Post-buckling analysis of anti-symmetric cross-ply composite plates under end-shortening

In this paper, a method based on Chebyshev polynomials is developed for examination of the post-buckling behaviour of thin rectangular anti-symmetric cross-ply composite laminated plates with different boundary conditions under end shortening in their plane. Classical laminated plate theory is used for developing equilibrium equations that it produces acceptable results for thin plates. In this method, the equilibrium equations are solved directly by substituting the displacement fields with equivalent finite Chebyshev polynomials. Using this method allows developing the mathematical model of composite laminated plates with different boundary conditions on all edges. Equations system is introduced by discretizing 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 anti-symmetric cross-ply composite plates under end-shortening in their plane with different boundary conditions are computed and compared with those available in the literature, wherever possible.