Least-squares finite element formulation for shear-deformable shells

Computer Methods in Applied Mechanics and Engineering

Volumn 194, Issue 21-24 SPEC. ISS., 2005, Pages 2464-2493

  Pontaza, J P ^a   Reddy, J N ^a  

^a Department of Electrical and Computer Engineering   (United States)

Author keywords

hp methods; Least squares finite element formulations; Shear deformable shells; Shells

Indexed keywords

BENDING (DEFORMATION); DEFLECTION (STRUCTURES); FINITE ELEMENT METHOD; LEAST SQUARES APPROXIMATIONS; MATHEMATICAL MODELS; MODAL ANALYSIS; OPTIMIZATION; SHEAR DEFORMATION; STRUCTURAL ANALYSIS;

EQUILIBRIUM EQUATIONS; HILBERT SPACE; SHEAR DEFORMABLE SHELLS;

SHELLS (STRUCTURES);

SHELL;

EID: 16244367441     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2004.07.041     Document Type: Article

References (33)

1. J.N. Reddy Energy principles and variational methods in applied mechanics 1998 John Wiley New York
2. J.N. Reddy An introduction to nonlinear finite element analysis 2004 Oxford University Press Oxford
3. S. Ahmad B.M. Irons O.C. Zienkiewicz Analysis of thick and thin shell structures by curved finite elements Int. J. Numer. Methods Engrg. 2 1970 419-451
4. Y. Leino J. Pitkäranta On the membrane locking of h-p finite elements in a cylindrical shell problem Int. J. Numer. Methods Engrg. 37 1994 1053-1070
5. J. Pitkäranta Y. Leino O. Ovakainen J. Piila Shell deformation states and the finite element method: A benchmark study of cylindrical shells Comput. Methods Appl. Mech. Engrg. 128 1995 81-121
6. H. Hakula Y. Leino J. Pitk̈ranta Scale resolution, locking, and high-order finite element modelling of shells Computer Methods Appl. Mech. Engrg. 133 1996 157-182
7. K.J. Bathe E.N. Dvorkin A formulation of general shell elements - the use of mixed interpolation of tensorial components Int. J. Numer. Methods Engrg. 22 1986 697-722
8. H.C. Huang Membrane locking and assumed strain elements Comput. Struct. 27 1987 671-677
9. K.U. Bletzinger M. Bischoff E. Ramm A unified approach for shear-locking-free triangular and rectangular shell finite elements Comput. Struct. 75 2000 321-334
10. M. Cho H.Y. Roh Development of geometrically exact new shell elements based on general curvilinear co-ordinates Int. J. Numer. Methods Engrg. 56 2003 81-115
11. D.N. Arnold F. Brezzi Locking-free finite element methods for shells Math. Comput. 66 1997 1-14
12. J.H. Bramble T. Sun A locking-free finite element method for Naghdi shells J. Comput. Appl. Math. 89 1997 119-133
13. M. Malinem J. Pitkäranta A benchmark study of reduced-strain shell finite elements: Quadratic schemes Int. J. Numer. Methods Engrg. 48 2000 1637-1671
14. C. Chinosi L. Della Croce T. Scapolla Hierarchic finite elements for thin Naghdi shell model Int. J. Solids Struct. 35 1998 1863-1880
15. P.B. Bochev M.D. Gunzburger Finite element methods of least-squares type SIAM Rev. 40 1998 789-837
16. B.N. Jiang The least-squares finite element method 1998 Springer-Verlag New York
17. J.P. Pontaza J.N. Reddy Spectral/hp least-squares finite element formulation for the Navier-Stokes equations J. Comput. Phys. 190 2003 523-549
18. J.P. Pontaza J.N. Reddy Space-time coupled spectral/hp least-squares finite element formulation for the incompressible Navier-Stokes equations J. Comput. Phys. 197 2004 418-459
19. B.N. Jiang The least-squares finite element method for elasticity. Part II: Bending of thin plates Int. J. Numer. Methods Engrg. 54 2002 1459-1475
20. Z. Cai X. Ye H. Zhang Least-squares finite element approximations for the Reissner-Mindlin plate Numer. Linear Algebra Appl. 6 1999 479-496
21. J.P. Pontaza J.N. Reddy Mixed plate bending elements based on least-squares formulation Intl J. Numer. Methods Engrg. 60 2004 891-922
22. A.E. Green W. Zerna Theoretical elasticity second ed. 1968 Oxford University Press
23. P.M. Naghdi Progress in Solid Mechanics, Vol. 4, Foundations of Elastic Shell Theory 1963 North-Holland Amsterdam
24. D. Chappelle K.J. Bathe Fundamental considerations for the finite element analysis of shell structures Comput. Struct. 66 1998 19-36
25. T.C. Warburton S.J. Sherwin G.E. Karniadakis Basis functions for triangular and quadrilateral high-order elements SIAM J. Scientific Comput. 20 1999 1671-1695
26. J.N. Reddy An introduction to the finite element method second ed. 1993 McGraw-Hill
27. C.M. Wang Y.C. Wang J.N. Reddy V. Thevendran Improved computation of stress resultants in the p-Ritz method J. Sruct. Engrg. 128 2002 249-257
28. P.S. Lee K.J. Bathe On the asymptotic behavior of shell structures and the evaluation in finite element solutions Comput. Struct. 80 2002 235-255
29. G. Cantin R.W. Clough A curved, cylindrical shell, finite element AIAA J. 6 1968 1057-1062
30. A.C. Scordelis K.S. Lo Computer analysis of cylindrical shells J. Am. Concrete Inst. 61 1964 539-561
31. R.H. MacNeal R.L. Harder A proposed standard set of problems to test finite element accuracy Finite Element Anal. Des. 1 1985 3-20
32. D. Chapelle D.L. Oliveira M.L. Bucalem MITC elements for a classical shell model Comput. Struct. 81 2003 523-533
33. I. Kreja R. Schmidt J.N. Reddy Finite elements based on a first-order shear deformation moderate rotation shell theory with applications to the analysis of composite structures Int. J. Non-Linear Mech. 32 1997 1123-1142