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Civil-Comp Proceedings
ISSN 1759-3433 CCP: 55
ADVANCES IN COMPUTATIONAL STRUCTURAL MECHANICS Edited by: B.H.V. Topping
Paper II.3
The Scaled Boundary Finite-Element Method - A Primer: Derivations J.P. Wolf and C. Song
Institute of Hydraulics and Energy, Department of Civil Engineering, Swiss Federal Institute of Technology, Lausanne, Switzerland Full Bibliographic Reference for this paper
J.P. Wolf, C. Song, "The Scaled Boundary Finite-Element Method - A Primer: Derivations", in B.H.V. Topping, (Editor), "Advances in Computational Structural Mechanics", Civil-Comp Press, Edinburgh, UK, pp 29-46, 1998. doi:10.4203/ccp.55.2.3
Keywords: boundary element, dynamics, finite element, radiation condition, soil-structure interaction, wave motion.
Abstract
The scaled boundary finite-element method is a semi-analytical
fundamental-solution-less boundary-element method
based solely on finite elements. Using the simplest wave propagation
problem and discretizing the boundary with a two-node
line finite element, which preserves all essential features,
two derivations of the scaled boundary finite-element equations
in displacement and dynamic stiffness are presented. In
the first, the scaled-boundary-transformation-based derivation,
the new local coordinate system consists of the distance measured
from the so-called scaling centre and the circumferential directions defined on the surface finite element. The governing
partial differential equations are transformed to ordinary
differential equations by applying the weighted-residual
technique. The boundary conditions are conveniently formulated
in the local coordinates. In the second, the mechanically-based
derivation, a similar fictitious boundary is introduced. A
finite-element cell is constructed between the two boundaries.
Standard finite-element assemblage and similarity lead to the
scaled boundary finite-element equations after performing the
limit of the cell width towards zero analytically.
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