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CivilComp Proceedings
ISSN 17593433 CCP: 99
PROCEEDINGS OF THE ELEVENTH INTERNATIONAL CONFERENCE ON COMPUTATIONAL STRUCTURES TECHNOLOGY Edited by: B.H.V. Topping
Paper 7
Calculation of Initial PostBuckling Behaviour of Moderately Thick Plates using an Exact Finite Strip S.A.M. Ghannadpour^{1}, H.R. Ovesy^{2} and E. ZiaDehkordi^{2}
^{1}Aerospace Engineering Department, Faculty of New Technologies and Engineering, Shahid Beheshti University G.C., Tehran, Iran
S.A.M. Ghannadpour, H.R. Ovesy, E. ZiaDehkordi, "Calculation of Initial PostBuckling Behaviour of Moderately Thick Plates using an Exact Finite Strip", in B.H.V. Topping, (Editor), "Proceedings of the Eleventh International Conference on Computational Structures Technology", CivilComp Press, Stirlingshire, UK, Paper 7, 2012. doi:10.4203/ccp.99.7
Keywords: exact strip, moderately thick plates, initial postbuckling stage, relative stiffness, firstorder shear deformation theory, VonKarman's equations.
Summary
An exact finite strip for the buckling and initial postbuckling analysis of moderately thick plates is presented in this paper using firstorder shear deformation theory (FSDT). The method presented, is designated by the name fullanalytical finite strip method (FSM), provides an efficient and extremely accurate buckling and initial postbuckling solution. Ovesy and Ghannadpour [1,2,3,4] have developed a fullanalytical FSM (Fa FSM) based on the classical plate theory (CPT) in which the VonKarman's equilibrium equation is solved exactly and thus the buckling mode shapes and loads are obtained with very high accuracy. Then the obtained mode shapes are used in the postbuckling phase and the VonKarman's compatibility equation is solved exactly and the inplane displacements are derived.
In this paper the preceding method has been extended based on the FSDT. The VonKarman's equilibrium set of equations for large deflection of a strip, with the assumption that the normal pressure is zero, is used based on the FSDT. The analytical solution of this set of equations depends on the magnitudes of material properties, geometrical dimensions of the model and the applied compressive load. The buckling loads and mode shapes corresponding to the outofplane deflection and rotations functions have been obtained from a transcendental eigenvalue problem that is derived using the boundary conditions, moments and forces at the two unloaded edges. An accurate initial postbuckling study can be extended with the assumption that the deflected form immediately after buckling is the same as that obtained for buckling. With the solution of the VonKarman's compatibility equation, the inplane displacement functions which are related to the Airy stress function are developed in terms of the unknown coefficient in the assumed outofplane deflection function. The inplane displacements obtained as well as outofplane displacements and rotations are used to develop the total strain energy expression. By solving the set of equations that is obtained from the minimum total potential energy theorem the unknown coefficients are obtained, thus the initial postbuckling behaviour is investigated. References
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