Variable stiffness composite beams subject to non-uniformly distributed loads: An analytical solution

An analytical solution is obtained for the 3D static deflection of variable stiffness composite beams subject to non-uniformly distributed loads. Governing differential equations with variable coefficients, reflecting the spatially variable stiffness properties, are presented in which four degrees of freedom are fully coupled. The general analytical solution in integral form is derived and closed-form expressions obtained using series expansion approximations. The static deflection of a number of variable stiffness composite beams that can be made by fibre steering are considered with various stacking sequences. The results obtained from the proposed method are validated against numerical results from the Chebyshev collocation method and excellent agreement is observed between the two. While the proposed methodology is applicable for variable stiffness composite beams with arbitrary span-wise variation of properties, it is also an efficient approach for capturing the complicated 3D static deflection of variable stiffness composite beams subject to non-uniformly distributed loads.