Download Vibration Analysis of Laminated Plates and Shells with Improved

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Title (14 point bold type)
Vibration Analysis of Laminated Plates and Shells with Improved
Degenerated Shell Element
Authors (14 point plain type)
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Hyo-Gyoung Kwak1 and Hyuk-Chun Noh2
Affiliation (12 point italic type)
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Department of Civil and Environmental Engineering, KAIST, Daejeon 305-701, Korea
2
Smart Infra-Structure Technology Center, KAIST, Daejeon 305-701, Korea
[email protected], [email protected]
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Indentation
ABSTRACT
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In this paper, 4 node degenerated shell element adopting the assumed strain fields to eliminate the
shear and membrane locking in the thin shell is applied in the nonlinear dynamic analysis of composite
materials. The nonlinearity in the isotropic and anisotropic material is considered through the flow
theory of plasticity. The influence of lamination on the structural behavior in static and dynamic is also
discussed.
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INTRODUCTION
Main heading
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One of the recent research interests in the structural analysis is in the area of plates and shells,
especially in the laminated composite form. Structural composites are widely adopted due to their high
specific stiffness and strengths. Obtaining the analytical solution for the laminated composite shells
with variety of geometrical configurations such as saddle, cylindrical, spherical quadratic and hypar
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are very difficult if it is not impossible in some cases.
The analysis of general shells is performed based on the various analytical and numerical
techniques (Dipankar et al. 1998, Swaddiwudhipong 1996). The frequency characteristics of the
eccentrically hollow shells are given by Chakravorty (Dipankar et al. 1998) and the investigation of
the doubly cantilevered shell of saddle, cylindrical and spherical shells are presented by Qatu using
Rits method. The material nonlinear behavior of anisotropic plates and shells are delivered by Huang.
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EQUATIONS OF MOTION
Main heading
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The stiffness matrix is approximated by the layered approach, where the through thickness
integration is performed by the summation of stiffness of each layers. In this case, the volume
integration is divided into area integration plus the summation through thickness. The integration in
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Professor
Post Doctoral Researcher
the parenthesis is replaced by the summation of contribution from each layer, which are transformed in
accordance with the skewed material axis.
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Anisotropic Material
Secondary heading
The yield criterion used in this study is the generalized Huber-Mises law. The yield function f for
the anisotropic material can be defined in the similar way to that of the isotropic material. The
anisotropic parameters 12 ,  23 etc. can be determined experimentally by the six independent yield
tests. In the case of the work-hardening material, the change in the anisotropic parameters due to the
increase of the yield stress is taken into account using the concept of plastic work.
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Third grade heading. Leave 3 spaces
Flow rule for the concrete material
Using the flow theory of plasticity, the material nonlinearity is
represented according to the following elasto-plastic constitutive matrix.
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

Dep  De  DaaT D A  aT Da
(1)
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where a is the flow vector and A denotes the hardening parameter.
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NUMERICAL EXAMPLES
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A cylindrical shell with the dimension as depicted in Fig. 3 is subjected to an impulsive patch load
of an initial velocity of 143.5103mm/s (5650 in/s) over an area of 259mm78.2mm along the crown
line is analyzed.
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Fig. 1. Cylindrical shell subjected to impulsive patch load
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A half is modeled taking into account of the symmetries of structure and of load. The time history
at the point y1=159.5mm (6.28in) and y2=239mm (9.42in) along the crown line of the shell shows
reasonable agreement with the experiment as given in Fig. 3 (b). In this analysis, no damping is
assumed.
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REFERENCES
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Dipankar Chkravorty, P. K. Sinha and J. N. Bandyoopadhyay, “Application of FEM on free and forced
vibration of laminated shells”, Journal of Engineering Mechanics, ASCE, Vol. 124, No. 1, January,
1998, pp. 1-8.
S. Swaddiwudhipong and Z. S. Liu, “Dynamic response of large strain elasto-plastic plate and shell
structures”, Thin Walled Structures, Vol. 26, No. 4, 1996, pp. 223-239.
Madenci, E and Barut, A. “A free-formulation-based flat shell element for non-linear analysis of thin
composite structures”, International Journal for Numerical Methods in Engineering, Vol. 37, 1994,
pp. 3825-3842.