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PROCEEDINGS OF THE EIGHTH INTERNATIONAL CONFERENCE ON CIVIL AND STRUCTURAL ENGINEERING COMPUTING
Edited by: B.H.V. Topping
Geometric Non-linear Analysis of General Shell Structures Using a Flat Triangular Shell Element
M.H. Jang, J.Y. Kim and T.J. Kwun
School of Architecture, Sungkyunkwan University, Korea
M.H. Jang, J.Y. Kim, T.J. Kwun, "Geometric Non-linear Analysis of General Shell Structures Using a Flat Triangular Shell Element", in B.H.V. Topping, (Editor), "Proceedings of the Eighth International Conference on Civil and Structural Engineering Computing", Civil-Comp Press, Stirlingshire, UK, Paper 78, 2001. doi:10.4203/ccp.73.78
Keywords: shell, geometrically non-linear, updated Lagrangian formulation.
Thin plates and shells represent a particular type of component widely used in the construction of structural system that offer large internal space, gymnasiums, cooling towers, space structures, fuselages of aircraft, etc . One basic property with plates and shells is that they have one dimension, i.e., thickness, much smaller than other two. Thin Plate and shell problems are often categorized as large- deflection problems as their deflection under working or extreme loading conditions may have an order of magnitude comparable to that of their thickness. To analysis the load-deflection behaviour of plates and shells, theories of nonlinear nature are required to consider the effect of large deformation. In this regard, a geometric stiffness matrix has to be included, in addition to the elastic stiffness matrix used in linear analysis of shell structures.
There are three approaches to applying finite element methods to shell structures:
For large deformation analysis by finite element method, the equations of equilibrium of a structure may be derived from two alternative approaches as the total Lagrangian and updated Lagrangian formulations[2,3]. From the theoretical standpoint, both approaches should lead to same results for the same nonlinear problem. The total Lagrangian formulation has found wide applications in problems involving geometrical nonlinearity and elastic stability. The updated Lagrangian formulation may be particularly useful for slender structures such as beams, plates and shells.
In this paper, finite element formulation for geometrical nonlinear analysis of general shells using a three-node flat triangular shell element is presented. The flat shell element is obtained by combining the DKT plate bending element of Discrete Kirchhoff Theory and a membrane element derived from the Linear Strain Triangular (LST) element. The geometrically nonlinear analysis is performed using an Updated Lagrangian Formulation. An incremental iterative method based on the arc length method in conjunction with Newton-Raphson method is implemented in the present study for static analysis. In order to estimate the accuracy of the present formulation in predicting the nonlinear response of large structures, diverse models are analyzed. The present results are in good agreement with the results available in the existing literature and those obtained using the commercial finite element software (ABAQUS). The presented formulation did not show any convergence problems. As results, it can be concluded that the presented procedure is very useful for nonlinear analysis of shell structures.
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