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Mathematical Problems in Engineering
Volume 2013, Article ID 276304, 16 pages
Research Article

An 8-Node Shell Element for Nonlinear Analysis of Shells Using the Refined Combination of Membrane and Shear Interpolation Functions

1Department of Civil Engineering, Gangneung-Wonju National University, 7 Jukheon, Gangneung 210-702, Republic of Korea
2Department of Civil & Railroad Engineering, Daewon University College, 599 Shinwol, Jecheon 390-702, Republic of Korea

Received 6 April 2013; Accepted 19 June 2013

Academic Editor: Hung Nguyen-Xuan

Copyright © 2013 Woo-Young Jung and Sung-Cheon Han. 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.


An improved 8-node shell finite element applicable for the geometrically linear and nonlinear analyses of plates and shells is presented. Based on previous first-order shear deformation theory, the finite element model is further improved by the combined use of assumed natural strains and different sets of collocation points for the interpolation of the different strain components. The influence of the shell element with various conditions such as locations, number of enhanced membranes, and shear interpolation is also identified. By using assumed natural strain method with proper interpolation functions, the present shell element generates neither membrane nor shear locking behavior even when full integration is used in the formulation. Furthermore, to characterize the efficiency of these modifications of the 8-node shell finite elements, numerical studies are carried out for the geometrically linear and non-linear analysis of plates and shells. In comparison to some other shell elements, numerical examples for the methodology indicate that the modified element described locking-free behavior and better performance. More specifically, the numerical examples of annular plate presented herein show good validity, efficiency, and accuracy to the developed nonlinear shell element.