Locking-free finite element methods for shells

Mathematics of Computation

Volumn 66, Issue 217, 1997, Pages 1-14

  Arnold, Douglas N ^a   Brezzi, Franco ^b  

^a PENNSYLVANIA STATE UNIVERSITY   (United States)

^b UNIVERSITY OF PAVIA   (Italy)

Author keywords

Finite element; Locking; Shell

Indexed keywords

EID: 0031540408     PISSN: 00255718     EISSN: None     Source Type: Journal    
DOI: 10.1090/s0025-5718-97-00785-0     Document Type: Article

References (18)

1. D. N. Arnold and F. Brezzi, Some new elements for the Reissner-Mindlin plate model, Boundary Value Problems for Partial Differential Equations and Applications (C. Baiocchi and J.-L. Lions, eds.). Masson, Paris, 1993, pp. 287-292. MR 94k:73066
2. D. N. Arnold and R. S. Falk, A uniformly accurate finite element method for the Reissner-Mindlin plate, SIAM J. Numer. Anal. 26 (1989), 1276-1290. MR 91c:65068
3. _, Asymptotic analysis of the boundary layer for the Reissner-Mindlin plate model, SIAM J. Math. Anal. 27 (1996), 486-514. CMP 96:09
4. I. Babuška and M. Suri, On locking and robustness in the finite element method, SIAM J. Numer. Anal. 29 (1992), 1261-1293. MR 94c:65128
5. K.-J. Bathe and E. Wilson, Numerical methods in finite element analysis, Prentice-Hall, Englewood Cliffs, NJ, 1976.
6. M. Bernadou, P. G. Ciarlet, and B. Miara, Existence theorems for two-dimensional linear shell theories, J. Elasticity 34 (1992), 111-138. MR 95f:73050
7. F. Brezzi and M. Fortin, Mixed and hybrid finite element methods, Springer-Verlag, New York-Heidelberg-Berlin, 1991. MR 92d:65187
8. F. Brezzi, M. Fortin, and D. Marini, Mixed finite element methods with continuous stresses, Math. Mod. Methods Appl. Sci. 3 (1993), 275-287. MR 94g:65121
9. P. Clement, Approximation by finite element functions using local regularization, RAIRO, Anal. Numér. 9 (1975), 33-76. MR 53:4569
10. L. Gastaldi, Uniform interior error estimates for the Reissner-Mindlin plate model, Math. Comp. 61 (1993), 539-568. MR 94a:65067
11. V. Girault and P. A. Raviart, Finite element methods for Navier-Stokes equations, Springer-Verlag, New York-Heidelberg-Berlin, 1986. MR 88b:65129
12. T. J. R. Hughes, The finite element method, linear static and dynamic finite element analysis, Prentice-Hall, Englewood Cliffs, NJ, 1987. MR 90i:65001
13. X. Liu, Interior estimates for some mixed finite element methods, Ph.D. thesis, Penn State Univ., 1993.
14. 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
15. P. M. Naghdi, The theory of shells and plates, Handbuch der Physik, Vol. VI a-2, Springer-Verlag, New York-Heidelberg-Berlin, 1972, pp. 425-640.
16. J. Pitkäranta, The problem of membrane, locking in finite element analysis of cylindrical shells, Numer. Math. 61 (1992), 523-542. MR 93b:65178
17. T.-X. Zhou, The partial projection method in the finite element discretization of the Reissner-Mindlin plate, J. Comput. Math 13 (1995), 172-191. CMP 95:12
18. O. C. Zienkiewicz and R. L. Taylor, The finite element method, McGraw-Hill, New York, NY, 1989. MR 96c:73069