A Frequency-Domain Approach for Transient Dynamic Analysis using Scaled Boundary Finite Element Method (I): Approach and Validation

摘要

The semi-analytical scaled boundary finite element method (SBFEM) has been successfully applied in elastostatics. Its application to elastodynamic problems, however, has lagged behind, primarily due to the lack of an effective solution procedure to the governing equilibrium equation system. The authors recently developed an easy-to-follow Frobenius solution procedure to this equation system [1]. This study further develops a frequency-domain approach for the general transient dynamic analysis, through combining the Frobenius solution procedure and the fast Fourier transform (FFT) technique. The complex frequency-response functions (CFRFs) are first computed using the Frobenius solution procedure. This is followed by a FFT of the transient load and an inverse FFT of the CFRFs to obtain the time history of responses. Two transient dynamic problems, subjected to Heaviside step load and triangular blast load, are modelled with a small number of degrees of freedom using the new approach. The numerical results agree very well with the analytical solutions and those from the FEM. Further applications of this approach to transient dynamic fracture problems are presented in the accompanying paper [2].