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Mathematical Problems in Engineering
Volume 2015 (2015), Article ID 676181, 11 pages
Research Article

ESL Based Cylindrical Shell Elements with Hierarchical Shape Functions for Laminated Composite Shells

1School of General Education, Yeungnam University, 280 Daehak-Ro, Gyeongsan, Gyeongbuk 712-749, Republic of Korea
2Department of Civil Engineering, Yeungnam University, 280 Daehak-Ro, Gyeongsan, Gyeongbuk 712-749, Republic of Korea

Received 7 October 2014; Accepted 7 February 2015

Academic Editor: Dane Quinn

Copyright © 2015 Jae S. Ahn 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.


We introduce higher-order cylindrical shell element based on ESL (equivalent single-layer) theory for the analysis of laminated composite shells. The proposed elements are formulated by the dimensional reduction technique from three-dimensional solid to two-dimensional cylindrical surface with plane stress assumption. It allows the first-order shear deformation and considers anisotropic materials due to fiber orientation. The element displacement approximation is established by the integrals of Legendre polynomials with hierarchical concept to ensure the -continuity at the interface between adjacent elements as well as -continuity at the interface between adjacent layers. For geometry mapping, cylindrical coordinate is adopted to implement the exact mapping of curved shell configuration with a constant curvature with respect to any direction in the plane. The verification and characteristics of the proposed element are investigated through the analyses of three cylindrical shell problems with different shapes, loadings, and boundary conditions.