Analysis of a bilinear finite element for shallow shells I: Approximation of inextensional deformations
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- by Ville Havu and Juhani Pitkäranta PDF
- Math. Comp. 71 (2002), 923-943 Request permission
Abstract:
We consider a bilinear reduced-strain finite element formulation for a shallow shell model of Reissner–Naghdi type. The formulation is closely related to the facet models used in engineering practice. We estimate the error of this scheme when approximating an inextensional displacement field. We make the strong assumptions that the domain and the finite element mesh are rectangular and that the boundary conditions are periodic and the mesh uniform in one of the coordinate directions. We prove then that for sufficiently smooth fields, the convergence rate in the energy norm is of optimal order uniformly with respect to the shell thickness. In case of elliptic shell geometry the error bound is furthermore quasioptimal, whereas in parabolic and hyperbolic geometries slightly enhanced smoothness is required, except for the degenerate cases where the characteristic lines are parallel with the mesh lines. The error bound is shown to be sharp.References
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Additional Information
- Ville Havu
- Affiliation: Institute of Mathematics, Helsinki University of Technology, P.O. Box 1100, 02015 Helsinki Univ. of Tech., Finland
- Email: Ville.Havu@hut.fi
- Juhani Pitkäranta
- Affiliation: Institute of Mathematics, Helsinki University of Technology, P.O. Box 1100, 02015 Helsinki Univ. of Tech., Finland
- Email: Juhani.Pitkaranta@hut.fi
- Received by editor(s): April 12, 2000
- Received by editor(s) in revised form: September 28, 2000
- Published electronically: November 20, 2001
- © Copyright 2001 American Mathematical Society
- Journal: Math. Comp. 71 (2002), 923-943
- MSC (2000): Primary 65N30; Secondary 74K25
- DOI: https://doi.org/10.1090/S0025-5718-01-01376-X
- MathSciNet review: 1898740