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CivilComp Proceedings
ISSN 17593433 CCP: 83
PROCEEDINGS OF THE EIGHTH INTERNATIONAL CONFERENCE ON COMPUTATIONAL STRUCTURES TECHNOLOGY Edited by: B.H.V. Topping, G. Montero and R. Montenegro
Paper 162
Geometrical Nonlinear 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 Nonlinear 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", CivilComp Press, Stirlingshire, UK, Paper 162, 2006. doi:10.4203/ccp.83.162
Keywords: finite elements, curved, elastic, shells, positions, large deformation.
Summary
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 [1] Pimenta et al. [2],
Campello et al. [3], Sze et al. [4], Hong et al. [5], Sansour & Kollmann [6] and
Bischof & Ramm [7] to confirm the current importance of the subject.
The work of Bischoff & Ramm [7] about the physical meaning of higher order kinematics and static variables for threedimensional 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 nonconventional nodal parameters. This formulation has its origin in the socalled positional formulation proposed in the works of Coda & Greco [8] and Greco & Coda [9] 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 [7], Pimenta et al. [2] or Sansour & Kollman [6] for example, but to offer an alternative way to achieve the numerical procedure for geometrically nonlinear analysis of shell using curved triangular (or any geometry) elements without the use of 'cumbersome notations' [7]. To facilitate even more the understanding of the positional process, nonlinear engineering strain is adopted, taking advantage of simple linear engineering stressstrain 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 threedimensional representation and requires a threedimensional 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. References
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