TY - JOUR
T1 - A Boundary Mapped Collocation Method for the Analysis of the Arbitrarily Shaped Plates
AU - Huang , Zhentian
AU - Lei , Dong
AU - Han , Zi
AU - Xie , Heping
AU - Zhu , Jianbo
JO - Advances in Applied Mathematics and Mechanics
VL - 1
SP - 350
EP - 372
PY - 2024
DA - 2024/12
SN - 17
DO - http://doi.org/10.4208/aamm.OA-2022-0166
UR - https://global-sci.org/intro/article_detail/aamm/23605.html
KW - Boundary mapped collocation method, moving least squares, Kirchhoff plate, meshless method.
AB - <p style="text-align: justify;">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.</p>