The partition of unity finite element method for elastic wave propagation in Reissner–Mindlin plates
Article first published online: 20 NOV 2006
Copyright © 2006 John Wiley & Sons, Ltd.
International Journal for Numerical Methods in Engineering
Volume 70, Issue 12, pages 1451–1479, 18 June 2007
How to Cite
Hu, N., Wang, H. H., Yan, B., Fukunaga, H., Roy Mahapatra, D. and Gopalakrishnan, S. (2007), The partition of unity finite element method for elastic wave propagation in Reissner–Mindlin plates. Int. J. Numer. Meth. Engng., 70: 1451–1479. doi: 10.1002/nme.1932
- Issue published online: 18 MAY 2007
- Article first published online: 20 NOV 2006
- Manuscript Accepted: 29 SEP 2006
- Manuscript Revised: 26 SEP 2006
- Manuscript Received: 24 MAR 2006
- wave propagation;
- Reissner–Mindlin plate;
- shear locking;
This paper reports a numerical method for modelling the elastic wave propagation in plates. The method is based on the partition of unity approach, in which the approximate spectral properties of the infinite dimensional system are embedded within the space of a conventional finite element method through a consistent technique of waveform enrichment. The technique is general, such that it can be applied to the Lagrangian family of finite elements with specific waveform enrichment schemes, depending on the dominant modes of wave propagation in the physical system. A four-noded element for the Reissner–Mindlin plate is derived in this paper, which is free of shear locking. Such a locking-free property is achieved by removing the transverse displacement degrees of freedom from the element nodal variables and by recovering the same through a line integral and a weak constraint in the frequency domain. As a result, the frequency-dependent stiffness matrix and the mass matrix are obtained, which capture the higher frequency response with even coarse meshes, accurately. The steps involved in the numerical implementation of such element are discussed in details. Numerical studies on the performance of the proposed element are reported by considering a number of cases, which show very good accuracy and low computational cost. Copyright © 2006 John Wiley & Sons, Ltd.