×

zbMATH — the first resource for mathematics

On the non-singular traction-BIE in elasticity. (English) Zbl 0832.73076
It is shown that the Cauchy principal value interpretations so commonly used in BIE developments are unnecessary. Starting with the Somigliana displacement identity and then continuing with the derivatives of these terms, the authors separate the singular parts of the integrands from the nonsingular ones and show that the integrals of the former type are either vanishing in the case of closed boundary contours or bounded in the case of open curves. Conforming boundary elements are employed, and the source points are located directly at the boundary nodes. In addition to smooth boundaries also corner points are considered, and the formulations with discontinuous boundary tractions and tangential derivatives of the boundary displacement are discussed, too.

MSC:
74S15 Boundary element methods applied to problems in solid mechanics
74B10 Linear elasticity with initial stresses
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Gray, Int. j. numer. methods eng. 29 pp 1135– (1990)
[2] Krishnaswamy, J. Appl. Mech. ASME. 57 pp 404– (1990)
[3] and , ’Traction BIE formulations and applications to non-planar and multiple cracks’, in , and (eds.). Fracture Mechanics: 22nd Symposium, Vol II, ASTM STP 1131 American Society for Testing and Materials, Philadelphia, 1992, pp. 314-332.
[4] Boundary Element Analysis in Computational Fracture Mechanics, Kluwer Academic Publishers, Dordrecht, Boston, 1988. · Zbl 0648.73039 · doi:10.1007/978-94-009-1385-1
[5] Chien, Comp. Mech. 8 pp 57– (1991)
[6] Liu, Eng. Anal. Boundary Elements 8 pp 301– (1991)
[7] Liu, Comput. Methods Appl. Mech. Eng. 96 pp 271– (1992)
[8] Guiggiani, ASME. J. Appl. Mech. 59 pp 604– (1992)
[9] Polch, Comput. Mech. 2 pp 253– (1987)
[10] Gray, Engineering analysis with boundary elements 6 pp 180– (1989)
[11] Cruse, Camput. Mech. 11 pp 1– (1993)
[12] Gray, J. Comput. Math. 32 pp 369– (1990)
[13] Lutz, Int. j. numer. methods eng. 35 pp 1737– (1992)
[14] Cruse, Int. j. numer. methods eng. 36 pp 237– (1993)
[15] Cruse, Int. J. Solids Struct. 5 pp 1259– (1969)
[16] Krishnasamy, Comput. Mech. 9 pp 267– (1992)
[17] Huang, Int. j. numer. methods eng. 36 pp 2643– (1993)
[18] Stress Concentration Factors, Wiley, New York, London, Sydney, Toronto, 1974.
[19] and , The Stress Analysis of Cracks Handbook Del Research Corporation. St. Louis, MO, 1985.
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.