Exact Solutions for the Linear Static Response of Composite Beams Under Arbitrary Loading and Boundary Conditions

The exact analytical solutions for static response of fully coupled composite beams subject to arbitrary loading and boundary conditions are presented. The analysis is based on the Euler-Bernoulli and Timoshenko beam theories. The governing equations are presented as a set of coupled inhomogeneous ordinary differential equations, and then expressed in a compact matrix form, which enables applying the method of direct integration to derive the exact analytical solutions. The solutions are obtained for arbitrary concentrated and non-uniformly distributed loads while classical and elastically retrained boundary conditions are considered in the formulation. Several numerical examples are given and the results are compared to those obtained from the Chebyshev Collocation Method. Different length-to-thickness ratios are considered to highlight the importance of shear deformation in short beams. The proposed analytical solutions are suitable for benchmarking and convergence studies of numerical solutions.