The scaled boundary finite-element method – a primer: derivations
By J. Wolf, Chongmin Song. 2000
305 citations recorded by the source corpus.
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.
Subfields: Civil and Structural Engineering, Control and Systems Engineering, Mechanics of Materials
View Paper: https://www.semanticscholar.org/paper/251b8492e5f754576a9756cb3b6dbaed166bb10f
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In Civil and Structural Engineering
- E. Ooi
- Sundararajan Natarajan
- Francis Tin-Loi
- Chongmin Song
- Stéphane P.A. Bordas
- Shijun Liao
- Wei Gao
- M. Bazyar
In Control and Systems Engineering
- Shijun Liao
- Wei Gao
- Sundararajan Natarajan
- E. Ooi
- Chongmin Song
- Stéphane P.A. Bordas
- Francis Tin-Loi
- H. Man
In Mechanics of Materials
- E. Ooi
- Sundararajan Natarajan
- Francis Tin-Loi
- Chongmin Song
- Stéphane P.A. Bordas
- Wei Gao
- H. Man
- Shijun Liao
Citations in the corpus
- A unified 3D‐based technique for plate bending analysis using scaled boundary finite element method (2012, result): “This section presents the derivation of the scaled boundary finite element equation for plate structures that shows analogy and consistency to the previous derivations [64].”
- Virtual and smoothed finite elements: A connection and its application to polygonal/polyhedral finite element methods (2015, methodology): “Boundary-based methods, for example, boundary element method [20, 21], scaled boundary FEM [22].”
- A continued‐fraction‐based high‐order transmitting boundary for wave propagation in unbounded domains of arbitrary geometry (2008, background): “The scaled boundary finite element formulation for elastodynamics is detailed in [41, 51 ] .F or the sake of completeness, a brief summary of the equations necessary for the development of the high-order transmitting boundary condition is presented in this section.”
- Homotopy Analysis Method in Nonlinear Differential Equations (2012, methodology): “So, the basic optimal HAM is computationally more efficient than the infinite-parameter optimal HAM suggested by Marinca and Herişanu (2008).”
- A review of the scaled boundary finite element method for two-dimensional linear elastic fracture mechanics (2017, methodology): “Modelling of singular stress field by the scaled boundary finite element method The theoretical formulation of the scaled boundary finite element method is detailed in Song and Wolf [49] and [86].”