Abstract
Using the method of singular integral equation and the crack-cutting technique, the rigorous solutions are obtained for a cylinder with a rectangular hole and a rectangular cylinder with a crack, which exactly satisfy the boundary conditions and the conditions at the corner points. After that the torsional rigidities and the stress intensity factors at the crack tip are determined. Next, for the doubly connected circular cylinder with a rectangular hole the expressions for the singular stresses around the concave corner points are derived and the generalized stress intensity factors are then defined. Since the crack-cutting technique is used in this paper, the solution of the matching rectangular cylinder is also obtained and its numerical results coincide with those in references. Thus the method proposed here is verified.
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References
Muskhelishvili N I. Some basic problems of mathematical theory of elasticity. Noordhoff, Groningen, Holland 1953
Muskhelishvili N I. Singular integral equations. Noordhoff, Groningen, Netherlands 1953
Erdogan F. Mixed boundary value problems. Mechanics Today, 1978, 4(1)
Wang Xiaochun, Tang Renji. On the torsion of a cylinder with several cracks.Applied Mathematics and Mechanics, 1988, 9: 745
Erdogan F, Gupta G D, Cook T S. Numerical Solution of singular integral equations. In: Sih GC ed. Methods of analysis and solutions of crack problems. Noordhoff, Leyden, 1973
Timoshenko S, Goodier J N. Theory of elasticity, New York: McGraw Hill, 1951
Tang Renji, Chen Weijiang. Boundary element method to solve torsion problem of cracked cylinder.Acta Mechanica Solida Sinica, 1990, 3:448
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The project supported by National Natural Science Foundation of China
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Renji, T., Yulan, L. Torsion problems for a cylinder with a rectangular hole and a rectangular cylinder with a crack. Acta Mech Sinica 8, 165–172 (1992). https://doi.org/10.1007/BF02487164
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DOI: https://doi.org/10.1007/BF02487164