Summary
This study deals with the geometrically nonlinear postbuckling response of cylindrically orthotropic thick annular plates subjected to inplane radial compressive load at the outer edge. Clamped and simply supported plates with a free hole and a plugged hole have been considered. Governing differential equations are expressed in terms of transverse displacementw, shear rotation Φ and stress function Ψ. Polynomial expansions are employed for these three field variables and the orthogonal point collocation method has been used to obtain the discretised equations. Buckling loads have been determined by solving a linear eigen-value problem using the method of inverse iterations. Postbuckling loads for different central deflections have been obtained by solving the nonlinear differential equations. The effect of thickness ratio, orthotropic parameter, annular ratio and the edge conditions has been investigated. The effect of shear deformation on the buckling loads increases with the orthotropic parameter β and the thickness-to-radius ratio.
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Abbreviations
- a, b, h :
-
Outer and inner radii and thickness of the plate
- E τ ,E θ ,v τ ,v θ :
-
Young's moduli, Poisson's ratios
- β:
-
Orthotropic parameter:E θ /E r
- Γ:
-
G rz /E r
- u *,u 0 * :
-
Radial displacement, radial displacement at mid plane
- r, θ, z :
-
Cylindrical polar coordinates
- ε, σ* :
-
Strains and stresses
- w *,w Φ,w Ψ :
-
Transverse displacement, shear rotation and stress function
- w, Φ, Ψ:
-
Dimensionless deflection, shear rotation and stress function
- N r ,N θ ,Q r :
-
Inplane stress resultants and transverse shear
- M r ,M θ :
-
Moment resultants
- k 2 :
-
Shear correction factor
- ϱ, ξ:
-
(r−b)/(a−b), b/(a−b)
- η:
-
a/h
- σ b r ,σ m θ :
-
Radial bending stress, circumferential membrane stress
- N,ϱ i :
-
Number and radii of collocation points
- λ:
-
Eigenvalue for buckling
References
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Dumir, P.C., Shingal, L. Axisymmetric postbuckling of orthotropic thick annular plates. Acta Mechanica 56, 229–242 (1985). https://doi.org/10.1007/BF01177120
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DOI: https://doi.org/10.1007/BF01177120