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Abstract
The natural element method (NEM) is a meshless method. The trial and test functions of the NEM are constructed using natural neighbor interpolations which are based on the Voronoi tessellation of a set of nodes. The NEM interpolation is linear between adjacent nodes on the boundary of the convex hull, which makes imposition of essential boundary conditions easy to implement. We investigate the performance of the NEM combined with the Newmark method for problems of elastodynamics in this article. Applications are considered for a cantilever beam with different initial load conditions. The NEM numerical results are compared with the finite element method. NEM shows promise for these applications.
Acknowledgments
This study is partially supported by the National Natural Science Foundation of China (no. 10972072) and National Basic Research Program of China (no. 2007CB714104) as well as the Special Fund of State Key Laboratory of Hydrology–Water Resources and Hydraulic Engineering at Hohai University (no. 2009585912). The third author is supported by the foundation of Huaibei Normal University (no. 2012XQ44). Their financial support is gratefully acknowledged.