Computational mechanics paper
Chen, X, Birk, C, Song, C 2014, 'Transient analysis of wave propagation in 3D soil by using the scaled boundary finite element method', in ST Smith (ed.), 23rd Australasian Conference on the Mechanics of Structures and Materials (ACMSM23), vol. II, Byron Bay, NSW, 9-12 December, Southern Cross University, Lismore, NSW, pp. 855-860. ISBN: 9780994152008.
An efficient method for modelling the propagation of elastic waves in unbounded domains is developed. It is applicable to 3D soil-structure interaction problems involving scalar and vector waves. The scaled boundary finite element method is employed to derive an equation for the displacement unit-impulse response matrix on the near field / far field interface. The unbounded domain is divided into multiple subdomains where the displacement unit-impulse response matrices for individual subdomains are calculated separately and in parallel, leading to a reduction of computational effort. As the displacement unit-impulse response matrices approach zero, the convolution integral representing the force-displacement relationship can be truncated. After the truncation the computational effort only increases linearly with time. Thus, a considerable reduction of computational effort is also achieved by this temporal localization. In addition, a recursive algorithm for calculating the convolution integral based on a piece-wise linear variation of the displacement unit-impulse response matrix is developed, so that the time step size for transient analysis can be arbitrarily small without significantly affecting the total computational effort. Numerical examples demonstrate the accuracy and high efficiency of the proposed method.