Summary
Serious problems arise when Gaussian quadrature is employed for the integrations required in the direct boundary element method (DBEM). You will run in a lot of trouble if you are going to compute domain points near the boundary. These problems can be overcome if you carry out the integration analytically. The technique is developped in this paper.
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References
Abdel-Akher, A.; Hartley, G. A.: Evaluation of Boundary Integrals for Plate Bending Int. J. Numer. Methods Eng., vol. 28, 75–93 (1989).
Abdel-Akher, A.; Hartley, G. A.: Boundary Integration and Interpolation Procedures for Plate Bending Int. J. Numer. Methods Eng., vol. 28, 1389–1408 (1989).
Blum, H.: Numerical Treatment of Corner and Crack Singularities Saarbrücken, 1987.
Hartmann, F.: Introduction to Boundary Elements, Springer 1989.
Hartmann, F.: The Mathematical Foundation of Structural Mechanics, Springer 1985.
Hartmann, F.: ELASTOSTATICS, in: Brebbia, C.A.: Progress in BOUNDARY ELEMENT METHODS, Pentech Press 1981.
Hartmann, F.; Zotemantel, R.: The Direct Boundary Element Method in Plate Bending Int. J. Numer. Methods Eng., vol. 23, 2049–2069 (1986).
Melzer, H.; Rannacher, R.: Spannungskonzentrationen in Eckpunkten der Kirchhof£schen Platte Bauingenieur 55 (1980) 181–184.
Stern, M.: A general boundary integral formulation for the numerical solution of plate bending problems Int. J. Solids Structures 15 (1979) pp. 769–782.
Vable, M.: An Algorithm based on the Boundary Element Method for Problems in Engineering Mechanics, Int. J. Numer. Methods Eng., vol. 21, 1625–1640 (1985).
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© 1992 Springer-Verlag Berlin Heidelberg
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Knöpke, B. (1992). The Analytical Integration of Boundary Integrals for Plate Bending. In: Kobayashi, S., Nishimura, N. (eds) Boundary Element Methods. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-06153-4_23
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DOI: https://doi.org/10.1007/978-3-662-06153-4_23
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-06155-8
Online ISBN: 978-3-662-06153-4
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