Meshless analysis of soil–structure interaction using an MFS–MLPG coupled approach

This paper presents a coupling strategy between the method of fundamental solutions (MFS) and the meshless local Petrov–Galerkin (MLPG) method for the analysis of soil–structure interaction problems in the frequency domain. The MFS is used to model the outer infinite (or semi-infinite) medium, correctly accounting for the far-field conditions in the soil, while the MLPG is used to simulate the elastodynamic behavior of an embedded solid structure. The MLPG formulation is based on the construction of shape functions using the MQ RBF and the test function employed to establish the nodal equations is the Heaviside function, leading to the so-called MLPG-5. Direct coupling between the MFS and the MLPG is assumed, which implies the construction of a system matrix that accounts for the full coupling effects. The proposed coupling approach accommodates the possibility of the methods having different node distributions along the boundary, thus rendering the model flexible by allowing different discretization requirements for the soil and for the structure. The algorithm is applied to 2D problems, and its behavior in terms of convergence and accuracy is analyzed by comparing the results with those provided by reference solutions. An application is presented to illustrate the potential of the proposed approach.