Exact solutions for extensible circular curved Timoshenko beams with nonhomogeneous elastic boundary conditions (Q1265364)

We derive a generalized Green function of \(n\)th-order ordinary differential equation with forcing function composed of the delta function and its derivatives. The generalized Green function is applied to obtain an exact solution for extensible circular curved Timoshenko beam with general nonhomogeneous elastic boundary conditions, subjected to any transverse, tangential and moments loads. The three coupled governing differential equations are uncoupled into one complete sixth-order ordinary differential characteristic equation in the tangential displacement. The explicit relations between the angle of rotation due to bending, the transverse displacement and the tangential displacement are obtained. The deflection curves due to a unit generalized displacement in nodal coordinate, and the exact element stiffness matrix are derived based on the solution for the general system. A finite element method can be developed based on the results for the dynamic analysis.