×

zbMATH — the first resource for mathematics

Analysis of shell-like structures by the boundary element method based on 3-D elasticity: Formulation and verification. (English) Zbl 0910.73068
We show that the conventional boundary integral equation (CBIE) for three-dimensional elasticity does not degenerate when applied to shell-like structures, contrary to the case when it is applied to crack-like problems where it does degenerate due to the closeness of the two crack surfaces. The treatment of the nearly singular integrals, which is a crucial step in the applications of BIEs to thin shapes, is presented in detail. To verify the theory, numerical examples of spherical and ellipsoidal vessels are presented using the BEM approach developed in this paper.

MSC:
74S15 Boundary element methods applied to problems in solid mechanics
74K15 Membranes
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Wempner, Appl. Mech. Rev. 42 pp 129– (1989) · doi:10.1115/1.3152426
[2] Babuska, USACM Newslett. 5 (1992)
[3] Cho, Comput. Methods Appl. Mech. Engng. 132 pp 135– (1996) · Zbl 0884.73063 · doi:10.1016/0045-7825(95)00985-X
[4] Finite Element Methods for Thin Shell Problems, Wiley, Chichester, 1996.
[5] ’Boundary integral equations for bending of thin plates’, in: (ed.), Progress in Boundary Elements, Chap. 6, Vol. 2, Pentech Press, London, 1983.
[6] Ye, Appl. Math. Modelling 9 pp 183– (1985) · Zbl 0582.73070 · doi:10.1016/0307-904X(85)90005-8
[7] Liu, Engng. Anal. Boundary Elements 4 pp 160– (1987) · doi:10.1016/0955-7997(87)90032-4
[8] and , ’A new regularized boundary integral formulation for thin elastic plate bending analysis’, in: and (eds.), Boundary Elements XIII, Tulsa, OK, 1991, Computation Mechanics Publications, pp. 523-533. · doi:10.1007/978-94-011-3696-9_42
[9] ’Static and dynamic analysis of shells’, in (ed.), Boundary Element Analysis of Plates and Shells, Springer, Berlin, 1991, pp. 93-140. · doi:10.1007/978-3-642-45694-7_3
[10] Krishnasamy, Int. J. Numer. Meth. Engng. 37 pp 107– (1994) · Zbl 0795.73076 · doi:10.1002/nme.1620370108
[11] Martinez, J. Acoust. Soc. Am. 90 pp 2728– (1991) · doi:10.1121/1.401868
[12] and , ’Scattering of acoustic and elastic waves by crack-like objects: the role of hypersingular integral equations’, in and (eds.), Review of Progress in Quantitative Nondestructive Evaluation, Plenum Press, Brunswick, Maine, 1991.
[13] and , ’Nearly singular and hypersingular integrals in the boundary element method’, in: and (eds.), Boundary Elements XV, Computational Mechanics Publications, Worcester, MA, 1993, pp. 453-468.
[14] and , ’Ultrasonic scattering from open cracks in 3-D using a composite boundary integral equation formulation’, in and (eds.), Review of Progress in Quantitative Nondestructive Evaluation, Plenum Press, New York, 1993, pp. 29-36.
[15] Liu, J. Acoust. Soc. Am. 102 pp 926– (1997) · doi:10.1121/1.419912
[16] Rizzo, Quart. Appl. Math. 25 pp 83– (1967) · Zbl 0158.43406 · doi:10.1090/qam/99907
[17] Cruse, Int. J. Solids Struct. 5 pp 1259– (1969) · Zbl 0181.52404 · doi:10.1016/0020-7683(69)90071-7
[18] Cruse, Comput. Struct. 4 pp 741– (1974) · doi:10.1016/0045-7949(74)90042-X
[19] Rizzo, Int. J. Numer. Meth. Engng. 11 pp 1753– (1977) · Zbl 0387.73007 · doi:10.1002/nme.1620111109
[20] Rudolphi, Math. Comput. Modelling 15 pp 269– (1991) · Zbl 0728.73081 · doi:10.1016/0895-7177(91)90071-E
[21] Liu, Engng. Anal. Boundary Elements 8 pp 301– (1991) · doi:10.1016/0955-7997(91)90043-S
[22] Boundary Element Analysis in Computational Fracture Mechanics, Kluwer Academic Publishers, Dordrecht, Boston, 1988. · Zbl 0648.73039 · doi:10.1007/978-94-009-1385-1
[23] Lin, J. Acoust. Soc. Am. 82 pp 1442– (1987) · doi:10.1121/1.395227
[24] Budreck, J. Appl. Mech. 55 pp 405– (1988) · Zbl 0663.73073 · doi:10.1115/1.3173690
[25] Krishnasamy, J. Appl. Mech. 57 pp 404– (1990) · Zbl 0729.73251 · doi:10.1115/1.2892004
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.