Semi-analytical integration of sub-parametric elements used in the BEM for three-dimensional elastodynamics

Computers and Structures

Volumn 71, Issue 6, 1999, Pages 595-615

  Davey, K ^a   Alonso Rasgado, M T ^a  

^a UNIVERSITY OF MANCHESTER   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY ELEMENT METHOD; INTEGRATION; MATHEMATICAL MODELS; NATURAL FREQUENCIES; VIBRATIONS (MECHANICAL);

ELASTODYNAMICS;

STRUCTURAL ANALYSIS;

EID: 0344339062     PISSN: 00457949     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0045-7949(98)00309-5     Document Type: Article

References (27)

1. Milroy J., Hinduja S., Davey K. The 3-D thermoelastic boundary element method: semi-analytical integration for subparametric triangular elements. International Journal for Numerical Methods in Engineering. 41:1998;1029-1055.
2. Milroy J., Hinduja S., Davey K. The 3-D thermoelastic boundary element method: analytical integration for linear isoparametric triangular elements. Journal of Applied Mathematical Modelling. 21:1997;763-782.
3. Golub G.H., van Loan C.F. Matrix computations. 2nd ed :1989;The Johns Hopkins University Press, London.
4. Davey K, Alonso Rasgado MT, Rosindale I. The 3-D elastodynamic boundary element method: semi-analytical integration for isoparmetric triangular elements. International Journal for Numerical Methods in Engineering [in press].
5. Rizzo F.J., Shippy D.J., Rezayat M. A boundary integral equation method for radiation and scattering of elastic waves in three dimensions. International Journal for Numerical Methods in Engineering. 21:1985;115-129.
6. Lachat J.C., Watson J.O. Effective numerical treatment of boundary integral equations: a formulation for three-dimensional elastostatics. International Journal for Numerical Methods in Engineering. 10:1976;991-1005.
7. Manolis G.D., Banerjee P.K. Conforming versus non-conforming boundary elements in three-dimensional elastostatics. International Journal for Numerical Methods in Engineering. 23:1986;1885-1904.
8. Rizzo F.J., Shippy D.J. An advanced boundary integral equation method for three-dimensional thermoelasticity. International Journal for Numerical Methods in Engineering. 11:1977;1753-1768.
9. Wu Zhang, Huan-Ran Xu. A general and effective way for evaluating the integrals with various orders of singularity in the direct boundary element method. International Journal for Numerical Methods in Engineering. 28:1989;2059-2064.
10. Yin-Sheng Li, Tatsuo Obata, Hideo Koguchi, Toshio Yada. Some improvements of accuracy and efficiency in three-dimensional direct boundary element method. International Journal for Numerical Methods in Engineering. 33:1992;1451-1464.
11. Dyka C.T., Remodi A.M., Millwaters H.R. 3-D boundary elements and the integration of strong singularities. Computers and Structures. 39:1991;513-523.
12. Shan Lu, Ye T.Q. Direct evaluation of singular integrals in elastoplastic analysis by the boundary element method. International Journal for Numerical Methods in Engineering. 32:1991;295-311.
13. Huang Q., Cruse T.A. Some notes on singular integral techniques in boundary element analysis. International Journal for Numerical Methods In Engineering. 36:1993;2643-2659.
14. Telles J.C.F. A self-adaptive co-ordinate transformation for efficient numerical evaluation of general boundary element integrals. International Journal for Numerical Methods in Engineering. 24:1987;959-973.
15. Silva Rego J.J., Wrobel L.C., Telles J.C.F. A new family of continuous/discontinuos 3-D boundary elements with application to acoustic wave propagation. International Journal for Numerical Methods in Engineering. 26:1993;1661-1679.
16. Katz C. Analytical integration of isoparametric 2-D boundary elements, Boundary Elements VII. In: Proceedings of the 7th International Conference. Berlin: Springer, 1985. vol. 2.
17. Cruse T.A. Numerical solutions in three dimensional elastostatics. International Journal of Solids and Structures. 5:1969;1259-1274.
18. Cruse T.A. An improved boundary-integral equation method for three dimensional elastic stress analysis. Computers and Structures. 4:1974;741-754.
19. Jeng G., Wexler A. Accurate numerical integration of singular boundary element kernels over boundaries with curvature. International Journal for Numerical Methods in Engineering. 11:1977;1455-1471.
20. Sahyi M.N., Ousset Y., Verchery G. Solution of radiation problems by collocation of integral formulation in terms of single and double layer potentials. Journal of Sound and Vibration. 74:1981;187-204.
21. Davey K., Hinduja S. Analytical, integration of linear three-dimensional triangular elements in BEM. Applied Mathematics and Modelling. 13:1989;450-461.
22. Guiggiani M., Casalini P. Direct computation of cauchy principle value integrals in advanced boundary elements. International Journal for Numerical Methods in Engineering. 24:1987;711-1720.
23. Heshan Liao, Zhixin Xu. A method for direct evaluation of singular integral in the direct boundary element method. International Journal for Numerical Methods in Engineering. 35:1992;1473-1485.
24. Cruse T.A., Rizzo F.J. A direct formulation and numerical solution of the general transient elastodynamic problem I. Journal of Mathematical Analysis and Applications. 22:1968;244-259.
25. Hammer P.C., Marlowe O.J., Stroud A.H. Numerical integration over simplexes and cones. Mathematical tables and other aids to computation. 10:1956;130-137.
26. Hammer P.C., Marlowe O.J., Stroud A.H. Numerical integration over simplexes. Mathematical tables and other aids to computation. 10:1956;137-139.
27. Stroud A.H., Secrest D. Gaussian quadrature formulas. 1966;Prentice-Hall, Englewood Cliffs, NJ.