Hydrodynamic Modeling of Infinite Reservoir using Finite Element Method
In this paper, the dam-reservoir interaction is
analyzed using a finite element approach. The fluid is assumed to be
incompressible, irrotational and inviscid. The assumed boundary
conditions are that the interface of the dam and reservoir is vertical
and the bottom of reservoir is rigid and horizontal. The governing
equation for these boundary conditions is implemented in the
developed finite element code considering the horizontal and vertical
earthquake components. The weighted residual standard Galerkin
finite element technique with 8-node elements is used to discretize
the equation that produces a symmetric matrix equation for the damreservoir
system. A new boundary condition is proposed for
truncating surface of unbounded fluid domain to show the energy
dissipation in the reservoir, through radiation in the infinite upstream
direction. The Sommerfeld-s and perfect damping boundary
conditions are also implemented for a truncated boundary to compare
with the proposed far end boundary. The results are compared with
an analytical solution to demonstrate the accuracy of the proposed
formulation and other truncated boundary conditions in modeling the
hydrodynamic response of an infinite reservoir.
[1] H. M. Westergaard, "Water pressure on dams during earthquake",
Transactions, ASCE, vol. 98, pp. 418-433, 1933.
[2] O. C. Zienkiewicz, B. Iron, and Nath, "Natural frequencies of complex
free or submerged structures by the finite element method", Symposium
on vibration in civil engineering, Butterworths, London, 1965.
[3] A. K. Chopra, "Earthquake behavior of reservoir-dam systems", Journal
of engineering mechanics division, vol. 94, pp. 1475-1500, 1968.
[4] A. K. Chopra, "Earthquake response of concrete gravity dams", Journal
of engineering mechanics division, vol. 96, pp. 443-454, 1970.
[5] O. C. Zienkiewicz and P. Bettess, "Dynamic fluid-structure interaction,
Numerical modeling of the coupled problem", John wiley, New york,
pp. 185-193, 1978.
[6] J. F. Hall and A. K. Chopra, "Two-dimensional dynamic analysis of
concrete gravity and embankment dams including hydrodynamic
effects", Earthquake engineering and structural dynamics, vol. 10, pp.
303-323, 1982.
[7] S. K. Sharan, "Finite element analysis of unbounded and incompressible
fluid domain", International journal on numerical methods in
engineering, vol. 21, pp. 1659-1669, 1985.
[8] S. K. Sharan, "Finite element modeling of infinite reservoirs", Journal
of engineering mechanics, vol. 111, pp. 1457-1469, 1985.
[9] D. Maity and S. K. Bhattacharyya, "Time-domain analysis of infinite
reservoir by finite element method using a novel far-boundary
condition", Finite element in analysis and design, vol. 32, pp. 85-96,
1999.
[1] H. M. Westergaard, "Water pressure on dams during earthquake",
Transactions, ASCE, vol. 98, pp. 418-433, 1933.
[2] O. C. Zienkiewicz, B. Iron, and Nath, "Natural frequencies of complex
free or submerged structures by the finite element method", Symposium
on vibration in civil engineering, Butterworths, London, 1965.
[3] A. K. Chopra, "Earthquake behavior of reservoir-dam systems", Journal
of engineering mechanics division, vol. 94, pp. 1475-1500, 1968.
[4] A. K. Chopra, "Earthquake response of concrete gravity dams", Journal
of engineering mechanics division, vol. 96, pp. 443-454, 1970.
[5] O. C. Zienkiewicz and P. Bettess, "Dynamic fluid-structure interaction,
Numerical modeling of the coupled problem", John wiley, New york,
pp. 185-193, 1978.
[6] J. F. Hall and A. K. Chopra, "Two-dimensional dynamic analysis of
concrete gravity and embankment dams including hydrodynamic
effects", Earthquake engineering and structural dynamics, vol. 10, pp.
303-323, 1982.
[7] S. K. Sharan, "Finite element analysis of unbounded and incompressible
fluid domain", International journal on numerical methods in
engineering, vol. 21, pp. 1659-1669, 1985.
[8] S. K. Sharan, "Finite element modeling of infinite reservoirs", Journal
of engineering mechanics, vol. 111, pp. 1457-1469, 1985.
[9] D. Maity and S. K. Bhattacharyya, "Time-domain analysis of infinite
reservoir by finite element method using a novel far-boundary
condition", Finite element in analysis and design, vol. 32, pp. 85-96,
1999.
@article{"International Journal of Architectural, Civil and Construction Sciences:62724", author = "M. A. Ghorbani and M. Pasbani Khiavi", title = "Hydrodynamic Modeling of Infinite Reservoir using Finite Element Method", abstract = "In this paper, the dam-reservoir interaction is
analyzed using a finite element approach. The fluid is assumed to be
incompressible, irrotational and inviscid. The assumed boundary
conditions are that the interface of the dam and reservoir is vertical
and the bottom of reservoir is rigid and horizontal. The governing
equation for these boundary conditions is implemented in the
developed finite element code considering the horizontal and vertical
earthquake components. The weighted residual standard Galerkin
finite element technique with 8-node elements is used to discretize
the equation that produces a symmetric matrix equation for the damreservoir
system. A new boundary condition is proposed for
truncating surface of unbounded fluid domain to show the energy
dissipation in the reservoir, through radiation in the infinite upstream
direction. The Sommerfeld-s and perfect damping boundary
conditions are also implemented for a truncated boundary to compare
with the proposed far end boundary. The results are compared with
an analytical solution to demonstrate the accuracy of the proposed
formulation and other truncated boundary conditions in modeling the
hydrodynamic response of an infinite reservoir.", keywords = "Reservoir, finite element, truncated boundary,hydrodynamic pressure", volume = "5", number = "8", pages = "350-5", }