Leung, Andrew Yee TakAndrew Yee TakLeung2022-05-202022-05-201991https://repository.sfu.edu.hk/handle/sfu/3250Natural shape functions are derived for curved and twisted beam finite elements including shear deformation. Natural shape functions are exact solutions of the governing equations subject to boundary forces only. Rigid-body modes are completely satisfied and all complications associated with curved finite elements by assumed shaped functions, parametric transformation, and numerical integration are eliminated. The formulation of the stiffness matrix is given in detail.enjournal article10.1016/0168-874X(91)90017-S