Aerospace Science and Technology
S. Amir M. Ghannadpour; M. Barekati
Volume 12, Issue 1 , March 2019, , Pages 15-26
Abstract
In this paper, a method based on Chebyshev polynomials is developed for examination of geometrically nonlinear behaviour of thin rectangular composite laminated plates under end-shortening strain. Different boundary conditions and lay-up configurations are investigated and classical laminated plate theory ...
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In this paper, a method based on Chebyshev polynomials is developed for examination of geometrically nonlinear behaviour of thin rectangular composite laminated plates under end-shortening strain. Different boundary conditions and lay-up configurations are investigated and classical laminated plate theory is used for developing the equilibrium equations. The equilibrium equations are solved directly by substituting the displacement fields with equivalent finite double Chebyshev polynomials. Using this method allows one to analyze the composite laminated plates with combination of different boundary conditions on all edges. The final nonlinear system of equations is obtained by discretizing both equilibrium equations and boundary conditions with finite Chebyshev polynomials. Nonlinear terms caused by the product of variables are linearized by using quadratic extrapolation technique to solve the system of equations. Since number of equations is always more than the number of unknown parameters, the least squares technique is used to solve the system of equations. Some results for angle-ply and cross-ply composite plates with different boundary conditions are computed and compared with those available in the literature, wherever possible.
Seyyed Amir Mahdi Ghannadpour; H.R. Ovesy; M. Nassirnia
Volume 8, Issue 1 , March 2011, , Pages 11-19
Abstract
ABSTRACT This paper presents the theoretical developments of two finite strip methods (i.e. semi-analytical and full-analytical) for the post-buckling analysis of isotropic plates. In the semi-analytical finite strip approach, all the displacements are postulated by the appropriate shape functions while ...
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ABSTRACT This paper presents the theoretical developments of two finite strip methods (i.e. semi-analytical and full-analytical) for the post-buckling analysis of isotropic plates. In the semi-analytical finite strip approach, all the displacements are postulated by the appropriate shape functions while in the development process of the full-analytical approach, the Von-Karman’s equilibrium equation is solved exactly to obtain the buckling loads and the out-of-plane buckling deflection modes. The investigation of plates buckling behaviour is then extended to the post-buckling study with the assumption that the deflected form after the buckling is the combination of first, second and higher (if required) modes of buckling. Thus, the full-analytical post-buckling study is effectively a multi term analysis. In this method the Von-Karman compatibility equation is used together with a consideration of the total strain energy of the strut. Through the solution of the compatibility equation, the in-plane displacement functions which are themselves related to the Airy stress function are developed in terms of the unknown coefficients in the assumed out-of-plane deflection function. The in-plane and out-of-plane deflection functions are substituted in the total strain energy expressions and the theorem of minimum total potential energy is applied to solve for the unknown coefficients.