An exact high order beam element

This work gives the exact stiffness coefficients for an high order isotropic beam element. The terms are found directly from the solutions of the differential equations that describe the deformations of the cross-section according to the high order theory, which include cubic variation of the axial displacements over the cross-section of the beam. The model has six degrees of freedom at the two ends, one transverse displacement and two rotations, and the end forces are a shear force and two end moments. Also given are the equivalent end forces and moments for several cases of loading along the member. The components of the end moments are investigated, and are found for exact results. Comparison is made with the Bernoulli-Euler and Timoshenko beam models.