A Laplace Transform Dual-Reciprocity Boundary Element Method for Axisymmetric Elastodynamic Problems
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.
[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.
[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.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:59326", author = "B. I. Yun", title = "A Laplace Transform Dual-Reciprocity Boundary Element Method for Axisymmetric Elastodynamic Problems", 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.", volume = "6", number = "6", pages = "674-7", }