Evaluation of Linear and Geometrically Nonlinear Static and Dynamic Analysis of Thin Shells by Flat Shell Finite Elements
The choice of finite element to use in order to predict
nonlinear static or dynamic response of complex structures becomes
an important factor. Then, the main goal of this research work is to
focus a study on the effect of the in-plane rotational degrees of
freedom in linear and geometrically non linear static and dynamic
analysis of thin shell structures by flat shell finite elements. In this
purpose: First, simple triangular and quadrilateral flat shell finite
elements are implemented in an incremental formulation based on the
updated lagrangian corotational description for geometrically
nonlinear analysis. The triangular element is a combination of DKT
and CST elements, while the quadrilateral is a combination of DKQ
and the bilinear quadrilateral membrane element. In both elements,
the sixth degree of freedom is handled via introducing fictitious
stiffness. Secondly, in the same code, the sixth degrees of freedom in
these elements is handled differently where the in-plane rotational
d.o.f is considered as an effective d.o.f in the in-plane filed
interpolation. Our goal is to compare resulting shell elements. Third,
the analysis is enlarged to dynamic linear analysis by direct
integration using Newmark-s implicit method. Finally, the linear
dynamic analysis is extended to geometrically nonlinear dynamic
analysis where Newmark-s method is used to integrate equations of
motion and the Newton-Raphson method is employed for iterating
within each time step increment until equilibrium is achieved. The
obtained results demonstrate the effectiveness and robustness of the
interpolation of the in-plane rotational d.o.f. and present deficiencies
of using fictitious stiffness in dynamic linear and nonlinear analysis.
[1] J. L. Batoz, and M. Ben Tahar, "Evaluation of new Quadrilateral thin
plate bending element", International Journal For Numerical Methods
in Engineering, vol. 18, pp. 1655-1677, 1982.
[2] J. L. Batoz, and M. Ben Tahar, "A Study of three-node Triangular plate
bending element", International Journal For Numerical Methods in
Engineering, vol. 15, pp. 1771-1812, 1980.
[3] A. Ibrahimbegovic, R. L. Taylor, and E. L. Wilson, "A robust
quadrilateral membrane finite element with drilling degrees of freedom",
International Journal for Numerical Methods in Engineering, vol. 30,
pp. 445-457, 1990.
[4] O. C. Zienkiewicks, The finite element method, L Mc G H, Third
edition, 1977.
[5] P. K. Gotsis, "Structural optimization of shell structures", Computers
and Structures, vol. 50(4), pp. 499-507, 1994.
[6] Ph. Jetteur, "A shallow shell element with in-plane rotational degrees of
freedom", rapport interne, INRIA, 1986.
[7] P. Seshu, and V. Ramamurti, "Effect of fictitious rotational stiffness
coefficient on natural frequencies", Journal of Sound and Vibration, vol.
133(l), pp. 177-179, 1989.
[8] D. J. Allman, "A compatible triangular element including vertex
rotations for plane elasticity analysis", Computers and Structures, vol.
19, pp. 1-8, 1984.
[9] D. Cook, "On the Allman triangle and a related quadrilateral element",
Computers and Structures, vol. 22, pp. 1065-1067, 1986.
[10] T. J. R. Hughes, and F. Brezzi, "On drilling degrees of freedom",
Computer Methods in Applied Mechanics and Engineering, vol. 72, pp.
105-121, 1989.
[11] D. Boutagouga, A. Gouasmia, and K. Djeghaba, "geometrically non
linear analysis of thin shell by a quadrilateral finite element with inplane
rotational degrees of freedom", European Journal of
Computational Mechanics, vol. 19(8), pp. 707-724, 2010.
[12] M. A. Dokainish, and K. Subbaraj, "A survey of direct time-integration
methods in computational structural dynamics- I. explicit methods",
Computers and Structures.vol. 32(6), pp. 1371-1386, 1989.
[13] K. Subbaraj, and M. A. Dokainish, "A survey of direct tome-integration
methods in computational structural dynamics- II. implicit methods",
Computers and Structures,vol. 32(6), pp. 1387-1401, 1989.
[14] C. W. Bert, and J. D. Stricklin, "Comparative evaluation of six different
numerical integration methods for non-linear dynamic systems". Journal
of Sound and Vibration, vol. 127(2), pp. 221-229, 1988.
[15] K. S. Surana, "Geometrically nonlinear formulation for the curved shell
elements", International Journal for Numerical Methods in Engineering,
vol. 19, pp. 581-615, 1983.
[16] E. Ramm, "The Riks/Wempner approach - An extension of the
displacement control method in non linear analyses", Recent Advances
in nonlinear Computational Mechanics, university of Swansea, England,
pp. 63-89, 1982.
[17] J. L. Meek, and Y. Wang, "Nonlinear static and dynamic analysis of
shell structures with finite rotation", Computer Methods in Applied
Mechanics and Engineering, vol. 162, pp. 301-315, 1998.
[1] J. L. Batoz, and M. Ben Tahar, "Evaluation of new Quadrilateral thin
plate bending element", International Journal For Numerical Methods
in Engineering, vol. 18, pp. 1655-1677, 1982.
[2] J. L. Batoz, and M. Ben Tahar, "A Study of three-node Triangular plate
bending element", International Journal For Numerical Methods in
Engineering, vol. 15, pp. 1771-1812, 1980.
[3] A. Ibrahimbegovic, R. L. Taylor, and E. L. Wilson, "A robust
quadrilateral membrane finite element with drilling degrees of freedom",
International Journal for Numerical Methods in Engineering, vol. 30,
pp. 445-457, 1990.
[4] O. C. Zienkiewicks, The finite element method, L Mc G H, Third
edition, 1977.
[5] P. K. Gotsis, "Structural optimization of shell structures", Computers
and Structures, vol. 50(4), pp. 499-507, 1994.
[6] Ph. Jetteur, "A shallow shell element with in-plane rotational degrees of
freedom", rapport interne, INRIA, 1986.
[7] P. Seshu, and V. Ramamurti, "Effect of fictitious rotational stiffness
coefficient on natural frequencies", Journal of Sound and Vibration, vol.
133(l), pp. 177-179, 1989.
[8] D. J. Allman, "A compatible triangular element including vertex
rotations for plane elasticity analysis", Computers and Structures, vol.
19, pp. 1-8, 1984.
[9] D. Cook, "On the Allman triangle and a related quadrilateral element",
Computers and Structures, vol. 22, pp. 1065-1067, 1986.
[10] T. J. R. Hughes, and F. Brezzi, "On drilling degrees of freedom",
Computer Methods in Applied Mechanics and Engineering, vol. 72, pp.
105-121, 1989.
[11] D. Boutagouga, A. Gouasmia, and K. Djeghaba, "geometrically non
linear analysis of thin shell by a quadrilateral finite element with inplane
rotational degrees of freedom", European Journal of
Computational Mechanics, vol. 19(8), pp. 707-724, 2010.
[12] M. A. Dokainish, and K. Subbaraj, "A survey of direct time-integration
methods in computational structural dynamics- I. explicit methods",
Computers and Structures.vol. 32(6), pp. 1371-1386, 1989.
[13] K. Subbaraj, and M. A. Dokainish, "A survey of direct tome-integration
methods in computational structural dynamics- II. implicit methods",
Computers and Structures,vol. 32(6), pp. 1387-1401, 1989.
[14] C. W. Bert, and J. D. Stricklin, "Comparative evaluation of six different
numerical integration methods for non-linear dynamic systems". Journal
of Sound and Vibration, vol. 127(2), pp. 221-229, 1988.
[15] K. S. Surana, "Geometrically nonlinear formulation for the curved shell
elements", International Journal for Numerical Methods in Engineering,
vol. 19, pp. 581-615, 1983.
[16] E. Ramm, "The Riks/Wempner approach - An extension of the
displacement control method in non linear analyses", Recent Advances
in nonlinear Computational Mechanics, university of Swansea, England,
pp. 63-89, 1982.
[17] J. L. Meek, and Y. Wang, "Nonlinear static and dynamic analysis of
shell structures with finite rotation", Computer Methods in Applied
Mechanics and Engineering, vol. 162, pp. 301-315, 1998.
@article{"International Journal of Architectural, Civil and Construction Sciences:50178", author = "Djamel Boutagouga and Kamel Djeghaba", title = "Evaluation of Linear and Geometrically Nonlinear Static and Dynamic Analysis of Thin Shells by Flat Shell Finite Elements", abstract = "The choice of finite element to use in order to predict
nonlinear static or dynamic response of complex structures becomes
an important factor. Then, the main goal of this research work is to
focus a study on the effect of the in-plane rotational degrees of
freedom in linear and geometrically non linear static and dynamic
analysis of thin shell structures by flat shell finite elements. In this
purpose: First, simple triangular and quadrilateral flat shell finite
elements are implemented in an incremental formulation based on the
updated lagrangian corotational description for geometrically
nonlinear analysis. The triangular element is a combination of DKT
and CST elements, while the quadrilateral is a combination of DKQ
and the bilinear quadrilateral membrane element. In both elements,
the sixth degree of freedom is handled via introducing fictitious
stiffness. Secondly, in the same code, the sixth degrees of freedom in
these elements is handled differently where the in-plane rotational
d.o.f is considered as an effective d.o.f in the in-plane filed
interpolation. Our goal is to compare resulting shell elements. Third,
the analysis is enlarged to dynamic linear analysis by direct
integration using Newmark-s implicit method. Finally, the linear
dynamic analysis is extended to geometrically nonlinear dynamic
analysis where Newmark-s method is used to integrate equations of
motion and the Newton-Raphson method is employed for iterating
within each time step increment until equilibrium is achieved. The
obtained results demonstrate the effectiveness and robustness of the
interpolation of the in-plane rotational d.o.f. and present deficiencies
of using fictitious stiffness in dynamic linear and nonlinear analysis.", keywords = "Flat shell, dynamic analysis, nonlinear, Newmark,
drilling rotation.", volume = "7", number = "2", pages = "112-7", }