带裂纹圆柱体扭转的强奇性积分方程解法<sup>*</sup>

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带裂纹圆柱体扭转的强奇性积分方程解法^*

基金项目: * 国家教委博士点基金资助项目

摘要: 本文以裂纹的翘曲位移间断为基本未知函数,把带裂纹圆柱体的扭转问题化为求解一组强奇性积分方程,并利用数值法,对星形及其它不同形状裂纹圆柱体的抗扭刚度和应力强度因子作了数值计算,计算结果令人满意.
- 裂纹柱扭转 /
- 强奇性积分方程 /
- 星形裂纹 /
- 抗扭刚度 /
- 应力强度因子
Abstract: In this paper, the functions of warping displacement interruption defined on the crack lines are taken for the fundamental unknown functions. The torsion problem of cracked circular cylinder is reduced to solving a system of integral equations with strongly singular kernels. Using the numerical method of these equations, the torsional rigidities and the stress intensity factors are calculated to solve the torsion problem of circular cylinder with star-type and other different types of cracks. The numerical results are satisfactory.
- torsion of cracked cylinder /
- strongly singular integral equation /
- star-type crack /
- torsional rigidity /
- stress intensity factor

[1]	Kaya,A.C.and F.Erdogan,On the solution of integral equations with strongly singular kernels,Quart.Appl.Math.,45(1987),105-122.
[2]	Kaya,A.C.and F.Erdogan,On the solution of integral equations with a generalized Cauchy kernel,Quart.Appl.Math.,45(1987),455-469.
[3]	Мусхелишвили Н.И.,《奇异积分方程》,赵惠元译.上海科学技术出版社(1988).
[4]	汤任基,带裂纹圆柱体的Saint-Venant扭转,力学学报,(4)(1982), 332-340
[5]	王晓春、汤任基,关于多裂纹圆柱休的扭转,应用数学和力学,9(8)(1988), 693-701
[6]	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).

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