Exact Shape Functions for Timoshenko Beam Element

Abstract

This paper derives exact shape functions for both non-uniform (non-prismatic section)

Structural analysis of non-prismatic beams: Critical issues, accurate stress recovery, and analytical definition of the Finite Element (FE) stiffness matrix

“…Trinh and Gan [67] derived shape functions for a linearly tapered Timoshenko solid beam element starting from the Hamilton principle. Finally, Tudjono et al [68] explicitly derived "exact" shape functions for both non-prismatic section and non-homogeneous Timoshenko beam elements.…”