A Boundary Mapped Collocation Method for the Analysis of the Arbitrarily Shaped Plates (Advances in Applied Mathematics and Mechanics, 2024)
An innovative meshless method is proposed in this paper for the bendingproblem of arbitrary Kirchhoff plates subjected to external force with various shapesand different boundary conditions. Without using a numerical integral, the deflectionof the thin plate is approximated by using the boundary mapped collocation approach.Moreover, the computational domain discretization is just dependent on discretizednodes on the axis, while tensor product nodes have been mapped in the domain automatically. Hence, in the boundary mapped collocation implementation, the approximation functions are derived by employing the one-dimensional moving least squarestechnique for two-dimensional and higher-dimensional problems. Further, the virtualboundary technique is introduced to enforce the boundary conditions in the proposedmethod. Additionally, four numerical experiments are presented to illustrate the excellent convergence and high precision of the proposed approach.