References
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85. Y. Basar, Finite-rotation theories for composite laminates. Acta Mechanica 98, 159–176
(1993)
86. L.N.B. Gummadi, A.N. Palazotto, Finite element analysis of arches undergoing large rotations
- I: theoretical comparison. Finite Elem. Anal. Des. 24, 213–235 (1997)
87. A.N. Palazotto, L.N.B. Gummadi, J.C. Bailey, Finite element analysis of arches undergoing
large rotations - II: classification. Finite Elem. Anal. Des. 24, 237252 (1997)
88. R.A. Arciniega, J.N. Reddy, Tensor-based finite element formulation for geometrically nonlinear analysis of shell structures. Comput. Methods Appl. Mech. Eng. 196, 1048–1073 (2007)
89. Y. Basar, Y. Ding, Shear deformation models for large-strain shell analysis. Int. J. Solids
Struct. 14, 1687–1708 (1997)
90. E.N. Dvorkin, K.J. Bather, A continuum mechanics based four-node shell element for general
non-linear analysis. Eng. Comput. 1, 77–88 (1984)
91. N. Stander, A. Matzenmiller, E. Ramm, An assessment of assumed strain methods in finite
rotation shell analysis. Eng. Comput. 6, 58–66 (1989)
92. K.Y. Sze, X.H. Liu, S.H. Lo, Popular benchmark problems for geometric nonlinear analysis
of shells. Finite Elem. Anal. Des. 40, 1551–1569 (2004)
93. I. Koˇ zar, A. Ibrahimbegovi´ c, Finite elemtent formulation of the finite rotation solid element.
Finite Elem. Anal. Des. 20, 101–126 (1995)
94. A. Masud, C.L. Tham, W.K. Liu, A stabilized 3-D co-rotational formulation for geometrically
nonlinear analysis of multi-layered composite shells. Comput. Mech. 26, 1–12 (2000)
95. S. Lopez, G.L. Sala, A finite element approach to statical and dynamical analysis of geometrically nonlinear structures. Finite Elem. Anal. Des. 46, 1093–1105 (2010)
96. P. Betsch, A. Menzel, E. Stein, On the parametrization of finite rotations in computational
mechanics-a classification of concepts with application to smooth shells. Comput. Methods
Appl. Mech. Eng. 155, 273–305 (1998)
97. N. Bruechter, E. Ramm, Shell theory versus degeneration-a comparison in large rotation finite
element analysis. Int. J. Numer. Methods Eng. 34, 39–59 (1992)
98. J.C. Simo, M.S. Rifai, D.D. Fox, On a stress resultant geometrically exact shell model. Part
VI: conserving algorithms for non-linear dynamics. Int. J. Numer. Methods Eng. 34, 117–164
(1992)
99. J.C. Simo, On a stress resultant geometrically exact shell model. Part VII: shell intersections
with 5/6 DOF finite element formulations. Comput. Methods Appl. Mech. Eng. 108, 319–339
(1993)
100. P. Betsch, F. Gruttmann, E. Stein, A 4-node finite shell element for the implementation of
general hyperelastic 3D-elasticity at finite strains. Comput. Methods Appl. Mech. Eng. 130,
57–79 (1996)
101. Y. Basar, M. Itskov, A. Eckstein, Composite laminates: nonlinear interlaminar stress analysis
by multi-layer shell elements. Comput. Methods Appl. Mech. Eng. 185, 367–397 (2000)
102. L. Wang, G. Thierauf, Finite rotations in non-linear analysis of elastic shells. Comput. Struct.
79, 2357–2367 (2001)
103. J. Pitkäranta, The problem of membrane locking in finite element analysis of cylindrical shells.
Numerische Mathematik 61, 523–542 (1992)
104. Y. Leino, J. Pitkäranta, On the membrane locking of h − p finite elements in a cylindrical
shell problem. Int. J. Numer. Methods Eng. 37, 1053–1070 (1994)
105. K.J. Bathe, A formulation of general shell elements-the use of mixed interpolation of tensorial
components. Int. J. Numer. Methods Eng. 22, 697–722 (1986)
106. F. Brezzi, K.J. Bathe, M. Fortin, Mixed-interpolated elements for Reissner-Mindlin plates.
Int. J. Numer. Methods Eng. 28, 1787–1801 (1989)
107. R.L. Muhanna, New assumed natural strain formulation of the shallow shell element. Commun. Numer. Methods Eng. 9, 989–1004 (1993)
108. H.C. Huang, E. Hinton, A new nine node degenerated shell element with enhanced membrane
and shear interpolation. Int. J. Numer. Methods Eng. 22, 73–92 (1986)
109. J.C. Simo, T.J.R. Hughes, On the variational foundations of assumed strain methods. J. Appl.
Mech. 53, 51–54 (1986)
27
85. Y. Basar, Finite-rotation theories for composite laminates. Acta Mechanica 98, 159–176
(1993)
86. L.N.B. Gummadi, A.N. Palazotto, Finite element analysis of arches undergoing large rotations
- I: theoretical comparison. Finite Elem. Anal. Des. 24, 213–235 (1997)
87. A.N. Palazotto, L.N.B. Gummadi, J.C. Bailey, Finite element analysis of arches undergoing
large rotations - II: classification. Finite Elem. Anal. Des. 24, 237252 (1997)
88. R.A. Arciniega, J.N. Reddy, Tensor-based finite element formulation for geometrically nonlinear analysis of shell structures. Comput. Methods Appl. Mech. Eng. 196, 1048–1073 (2007)
89. Y. Basar, Y. Ding, Shear deformation models for large-strain shell analysis. Int. J. Solids
Struct. 14, 1687–1708 (1997)
90. E.N. Dvorkin, K.J. Bather, A continuum mechanics based four-node shell element for general
non-linear analysis. Eng. Comput. 1, 77–88 (1984)
91. N. Stander, A. Matzenmiller, E. Ramm, An assessment of assumed strain methods in finite
rotation shell analysis. Eng. Comput. 6, 58–66 (1989)
92. K.Y. Sze, X.H. Liu, S.H. Lo, Popular benchmark problems for geometric nonlinear analysis
of shells. Finite Elem. Anal. Des. 40, 1551–1569 (2004)
93. I. Koˇ zar, A. Ibrahimbegovi´ c, Finite elemtent formulation of the finite rotation solid element.
Finite Elem. Anal. Des. 20, 101–126 (1995)
94. A. Masud, C.L. Tham, W.K. Liu, A stabilized 3-D co-rotational formulation for geometrically
nonlinear analysis of multi-layered composite shells. Comput. Mech. 26, 1–12 (2000)
95. S. Lopez, G.L. Sala, A finite element approach to statical and dynamical analysis of geometrically nonlinear structures. Finite Elem. Anal. Des. 46, 1093–1105 (2010)
96. P. Betsch, A. Menzel, E. Stein, On the parametrization of finite rotations in computational
mechanics-a classification of concepts with application to smooth shells. Comput. Methods
Appl. Mech. Eng. 155, 273–305 (1998)
97. N. Bruechter, E. Ramm, Shell theory versus degeneration-a comparison in large rotation finite
element analysis. Int. J. Numer. Methods Eng. 34, 39–59 (1992)
98. J.C. Simo, M.S. Rifai, D.D. Fox, On a stress resultant geometrically exact shell model. Part
VI: conserving algorithms for non-linear dynamics. Int. J. Numer. Methods Eng. 34, 117–164
(1992)
99. J.C. Simo, On a stress resultant geometrically exact shell model. Part VII: shell intersections
with 5/6 DOF finite element formulations. Comput. Methods Appl. Mech. Eng. 108, 319–339
(1993)
100. P. Betsch, F. Gruttmann, E. Stein, A 4-node finite shell element for the implementation of
general hyperelastic 3D-elasticity at finite strains. Comput. Methods Appl. Mech. Eng. 130,
57–79 (1996)
101. Y. Basar, M. Itskov, A. Eckstein, Composite laminates: nonlinear interlaminar stress analysis
by multi-layer shell elements. Comput. Methods Appl. Mech. Eng. 185, 367–397 (2000)
102. L. Wang, G. Thierauf, Finite rotations in non-linear analysis of elastic shells. Comput. Struct.
79, 2357–2367 (2001)
103. J. Pitkäranta, The problem of membrane locking in finite element analysis of cylindrical shells.
Numerische Mathematik 61, 523–542 (1992)
104. Y. Leino, J. Pitkäranta, On the membrane locking of h − p finite elements in a cylindrical
shell problem. Int. J. Numer. Methods Eng. 37, 1053–1070 (1994)
105. K.J. Bathe, A formulation of general shell elements-the use of mixed interpolation of tensorial
components. Int. J. Numer. Methods Eng. 22, 697–722 (1986)
106. F. Brezzi, K.J. Bathe, M. Fortin, Mixed-interpolated elements for Reissner-Mindlin plates.
Int. J. Numer. Methods Eng. 28, 1787–1801 (1989)
107. R.L. Muhanna, New assumed natural strain formulation of the shallow shell element. Commun. Numer. Methods Eng. 9, 989–1004 (1993)
108. H.C. Huang, E. Hinton, A new nine node degenerated shell element with enhanced membrane
and shear interpolation. Int. J. Numer. Methods Eng. 22, 73–92 (1986)
109. J.C. Simo, T.J.R. Hughes, On the variational foundations of assumed strain methods. J. Appl.
Mech. 53, 51–54 (1986)