Singular Integral Equations and Boundary Element Method of Cracks in Thermally Stressed Planar Solids
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摘要: 从边界积分方程出发,导出了二维裂纹体热传导问题及热弹性问题的积分方程组,继而使用奇异积分方程与边界元相结合的方法,为其建立了相应的数值求解方法。此外,利用奇异积分方程的主部分析法,严格地证明了裂纹尖端温度梯度场的1/√r 奇异性,并且给出了奇性温度梯度场的精确解。最后。对一些典型例子,做了数值计算。Abstract: Using the method of the boundary integral equation,a set of singular integral equations of the heat transfer problems and the thermo-elastic problems of a crack embedded in a two-dimensional finite body is derived,and then its numerical method is proposed by the numerical method of the singular integral equations combined with boundary element method.Moreover,the singular nature of temperature gradient field near the crack front is proved by the main-part analysis method of the singular integral equation,and the singular temperature gradients are exactly obtained.Finally,several typical examples are calculated.
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Key words:
- heat transfer /
- crack /
- singular equation /
- boundary element method /
- stress intensity factor
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[1] Motz H.The treatment of singularities of partial differential equation by relaxation methods[J].Quart J Appl Meth,1946,4(4):371～377. [2] Hellen T K,Cesari F,Maitan A.The application of fracture mechanics in thermally stressed structure[J].Int J Pres Ves Piping,1982,10(2):181～204. [3] Chen W H,Tu Y M.Thermal analysis for 2D fracture problems using the BE alternating method[J].Comput Struct,1993,50(3):401～408. [4] 汤任基.断裂力学中的两类奇异积分方程[J].上海交通大学学报,1990,24:(5/6):36～45. [5] Kaya A C,Erdogan F.On the solution of integral equation with singular kernels[J].Quart Appl Math,1987,45(1):105～122. [6] Qin T Y,Tang R J.Finite-part integral and boundary element method to solve embedded planar crack problems[J].Int J Fracture,1993,60(3):373～381. [7] 王元淳.平面非定常热弹性问题的边界元分析[J].上海交通大学学报,1988,22(2):48～51. [8] Erdogan F.Mixed boundary value problems[A].In:Nemat-Nasser S Ed.Mechanics Today,Vol.4,New York:Pergamon Press,1978,1～86. -
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