关于多裂纹圆柱体的扭转*
On the Torsion of a Cylinder with Several Cracks
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摘要: 本文在文[1]基础上,导出了含有任意分布裂纹系的圆柱扭曲函数的解析表达式,从而把问题化为以未知位错密度函数表示的奇异积分方程组.文中利用奇异积分方程的数值方法[2,7],对带有多根裂纹的圆柱的抗扭刚度和应力强度因子作了若干数值计算.此外,本文还首次将裂纹切割法[5]推广用于求解矩形柱的扭转,数值结果表明方法是成功的.Abstract: In this paper,based on paper [1],the analytic expression of the torsion Junction for a cylinder containing arbitrary oriented cracks is obtained.The problem is reduced to solve a system of singular integral equations for the unknown dislocation density functions.Using the numerical method of the singular integral equations[2,7],the torsional rigidities and stress intensity factors are evaluated for several multicracked cylinders.Next,the crk-cutting method[5] is firstly extended to lve the torsion problem for a rectangular prism.The numerical results show that the method presented here is successful.
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[1] 汤任基,带裂纹圆柱体的Saint-Venant扭转,力学学报,4(1982). [2] 王晓春,多裂纹柱体与非圆往体的扭转,兰州大学硕士论文(1986). [3] 尹昌言,有穿透裂纹的圆柱体扭转应力及应力强度因子,固体力学学报,3(1982). [4] 钱伟长、林鸿荪、胡海昌、叶开沅,《弹性柱体的扭转理论》,科学出版社(1956). [5] 汤任基,夹紧矩形板拉伸及角点应力奇异性分析的积分方程解法,力学学报,1(1986). [6] Мусхелишвили Н.И.,《奇异积分方程》,上海科学技术出版社(1966). [7] Erdogan,F.,Mixed boundary-value problems in mechanics,Mechanics Today,4(1978). [8] Timoshenko,S.P.and J.N.Goodier,Theory of Elasticity,third edition,New York(1970). -
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