Exact solution for the deflection of composite beams under non-uniformly distributed loads

Exact and analytical solutions for the static response of fully coupled composite beams subject to non-uniformly distributed loads are presented. The governing equations are obtained based on the Euler-Bernoulli theory, in which four degrees of freedom, i.e. in-plane bending, out-of-plane bending, twist and axial elongation are fully coupled. The direct integration method is employed to obtain the general analytical solution in integral form. By substituting particular load functions, this solution is transformed into an exact closed-form solution. Power series representation is provided for the cases in which loads are described by non-integrable functions or by a set of numerical values. To verify the results obtained from the analytical solutions, numerical results from the Chebyshev Collocation Method are also presented. To investigate the effects of anisotropy, different stacking sequences showing various coupled behavior are used to obtain the numerical results for various boundary conditions. Due to the fact that the stiffness properties are expressed in engineering constants, the proposed formulation is not limited by the cross-sectional shape of the beam, and therefore it is appropriate for engineering design. In addition, the presented exact analytical solutions can be used as benchmark problems for evaluating the accuracy and convergence of various analytical and numerical methods.