Method of fundamental solution for thin plate resting on elastic foundation with in-plane forces

This study aims to investigate the Method of Fundamental Solution (MFS) to the thin plate (Kirchhoff theory) resting on the elastic foundation subjected to in-plane forces under either static or dynamic load. The fundamental solutions with Bessel's functions are derived in both static and dynamic cases. According to the principle of superposition, the boundary conditions are satisfied at collocation points in terms of densities of concentrated force at source points outside the domain. Double-Source Algorithm (DSA) and Single-Source Algorithm (SSA) are proposed to deal with fourth-order partial differential equations. Numerical comparisons have been made with analytical solution and other numerical solutions to demonstrate the accuracy of the method of fundamental solution.