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The imperfection shape is the linear bifurcation buckling mode of the clamped-clamped thick column, and the imperfection amplitude is equal to 0.01L (L = length of the column). The aspect ratio of the thick column, L/thickness = 5.0.
The transverse shear modulus ratio,
Gxz/Exx = 0.16, and
Exx = axial modulus
Ezz = transverse modulus
Pcr = linear bifurcation buckling load
P = applied axial compression
w = normal deflection at column midlength and mid-thickness (at the Point V)
L = length of column
“Pinching” means development of a localized “wrinkling” or “creasing” deformation, which is seen in parts D and E in the next slide.
The overall and localized deformations are shown in the next slide for the load-deflection points A, B, D, E on the load-deflection curve corresponding to the transversely soft material (Ezz/Exx= 0.045).
This and the next slide are from:
Alessandro Beghini (1), Zdenek P. Bazant (2), Anthony M. Waas (3) and Shiladitya Basu (3)
(1) Skidmore, Owings & Merrill LLP, Chicago, IL 60604, USA
(2) Department of Civil and Environmental Engineering, Northwestern University, Evanston, IL 60208, USA
(3) Department of Aerospace Engineering, University of Michigan, Ann Arbor, MI 48109, USA
“Postcritical imperfection sensitivity of sandwich or homogenized orthotropic columns soft in shear and in transverse deformation”, International Journal of Solids and Structres, Vol. 43, pp 5501-5t24, 2006
ABSTRACT: The previous energetic variational analysis of critical loads and of the choice of finite strain measure for structures very weak in shear, remaining in a state of small strain, is extended to the initial postcritical behavior. For this purpose, consideration of the transverse deformation is found to be essential. It is shown that imperfection sensitivity of such structures, particularly laminate-foam sandwich plates, can arise for a certain range of stiffness and geometric parameters, depending on the proper value of parameter m of the Doyle–Ericksen finite strain tensor, as determined in the previous analysis. The bifurcation is symmetric and Koiter’s 2/3-power law is followed. The analytical predictions of maximum load reductions due to imperfection sensitivity are verified by finite element simulations. The possibility of interaction between different instability modes, particularly lateral deflection and bulging, is also explored, with the conclusion that lateral deflection dominates in common practical situations.
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