Buckling and postbuckling behavior of shear deformable anisotropic laminated beams with initial geometric imperfections subjected to axial compression

• Buckling and postbuckling analysis of laminated beams with generic initial geometric imperfection.
• Closed form solution based on Newton’s iterative and Galerkin’s methods.
• Significant effects of boundary conditions, material and geometric properties on postbuckling response.

Buckling and postbuckling behavior of shear deformable anisotropic laminated composite beams with initial imperfection subjected to axial compression is presented. The material in each layer of beams is assumed to be linearly elastic, anisotropic and fiber-reinforced. The governing equations are based on the higher order shear deformation beam theory with a von Kármán-type of kinematic nonlinearity. Composite beams with the fixed–fixed, fixed–hinged, and hinged–hinged boundary conditions are considered. A generic imperfection function for one-dimensional composite beams is adopted to model various possible initial geometric (e.g., sine, local, and global type) imperfections. The nonlinear prebuckling deformation and initial geometric imperfection of the beam are both taken into account. A numerical solution of nonlinear partial–integral differential form in terms of the transverse deflection is employed to determine the buckling load and postbuckling equilibrium path of composite beams. The results obtained by combining the Newton’s iterative method with the Galerkin’s method are theoretically exact from the transverse and longitudinal displacements for anisotropic laminated beams under the axial compressive loads using the secondary parameter conversion technique, and they are validated by comparing with those available in the literature. The numerical illustrations are presented for the postbuckling response of laminated beams with different types of boundary conditions, ply arrangements (layups), geometric and physical properties. The results reveal that the geometric and physical properties and boundary conditions have a significant effect on postbuckling behavior of anisotropic laminated composite beams.