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Mathematical Problems in Engineering
Volume 2015, Article ID 301054, 9 pages
Research Article

Robustness of Hierarchical Laminated Shell Element Based on Equivalent Single-Layer Theory

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 15 September 2014; Accepted 26 February 2015

Academic Editor: Sellakkutti Rajendran

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.


This paper deals with the hierarchical laminated shell elements with nonsensitivity to adverse conditions for linear static analysis of cylindrical problems. Displacement approximation of the elements is established by high-order shape functions using the integrals of Legendre polynomials to ensure continuity at the interface between adjacent elements. For exact linear mapping of cylindrical shell problems, cylindrical coordinate is adopted. To find global response of laminated composite shells, equivalent single-layer theory is also considered. Thus, the proposed elements are formulated by the dimensional reduction from three-dimensional solid to two-dimensional plane which allows the first-order shear deformation and considers anisotropy due to fiber orientation. The sensitivity tests are implemented to show robustness of the present elements with respect to severe element distortions, very high aspect ratios of elements, and very large radius-to-thickness ratios of shells. In addition, this element has investigated whether material conditions such as isotropic and orthotropic properties may affect the accuracy as the element distortion ratio is increased. The robustness of present element has been compared with that of several shell elements available in ANSYS program.