内边界裂纹复合圆柱的Saint-Venant扭转*
Saint-Venant’s Torsion Problem for a Composite Circular Cylinder with an Internal Edge Crack
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摘要: 本文使用мусхелишвили单层势函数和柱体扭转单裂纹解,将复合材料裂纹柱体扭转的内边界裂纹问题归结为解一组广义柯西核的混合型的积分方程,然后使用奇异积分方程的Gauss-Jacobi求积公式,建立了数值法,并计算了若干数值例子,得到了复合材料裂纹柱体扭转的抗扭刚度及应力强度因子.与已有的文献相比符合得很好.Abstract: In this paper the writer uses Muskhelishvili single-layer potential function solution and single crack solution for the torsion problem of a circular cylinder to discuss the torsion problem of a composite cylinder with an internal crack, and the problem is reduced to a set of mixed-type integral equation with generalized Cauchy-kernel. Then, by using the integration formula of Gauss-Jacobi, the numerical method is established and several numerical examples are calculated. The torsional rigidity and the stress intensity factors are obtained. The results of these examples fit the results obtained by the previous papers better.
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[1] мусхелишвили Н.И.,《数学弹性力学中的几个基本问题》,赵惠元译,科学出版社(1958). [2] Coyle,E.J.and M.Crochet,Analysis of cylindrical joints of composites materials of torsional loadings,Journal of Reinforced Plastic and Composites,1,3(1982),195-205. [3] Kuo,Y.M.and H.D.Conway,The torsion of composite tubes and cylinders,International Journal of Solids and Structures,9(1973),1553-1565. [4] 马稚青、汤任基,带裂纹组合柱的扭转,上海力学.(1)(1992),15-21. [5] 汤任基,带裂纹圆柱体的Saint-Venant扭转,力学学报.(4)(1982),320-340. [6] Erdogan,F.,G.D.Gupta and T.S.Cook,Numerical Solution of Singular Integral Equations in Fracture Mechanics,G.C.SIH,1(1973). -
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