Parametric Study on Stability Analysis of a Thin Shell Structure under Own Weight
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Date
2020-05
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Addis Ababa University
Abstract
Paraboloid shells are translational shells formed from two parabolas placed at the right
angle to each other and by the translation of one parabola over the other. Elliptical
paraboloid is formed by two unequal parabolas with the same curvature sign.
Thin concrete elliptic paraboloid shell with large spans are susceptible to buckling.
Determining the critical buckling load, internal forces and free vibration is difficult
because of the lack of experimental study on such shell type.
The research is focused on the analysis of an elliptic paraboloid shell structure under its
own weight. Geometrical and material linearity are considered in modeling and analysis
of the structure in this study. The objective of the research is the parametric study on
stability analysis of a thin shell structure under its own weight.
In this study, the internal forces, moments, deformation, stability, and free vibration of
elliptic parabolic shell analysis are performed by theoretical and finite element methods.
Theoretical analysis is done by shallow shell theory and the finite element analysis is
carried out by using DLUBAL RFEM 5.3.1.
Theoretical formulas in this study are coded by the MATLAB program. The codes are
used to determine internal force, moments, in-plane shear, displacement, critical load and
time, angular frequency, natural frequency in free vibration are written in the appendix.
The influences of the different parameters on the critical loads of the shells are thereby
studied. The parameter considered is thickness, the radius of curvature, modulus of
elasticity and side rise of the shell to determine the critical buckling load. Free vibration
analysis of rectangular and square planned elliptic paraboloid shell structures was done.
Finally, the internal forces, displacement, critical buckling load, and free vibration analysis
result in the study presented graphically and discussed in detail. The result of the finite
element analysis is then compared with the theoretical analysis results.
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Keywords
Shell Structure, Thin Shell Structure, Stability Analysis