@Article{cmes.2022.019828,
AUTHOR = {Zhijuan Meng, Yanan Fang, Yumin Cheng},
TITLE = {A Fast Element-Free Galerkin Method for 3D Elasticity Problems},
JOURNAL = {Computer Modeling in Engineering \& Sciences},
VOLUME = {132},
YEAR = {2022},
NUMBER = {1},
PAGES = {55--79},
URL = {http://www.techscience.com/CMES/v132n1/48084},
ISSN = {1526-1506},
ABSTRACT = {In this paper, a fast element-free Galerkin (FEFG) method for three-dimensional (3D) elasticity problems is
established. The FEFG method is a combination of the improved element-free Galerkin (IEFG) method and the
dimension splitting method (DSM). By using the DSM, a 3D problem is converted to a series of 2D ones, and
the IEFG method with a weighted orthogonal function as the basis function and the cubic spline function as the
weight function is applied to simulate these 2D problems. The essential boundary conditions are treated by the
penalty method. The splitting direction uses the finite difference method (FDM), which can combine these 2D
problems into a discrete system. Finally, the system equation of the 3D elasticity problem is obtained. Some specific
numerical problems are provided to illustrate the effectiveness and advantages of the FEFG method for 3D elasticity
by comparing the results of the FEFG method with those of the IEFG method. The convergence and relative error
norm of the FEFG method for elasticity are also studied.},
DOI = {10.32604/cmes.2022.019828}
}