Nonlinear Bending of Shear Deformable Anisotropic Laminated Beams Resting on Two-Parameter Elastic Foundations Based on an Exact Bending Curvature Model

Abstract

Nonlinear bending analysis of shear deformable anisotropic laminated composite beams with various kinds of distributed loads resting on a two-parameter elastic foundation is investigated. The material of each layer of the beam is assumed to be linearly elastic and fiber reinforced. A new nonlinear beam model involving the exact expression of the bending curvature is introduced. The governing equations are based on higher-order shear deformation beam theory with a von Kármán type of kinematic nonlinearity that includes bending-stretching, bending-twisting, and stretching-twisting couplings. Two kinds of end conditions, namely movable and immovable, are considered. The analysis uses a two-step perturbation technique combined with the Galerkin method to determine the relationship between distributed loads and deflections of a composite beam with or without initial loads. The numerical illustrations concern the static bending behavior of laminated beams with different geometric and material parameters, distributed loads, and end conditions, and its effect on the elastic foundation. The results based on the curvature model reveal that the geometric and physical properties, end conditions, axial force, distributed loads, and foundation stiffness have a significant influence on the large-amplitude bending behavior of anisotropic laminated composite beams.