×

Efficient algorithm for edge cracked geometries. (English) Zbl 1110.74864

Summary: The stress field in a finite, edge cracked specimen under load is computed using algorithms based on two slightly different integral equations of the second kind. These integral equations are obtained through left regularizations of a first kind integral equation. In numerical experiments it is demonstrated that the stress field can be accurately computed. Highly accurate stress intensity factors and \(T\)-stresses are presented for several setups and extensive comparisons with results from the literature are made. For simple geometries the algorithms presented here achieve relative errors of less than \(10^{-10}\). It is also shown that the present algorithms can accurately handle both geometries with arbitrarily shaped edge cracks and geometries containing several hundred edge cracks. All computations were performed on an ordinary workstation.

MSC:

74S15 Boundary element methods applied to problems in solid mechanics
74G70 Stress concentrations, singularities in solid mechanics
74R10 Brittle fracture
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Denda, Computer Methods in Applied Mechanics and Engineering 141 pp 247– (1997)
[2] Fett, Fatigue & Fracture of Engineering Materials & Structures 22 pp 301– (1999)
[3] Fett, Engineering Fracture Mechanics 69 pp 69– (2002)
[4] Gu, Applied Mathematical Modelling 17 pp 394– (1993)
[5] Lavit, Journal of Applied Mathematics and Mechanics 58 pp 161– (1994)
[6] Lim, International Journal for Numerical Methods in Engineering 55 pp 293– (2002)
[7] Mukhopadhyay, Engineering Fracture Mechanics 59 pp 269– (1998)
[8] Mukhopadhyay, Engineering Fracture Mechanics 61 pp 655– (1998)
[9] Mukhopadhyay, Engineering Fracture Mechanics 64 pp 141– (1999)
[10] Portela, International Journal for Numerical Methods in Engineering 33 pp 1269– (1992)
[11] Sáez, International Journal for Numerical Methods in Engineering 38 pp 1681– (1995)
[12] Sutradhar, Engineering Analysis with Boundary Elements 28 pp 1335– (2004)
[13] Yang, Engineering Fracture Mechanics 64 pp 589– (1999)
[14] Banks-Sills, Applied Mechanics Reviews 44 pp 447– (1991)
[15] Chen, International Journal of Fracture 107 pp 177– (2001)
[16] Kim, Engineering Fracture Mechanics 57 pp 715– (1997)
[17] Meshii, Engineering Fracture Mechanics 70 pp 657– (2003)
[18] Rahulkumar, International Journal for Numerical Methods in Engineering 40 pp 1091– (1997)
[19] Xiao, Engineering Fracture Mechanics 63 pp 1– (1999)
[20] Yosibash, International Journal of Fracture 62 pp 325– (1993)
[21] Duflot, International Journal for Numerical Methods in Engineering 59 pp 1945– (2004)
[22] Fan, Computers and Structures 82 pp 445– (2004)
[23] Iarve, International Journal for Numerical Methods in Engineering 56 pp 869– (2003)
[24] Lee, International Journal for Numerical Methods in Engineering 59 pp 1119– (2004)
[25] Lee, International Journal for Numerical Methods in Engineering 61 pp 22– (2004)
[26] Wilkening, SIAM Journal on Applied Mathematics 64 pp 1839– (2004)
[27] Vigdergauz, Engineering Fracture Mechanics 53 pp 545– (1996)
[28] Helsing, ASME Journal of Applied Mechanics 67 pp 658– (2000)
[29] Some Basic Problems of the Mathematical Theory of Elasticity (3rd edn). P. Noordhoff: Groningen, 1953.
[30] Boundary Value Problems (2nd edn). Pergamon Press: Oxford, 1966.
[31] Singular Integral Equations (2nd edn). P. Noordhoff: Groningen, 1953.
[32] Englund, International Journal for Numerical Methods in Engineering 63 pp 926– (2005)
[33] Helsing, International Journal for Multiscale Computational Engineering 2 pp 47– (2004)
[34] Brown, SIAM Journal on Matrix Analysis and Applications 18 pp 37– (1997)
[35] Fracture Mechanics: Fundamentals and Applications (2nd edn). CRC Press: Boca Raton, FL, 1995. · Zbl 0999.74001
[36] Helsing, SIAM Journal on Applied Mathematics 59 pp 965– (1999)
[37] Henshell, International Journal for Numerical Methods in Engineering 9 pp 495– (1975)
[38] Greengard, Journal of Computational Physics 73 pp 325– (1987)
[39] Englund, Engineering Analysis with Boundary Elements 27 pp 533– (2003)
[40] Murakami, Engineering Fracture Mechanics 10 pp 497– (1978)
[41] Sham, International Journal of Fracture 48 pp 81– (1991)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.