Abstract
In this paper, a finite element model for the nonlinear analysis of laminated shell structures and through-thickness functionally graded shells is presented. A tensor-based finite element formulation is presented to describe the deformation and constitutive laws of a shell in a natural and simple way by using curvilinear coordinates. In addition, a family of high-order elements with Lagrangian interpolations is used to avoid membrane and shear locking; no mixed interpolations are employed. A first-order shell theory with seven parameters is derived with exact nonlinear deformations and under the framework of the Lagrangian description. This approach takes into account thickness changes and, therefore, 3D constitutive equations are utilized. Numerical comparisons of the present results with those found in the literature for typical benchmark problems involving isotropic and laminated composite plates and shells as well as functionally graded plates and shells are found to be excellent and show the validity of the developed finite element model. Moreover, the simplicity of this approach makes it attractive for applications in contact mechanics and damage propagation in shells.
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References
R.A. Arciniega, On a tensor-based finite element model for the analysis of shell structures, PhD dissertation, Dept. of Mechanical Engineering, Texas A&M University, December 2005.
J.N. Reddy, An Introduction to Nonlinear Finite Element Analysis, Oxford University Press, Cambridge, UK, 2004.
J.N. Reddy, Mechanics of Laminated Composite Plates and Shells: Theory and Analysis, 2nd edition, CRC Press, Boca Raton, Florida, 2004.
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Reddy, J.N., Arciniega, R.A. (2006). Nonlinear Analysis of Composite and FGM Shells using Tensor-Based Shell Finite Elements. In: Motasoares, C.A., et al. III European Conference on Computational Mechanics. Springer, Dordrecht. https://doi.org/10.1007/1-4020-5370-3_31
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DOI: https://doi.org/10.1007/1-4020-5370-3_31
Publisher Name: Springer, Dordrecht
Print ISBN: 978-1-4020-4994-1
Online ISBN: 978-1-4020-5370-2
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