Developing a New Semi- Analytical Method for Solving Elastodynamic Problems in the Frequency Domain

In this paper, a new semi-analytical method is developed for analyzing concrete gravity dams in the frequency domain. Among different numerical methods, the finite element method (FEM), the boundary element method (BEM), and the scaled boundary finite element method (SBFEM) are more popular. BEM requires basically reduced surface discretization and may be considered as an appealing alternative to FEM for elastodynamic problems but requires fundamental solution of the governing differential equations. Although coefficient matrices of BEM are much smaller than those of FEM, they are routinely non-positive definite, non-symmetric, and fully populated. The SBFEM combines the advantages of the FEM and the BEM. The SBFEM is a semi-analytical method for solving partial differential equations by transforming the governing partial differential equations to ordinary differential equations. In the SBFEM, similar to the BEM, the boundary of the problem’s domain is discretized, while no fundamental solution is required. A modified form of the SBFEM with diagonal coefficient matrices has been proposed (Fakharian amd Khodakarami, 2015) for solving elastodynamic problems in the time domain. In this study, the semi-analytical approach for solving elastodynamic problems in the frequency domain has been applied, the governing equations in local coordinate system has been developed and two concrete gravity dams with rigid foundations and empty reservoir have been analyzed under the earthquake harmonic load.