A Closed Form Solution for Reissner's Planar Finite Strain Beam Using Jacobi Elliptical Functions
Abstract In the paper, we introduce an analytical solution for a large deflection, finite strain, and planar Reissner beam that is subject to an end force and a bending moment. The solution is provided in terms of Jacobi elliptic functions. The obtained analytical solution is enhanced with numerical examples. The buckling and post buckling behavior of a beam under an axial compressive load applied at its end and subject to various boundary conditions is also discussed in detail. In particular, the buckling factor is derived for all boundary conditions.