A Laplace Transform Dual-Reciprocity Boundary Element Method for Axisymmetric Elastodynamic Problems

Authors: B. I. Yun

Abstract:

A dual-reciprocity boundary element method is presented for the numerical solution of a class of axisymmetric elastodynamic problems. The domain integrals that arise in the integrodifferential formulation are converted to line integrals by using the dual-reciprocity method together suitably constructed interpolating functions. The second order time derivatives of the displacement in the governing partial differential equations are suppressed by using Laplace transformation. In the Laplace transform domain, the problem under consideration is eventually reduced to solving a system of linear algebraic equations. Once the linear algebraic equations are solved, the displacement and stress fields in the physical domain can be recovered by using a numerical technique for inverting Laplace transforms.

Keywords: Axisymmetric elasticity, boundary element method, dual-reciprocity method, Laplace transform.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1074912

References:

[1] T. A. Cruse, D. W. Snow, and R. B. Wilson, "Numerical solutions in axisymmetric elasticity", Computers and Structures, vol. 7, pp. 445-451, 1977.
[2] L. C. Wrobel and C. A. Brebbia, "A formulation of the boundary element method for axisymmetric transient heat conduction", International Journal of Heat and Mass Transfer, vol. 24, pp. 843-850, 1981.
[3] H. Gr├╝ndemann, "A general procedure transferring domain integrals onto boundary integrals in BEM", Engineering Analysis with Boundary Elements, vol. 6, pp. 214-222, 1990.
[4] K. H. Park, "A BEM formulation for axisymmetric elasticity with arbitrary body force using particular integrals", Computers and Structures, vol. 80, pp. 2507-2514, 2002.
[5] C. A. Brebbia and D. Nardini, "Dynamic analysis in solid mechanics by an alternative boundary element procedure", Soil Dynamics and Earthquake Engineering, vol. 2, pp. 228-233, 1983.
[6] A. C. Neves and C. A. Brebbia, "The multiple reciprocity boundary element method in elasticity: A new approach for transforming domain integrals to the boundary", International Journal for Numerical Methods in Engineering, vol. 31, pp. 709-727, 1991.
[7] J. P. Agnantiaris, D. Polyzos, and D. E. Beskos, "Free vibration analysis of non-axisymmetric and axisymmetric structures by the dual reciprocity BEM", Engineering Analysis with Boundary Elements, vol. 25, pp. 713- 723, 2001.
[8] A. A. Bakr, The Boundary Integral Equation Method in Axisymmetric Stress Analysis Problems. Berlin-Heidelberg-New York-Tokyo, Springer- Verlag, 1986.
[9] X. M. Gao and T. G. Davies, Boundary Element Programming in Mechanics. Cambridge University Press, 2002.
[10] B. I. Yun and W. T. Ang, "A dual-reciprocity boundary element approach for axisymmetric nonlinear time-dependent heat conduction in a nonhomogeneous solid", Engineering Analysis with Boundary Elements, vol. 34, pp. 697-706, 2010.
[11] H. Stehfest, "Numerical inversion of Laplace transforms", Communications of the ACM, vol. 13, pp. 47-49, 1970.