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A PENALTY METHOD APPROACH TO BOUNDARY CONDITIONS FOR THE SCALED BOUNDARY METHOD WITH A REDUCED SET OF BASE FUNCTIONS
 

Summary: A PENALTY METHOD APPROACH TO BOUNDARY CONDITIONS FOR THE
SCALED BOUNDARY METHOD WITH A REDUCED SET OF BASE FUNCTIONS
Steven R. Chidgzey, Andrew J. Deeks, Charles E. Augarde
School of Civil and Resource Engineering, The University of Western Australia, Stirling
Highway, Crawley WA, 6009, Australia
School of Engineering-Durham, University of Durham, South Road, Durham,
DH1 3LE, UK
Introduction
The scaled boundary method is a semi-analytical method developed by Wolf and Song
(1996) to derive the dynamic stiffness matrices of unbounded domains. A virtual work
derivation for elastostatics developed by Deeks and Wolf (2002) improved the accessibility
of the method by reformulating the complicated mathematics of the original derivation.
Recently a novel solution procedure for the method was developed by Song (2004a), based
on the theory of matrix functions and the real Schur decomposition. It has been proven that
the base functions obtained from the Schur decomposition are weighted block-orthogonal
(Song 2004b). A reduced set of base functions can be constructed by retaining the terms with
the smallest real parts of the eigenvalues, which requires only a partial Schur decomposition
(a subset of the eigenvectors). Significant reduction in computation time is achieved without
significant loss of accuracy (Song 2004b). This approach has so far only been applied to
unbounded domains where all the base functions automatically satisfy both Dirichlet and

  

Source: Augarde, Charles - School of Engineering, University of Durham

 

Collections: Engineering