Shape functions for high-order shear deformation beam element

Abstract

In this article, shape functions for higher-order shear deformation beam theory are derived. For the two nodded beam element, transverse deflection is assumed as cubic polynomial. By using equations of equilibrium of high-order theory that are already derived by J. N. Reddy in 1997, equation for slope of high- order theory is found. Finally with the boundary conditions of beam element and assumed kinematics of high-order theory, shape functions are derived.