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Mathematical Problems in Engineering
Volume 2015, Article ID 638783, 13 pages
Research Article

Enriched Element-Free Galerkin Method for Fracture Analysis of Functionally Graded Piezoelectric Materials

School of Mechanical Science and Engineering, Jilin University, No. 5988 Renmin Street, Changchun 130022, China

Received 16 January 2015; Revised 30 March 2015; Accepted 15 April 2015

Academic Editor: Timon Rabczuk

Copyright © 2015 Guang Wei Meng et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A new method using the enriched element-free Galerkin method (EEFGM) to model functionally graded piezoelectric materials (FGPMs) with cracks was presented. To improve the solution accuracy, extended terms were introduced into the approximation function of the conventional element-free Galerkin method (EFGM) to describe the displacement and electric fields near the crack. Compared with the conventional EFGM, the new approach requires smaller domain to describe the crack-tip singular field. Additionally, the domain of the nodes was not affected by the crack. Therefore, the visibility method and the diffraction method were no longer needed. The mechanical response of FGPM was discussed, when its material parameters changed exponentially in a certain direction. The modified -integrals for FGPM were deduced, whose results were compared with the results of the conventional EFGM and the analytical solution. Numerical example results illustrated that this method is feasible and precise.