A reduced constraint hp finite element method for shell problems

Mathematics of Computation

Volumn 66, Issue 217, 1997, Pages 15-29

  Suri, Manil ^a  

^a UNIVERSITY OF MARYLAND BALTIMORE COUNTY   (United States)

Author keywords

Finite element; hp; Locking; Shell

Indexed keywords

EID: 0042941127     PISSN: 00255718     EISSN: None     Source Type: Journal    
DOI: 10.1090/s0025-5718-97-00806-5     Document Type: Article

References (17)

1. D. N. Arnold and F. Brezzi, Locking-free finite element methods for shells, Math. Comp. 66 (1997), (to appear).
2. J.-P. Aubin, Applied Functional Analysis, Wiley, New York, 1979. MR 81a:46083
3. I. Babuška and M. Suri, The h-p version of the finite element method with quasiuniform meshes, RAIRO Modél. Math. Anal. Numér. 21 (1987), 199-238. MR 88d:65154
4. _, On locking and robustness in the finite element method, SIAM J. Numer. Anal. 29 (1992), 1261-1293. MR 94c:65128
5. M. Bernadou, P. G. Ciarlet and B. Miara, Existence theorems for two-dimensional linear shell theories, J. Elasticity 34 (1994), 111-138. MR 95f:73050
6. C. Bernardi and Y. Maday, Approximations spectrales de problèmes aux limites elliptiques, Springer-Verlag, Berlin and New York, 1992. MR 94f:65112
7. F. Brezzi and K. J. Bathe, Studies of finite element procedures - the inf-sup condition, equivalent forms and applications, Reliability of Methods for Engineering Analysis (I. J. Bathe and D. R. J. Owen, eds.), Pineridge Press, Swansea, 1986. pp. 1787-1801.
8. F. Brezzi and M. Fortin, Mixed and hybrid finite element methods, Springer-Verlag, New York-Heidelberg-Berlin, 1991. MR 92d:65187
9. P. M. Naghdi, Foundations of elastic shell theory, Progress in Solid Mechanics, Vol. 4 (I. N. Sneddon and R. Hill, eds.), North-Holland, Amsterdam, 1963, pp. 1-90. MR 29:790
10. _, The theory of shells and plates, Handbuch der Physik, Vol. VI a-2, Springer-Verlag, New York-Heidelberg-Berlin, 1972, pp. 425-640.
11. J. Piila and J. Pitkäranta, Energy estimates relating different linear elastic models of a thin cylindrical shell. I, II, I: SIAM J. Math. Anal. 24 (1993), 1-22, II: SIAM J. Math. Anal. 26 (1995), 820-849. MR 94a:73032; MR 96e:73068
12. J. Piila and J. Pitkäranta, Energy estimates relating different linear elastic models of a thin cylindrical shell. I, II, I: SIAM J. Math. Anal. 24 (1993), 1-22, II: SIAM J. Math. Anal. 26 (1995), 820-849. MR 94a:73032; MR 96e:73068
13. J. Pitkäranta, The problem of membrane locking in finite element analysis of cylindrical shells, Numer. Math. 61 (1992), 523-542. MR 93b:65178
14. J. Pitkäranta and M. Suri, Design principles and error analysis for reduced-shear plate bending finite elements, Numer. Math. (to appear)
15. L. R. Scott and M. Vogelius, Norm estimates for a maximal right inverse of the divergence operator in spaces of piecewise polynomials, RAIRO Modél. Math. Anal. Numér. 19 (1985), 111-143. MR 87i:65190
16. R. Stenberg and M. Suri, Mixed hp finite element methods for problems in elasticity and Stokes flow, Numer. Math. 72 (1996), 367 389. CMP 96:06
17. M. Suri, I. Babuška and C. Schwab. Locking effects in the finite element approximation of plate models, Math. Comp. 64 (1995), 461-482. MR 95f:65207