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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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