A 2.5D coupled FEM-BEM-MFS methodology for longitudinally invariant soil-structure interaction problems

A 2.5D coupled FEM–SBM methodology for soil–structure dynamic interaction problems

“…inside the structure domain), uniformly distributed in a concentric circumference to the cylindrical shell. The radius of this auxiliary boundary for the virtual sources has been optimised using the method presented in [15], reaching a value of 85 cm. This optimisation is performed accounting for point B as the control point.…”

“…It is found that these discrepancies are coming from the instability of the 2.5D MFS method at high wavenumbers. Also, the accuracy of the results is sensitive to the control points chosen in the control technique [15] and, consequently, the location of the virtual sources [39,40]. Fig.…”

“…7, the 2.5D FEM-SBM has a better performance than 2.5D FEM-BEM for low frequency (10 Hz) but worsens for higher ones (80 Hz). 2.5D FEM-MFS has proven a potential to be more accurate than the other methods, but it requires a proper optimisation process [15] to determine the sources location, which is challenging (or even impossible) for complex geometries. In contrast, at high frequencies, more than 10 𝑁∕𝜆 is required by the 2.5D FEM-SBM approach to achieve approximately one percent error.…”

“…In order to avoid the constraints due to mesh-based approaches and to increase the computational efficiency of the numerical method, https://doi.org/10.1016/j.engstruct.2021.113371 Received 25 May 2021; Received in revised form 18 September 2021; Accepted 12 October 2021 meshless methods have been proposed to model the soil medium in the framework of soil-structure interaction problems. The method of fundamental solutions (MFS) is a meshless method that has been proposed by several authors as an interesting alternative for dealing with these kinds of problems [13][14][15]. The MFS constructs a set of virtual forces, computed by complying with a particular boundary condition, to obtain an equivalent representation of the structure on the medium.…”

“…However, MFS accuracy is subjected to the distribution of virtual sources (or virtual forces, in elastodynamics), particularly in terms of amount and location, being this the major challenge of using this approach. To overcome this drawback, Liravi et al [15] proposed a 2.5D FEM-BEM-MFS approach which uses the BEM to obtain the soil stiffness matrix (MFS still stands for the wave propagation part) and also presents a control methodology to reduce the existing errors associated with the MFS predictions. However, both FEM-MFS and FEM-BEM-MFS methods exhibit complications dealing with complex boundary shapes, due to the difficulties arising in the selection of virtual sources distribution for these geometries.…”