A Boundary Mapped Collocation Method for the Analysis of the Arbitrarily Shaped Plates

An innovative meshless method is proposed in this paper for the bending problem of arbitrary Kirchhoff plates subjected to external force with various shapes and different boundary conditions. Without using a numerical integral, the deflection of the thin plate is approximated by using the boundary mapped collocation approach. Moreover, the computational domain discretization is just dependent on discretized nodes 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 squares technique for two-dimensional and higher-dimensional problems. Further, the virtual boundary technique is introduced to enforce the boundary conditions in the proposed method. Additionally, four numerical experiments are presented to illustrate the excellent convergence and high precision of the proposed approach.