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Computers & structures, 2000-11, Vol.78 (1), p.191-210
2000

Details

Autor(en) / Beteiligte
Titel
The scaled boundary finite-element method – a primer: derivations
Ist Teil von
  • Computers & structures, 2000-11, Vol.78 (1), p.191-210
Ort / Verlag
Elsevier Ltd
Erscheinungsjahr
2000
Link zum Volltext
Quelle
Elsevier ScienceDirect Journals Complete
Beschreibungen/Notizen
  • 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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