Initial imperfection effects on postbuckling response of laminated plates under end-shortening strain using Chebyshev techniques

•The postbuckling of composite imperfect plates is investigated using double Chebyshev polynomials.•Nonlinear terms are linearized by quadratic extrapolation technique.•Since number of equations is more than parameters, the least squares technique is used.•Plates with different boundary conditions, imperfections and layup configurations are modeled.•It is seen that the shape of imperfection significantly affects postbuckling behaviour of the plate.

The effects of initial imperfection on postbuckling behaviour of laminated plates subject to end shortening stain are investigated in this paper. Different boundary conditions and lay-up configurations are considered 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. This technique allows imposing different combinations of boundary conditions on all edges of composite laminated plates. 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.