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

摘要: 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 Neumann boundary conditions, and these boundary conditions are only applied on the side faces and at infinity. To extend the reduced base function method to problems involving bounded domains, this paper proposes the use of a penalty method approach.