-empirical method. Comparing the results from this expression with those from Durelli’s photo-elastic experiment, Isida’s formula and finite element analysis, its accuracy was proved to be adequate and its application scope was wider. Then another explicit stress concentration factor expression for a tension strip with an eccentric elliptical hole was also obtained by using the similar method. Comparing results from the expression with the ones from Isida’s formula and finite element analysis, it is shown that this formula is with a wider application scope and more accurate. And when the eccentricity of elliptical hole was in a certain range, the error is less than 8%. Based on the relation between stress concentration central and stress intensity factor, a stress intensity factor expression for tension strips with a center or an eccentric crack was derived with the obtained stress concentration factor expressions. Compared with existing formulae and finite element analysis, this stress intensity factor expression is also with sufficient accuracy.
•  [1] 潘家铮. 坝体内的孔口和廊道[M]. 北京: 水力电业出版社, 1959: 1-112. (PAN Jia-zheng. Holes and Galleries in Dam[M]. Beijing: Water Power Press, 1959: 1-112. (in Chinese)) [2] 陈绍蕃. 钢结构设计原理[M]. 北京: 科学出版社, 1998: 301-316. (CHEN Shao-fan. Principles of Steel Structure Design[M]. Beijing: Science Press, 1998: 301-316. (in Chinese)) [3] 左宏，陈宜亨，郑长卿. 复合型韧性断裂实验及控制参数[J]. 力学学报, 1999, 31(5): 534-540. (ZUO Hong, CHEN Yi-heng, ZHENG Chang-qing. Mixed mode ductile fracture experiment and its controlling parameter[J]. Acta Mechanica Sinica, 1999, 31(5): 534-540. (in Chinese)) [4] 吴德飞, 童根树. 含初始缺陷钢结构损伤累积至断裂及后期的调查分析[J]. 工程力学, 2006, 23(8): 160-167. (WU De-fei, TONG Gen-shu. Damage accumulation, fracture and post fracture analyses for initially flawed steel structures[J]. Engineering Mechanics, 2006, 23(8): 160-167. (in Chinese)) [5] 王启智, 吴大鹏. 拉伸偏心圆孔板的应力集中系数表达式[J]. 力学与实践, 1999, 21(3): 18-20. (WANG Qi-zhi, WU Da-peng. Expression of stress concentration factors for an eccentric circular hole in a tension strip[J]. Mechanics and Engineering, 1999, 21(3): 18-20. (in Chinese)) [6] 王启智, 戴峰. 拉伸半无限圆孔板应力集中系数表达式[J]. 力学与实践, 2001, 23(6): 33-35. (WANG Qi-zhi, DAI Feng. The expression of stress concentration factor for tension semi-infinite plate with a circular hole[J]. Mechanics and Engineering, 2001, 23(6): 33-35. (in Chinese)) [7] 王启智, 宋小林. 拉伸正交各向异性有限宽板偏心圆孔的应力集中系数表达式[J]. 复合材料学报, 2003, 20(6): 80-86. (WANG Qi-zhi, SONG Xiao-lin. Expression of stress concentration factors for an eccentric circular hole in a tension orthotropic finite-width strip[J]. Acta Materiae Compositae Sinica, 2003, 20(6): 80-86. (in Chinese)) [8] 彼得森. 应力集中系数[M]. 北京: 中国工业出版社, 1990: 85-88. (Peterson R E. Stress Concentration Factors[M]. Beijing: China Industry Press, 1990: 85-88. (in Chinese)) [9] 西田正孝. 应力集中[M]. 北京: 机械工业出版社, 1986: 277-280. (Nishida M. Stress Concentration[M]. Beijing: China Machine Press, 1986: 277-280. (in Chinese)) [10] 航空工业部科技委. 应力集中系数手册[M]. 北京: 高等教育出版社, 1990: 136-137. (Science and Technology Committee of Aeronautical Industry Ministry. The Handbook of Stress Concentration Factors[M]. Beijing: Higher Education Press, 1990: 136-137. (in Chinese)) [11] Isida M. On tension of a strip with a central elliptical hole[J]. Transaction of JSME, 1955, 21(107): 407-513 (Part Ⅰ); 514-518 (Part Ⅱ). [12] Xu X W, Sun L X, Fan X Q. Stress concentration of finite element composite laminate with elliptical holes[J]. Computers & Structures, 1995, 57(1): 29-34. [13] 毛春见,许希武,郭树祥. 含椭圆孔有限大薄板弯曲应力分析[J]. 固体力学学报, 2010, 31(1): 80-85. (MAO Chun-jian, XU Xi-wu, GUO Shu-xiang. Stress analysis of a finite anisotropic thin plate with an elliptical hole[J]. Chinese Journal of Solid Mechanics, 2010, 31(1): 80-85. (in Chinese)) [14] Xu X W, Sun L X, Fan X Q. Stress concentration of finite element composite laminates weakened by multiple elliptical holes[J]. International Journal of Solids & Structures, 1995, 32(20): 3001-3014. [15] Durelli A J, Parks V J, Feng H C. Stress around an elliptical hole in a finite plate subjected axial loading[J]. Journal of Applied Mechanics, 1966, 33(1): 192-195. [16] Inglis C E. Stresses in a plate due to presence of cracks and sharp corners[J]. Transaction of the Institution of Naval Architects, 1913, 55: 219-242. [17] Muskhelishvili N I. Some Basic Problems of the Mathematical Theory of Elasticity[M]. Holland: Noordhoff Leyden, 1953: 307-434. [18] Timoshenko S, Goodier J N. Theory of Elasticity[M]. 3rd ed. Beijing: Tsinghua University Press, 2004: 122-194. [19] Jaeger J C, Cook N G W, Zimmerman R W. Fundamentals of Rock Mechanics[M]. 4th ed. London：Blackwell, 2007: 231-237. [20] Koiter W T. An elementary solution of two stress concentration problems in the neighborhood of a hole[J]. Quarterly of Applied Mathematics, 1957, 15: 303-308. [21] Glinka G. Calculation of inelastic notch-tip strain-stress histories under cyclic loading[J]. Engineering Fracture Mechanics, 1985, 22(5): 839-854. [22] 罗林, 王启智. 用U形切槽梁同时测定准脆性材料的拉伸强度和断裂韧度: 理论分析[J]. 工程力学, 2009, 26(9): 244-250. (LUO Lin, WANG Qi-zhi. Concurrent measurement of tensile strength and fracture toughness of quasi-brittle materials using U-notched beams: theoretical analysis[J]. Engineering and Mechanics, 2009, 26(9): 244-250. (in Chinese)) [23] 中国航空研究院. 应力强度因子手册[M]. 北京：科学出版社, 1993: 270-271. (Chinese Institute of Aeronautics. The Handbook of Stress Intensity Factors[M]. Beijing: Science Press, 1993: 270-271. (in Chinese)) [24] Wang Q Z. The crack-line (plane) stress field method for estimating SIFs—a review[J]. Engineering Fracture Mechanics, 1996, 55(4): 593-603.

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