Geometrically nonlinear dynamic analysis of thin shells by a four-node quadrilateral element with in-plane rotational degree of freedom
Keywords:
shells, plates, nonlinear dynamic analysis, quadrilateral, drilling rotation, Newmark, finite elementsAbstract
A simple and effective finite element incremental formulation based on the updated lagrangian corotational description for geometrically nonlinear dynamic analysis of shell structure is presented in this work. The flat shell element used is the classical four-node quadrilateral DKQ shell finite element, combined with the improvements of the in-plane behaviour by incorporation of the drilling rotation degree of freedom. The main goal is to have a good flat shell element of quadrilateral geometry, leading to reliable solutions in linear and geometrically nonlinear dynamic analysis. The Newmark’s direct time integration method is adopted to integrate the equations of motion, while the Newton–Raphson method is used for iterating within each time step increment until equilibrium is achieved. The results obtained through a series of selected examples demonstrate the effectiveness of the used shell finite element to predict the nonlinear dynamic response of complex structures, and the robustness of this nonlinear dynamic investigation taking account of both linear and non-linear dynamic problems.
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References
Ali, S. A., & Al-Noury, S. I. (1986). Nonlinear dynamic response of rectangular plates. Computers
and Structures, 22, 433–437.
Allman, D. J. (1984). A compatible triangular element including vertex rotations for plane elasticity
analysis. Computers and Structures, 19, 1–8.
Argyris, J., Papadrakakis, M., & Mouroutis, Z. S. (2003). Nonlinear dynamic analysis of shells
with the triangular element TRIC. Computer Methods in Applied Mechanics and Engineering,
, 3005–3038.
Batoz, J. L., & Ben Tahar, M. (1982). Evaluation of new Quadrilateral thin plate bending
element. International Journal for Numerical Methods in Engineering, 18, 1655–1677.
Bert, C. W., & Stricklin, J. D. (1988). Comparative evaluation of six different numerical integration
methods for non-linear dynamic systems. Journal of Sound and Vibration, 127, 221–229.
Boutagouga, D., Gouasmia, A., & Djeghaba, K. (2010). Geometrically nonlinear analysis of thin
shell by a quadrilateral finite element with in-plane rotational degrees of freedom. European
Journal of Computational Mechanics, 19, 707–724.
Clough, R. W., & Wilson, E. L. (1971). Dynamic finite element analysis of arbitrary thin shells.
Computers and Structures, 1, 33–56.
Dokainish, M. A., & Subbaraj, K. (1989). A survey of direct time-integration methods in computational
structural dynamics-I. Explicit methods. Computers and Structures, 32, 1371–1386.
Hughes, T. J. R., & Brezzi, F. (1989). On drilling degrees of freedom. Computer Methods in
Applied Mechanics and Engineering, 72, 105–121.
Hughes, T. J. R., Brezzi, F., Masud, A., & Harari, I. (1989). Finite elements with drilling degrees
of freedom: theory and numerical evaluations. Fifth International Symposium on Numerical
Methods in Engineering..Ashurst, UK, 3–17.
Ibrahimbegovic, A., Taylor, R. L., & Wilson, E. L. (1990). A robust quadrilateral membrane
finite element with drilling degrees of freedom. International Journal for Numerical Methods
in Engineering, 30, 445–457.
Kang, L., Zhang, Q., & Wang, Z. (2009). Linear and geometrically nonlinear analysis of novel
flat shell element with rotational degrees of freedom. Finite Elements in Analysis and Design,
, 386–392.
Meek, J. L., & Wang, Y. (1998). Nonlinear static and dynamic analysis of shell structures with
finite rotation. Computer Methods in Applied Mechanics and Engineering, 162, 301–315.
Neto, M. A., Leal, R. P., & Yu, W. (2012). A triangular finite element with drilling degrees of
freedom for static and dynamic analysis of smart laminated structures. Computers and Structures,
–109, 61–74.
Pajot, J. M., & Maute, K. (2006). Analytical sensitivity analysis of geometrically nonlinear structures
based on the co-rotational finite element method. Finite Elements in Analysis and
Design, 42, 900–913.Subbaraj, K., & Dokainish, M. A. (1989). A survey of direct tome-integration methods in computational
structural dynamics- II. Implicit methods. Computers and Structures, 32, 1387–1401.
