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PROCEEDINGS OF THE EIGHTH INTERNATIONAL CONFERENCE ON COMPUTATIONAL STRUCTURES TECHNOLOGY
Edited by: B.H.V. Topping, G. Montero and R. Montenegro
Geometrical Non-linear Analysis of Shells: A New Positional Finite Element Method
H.B. Coda and R.P. Paccola
Department of Structural Engineering, University of São Paulo, São Carlos, Brazil
H.B. Coda, R.P. Paccola, "Geometrical Non-linear Analysis of Shells: A New Positional Finite Element Method", in B.H.V. Topping, G. Montero, R. Montenegro, (Editors), "Proceedings of the Eighth International Conference on Computational Structures Technology", Civil-Comp Press, Stirlingshire, UK, Paper 162, 2006. doi:10.4203/ccp.83.162
Keywords: finite elements, curved, elastic, shells, positions, large deformation.
The good representation of shells exhibiting large displacement, rotation and strain is a continuous activity of a large number of research works. Some recent works may be cited as for example: Petchsasithon & Gosling  Pimenta et al. , Campello et al. , Sze et al. , Hong et al. , Sansour & Kollmann  and Bischof & Ramm  to confirm the current importance of the subject.
The work of Bischoff & Ramm  about the physical meaning of higher order kinematics and static variables for three-dimensional shell formulation clarifies all aspects of shell modeling and provide more physical insight to the shell behaviour. These aspects are crucial for proposing coherent models for finite element shell analysis.
This work presents an alternative shell formulation based on a non-conventional nodal parameters. This formulation has its origin in the so-called positional formulation proposed in the works of Coda & Greco  and Greco & Coda  for two dimensional frame analysis. The novelty of the proposed technique is the parameters considered, i.e., nodal positions (not displacements) and generalized vector components that comprises both direction cossines and shell thickness at the same time.
The objective of this work is not to achieve a better model than the ones proposed by Bischoff & Ramm , Pimenta et al.  or Sansour & Kollman  for example, but to offer an alternative way to achieve the numerical procedure for geometrically non-linear analysis of shell using curved triangular (or any geometry) elements without the use of 'cumbersome notations' . To facilitate even more the understanding of the positional process, non-linear engineering strain is adopted, taking advantage of simple linear engineering stress-strain relations.
The resulting formulation presents six degrees of freedom by node and considers linear thickness variation during the deformation process. Curved triangular elements with cubic approximation for both positions and generalized vector components are adopted. The modified positional mapping, as presented, fulfils a three-dimensional representation and requires a three-dimensional relaxed constitutive relation to avoid Poisson thickness locking. Several numerical simulations are presented in order to illustrate and confirm the accuracy and applicability of the formulation.
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