Refined sectional analysis with shear center prediction for nonhomogeneous anisotropic beams with nonuniform warping

Abstract

A two-dimensional (2D) finite element (FE) sectional analysis system is developed for nonhomogeneous anisotropic beams established on a refined displacement-based elasticity theory. The classical effects due to elastic couplings, and nonclassical effects pertaining to three-dimensional (3D) warping displacements are incorporated in the formulation. The formulation allows for a generalized refined model with 12 × 12 stiffness matrix which subsequently encapsulates the Timoshenko model, Vlasov model for restrained torsion, and refined model for fully nonuniform warping (NUW). In addition, the shear center and tension center offsets are computed as cross-sectional properties based on the extended Trefftz’ theory for anisotropic beams. The accuracy of the sectional analysis is substantiated for isotropic as well as anisotropic, closed and open section beams with and without end restraints. The results indicate reliable predictions of the elastic properties for isotropic as well as anisotropic beams compared with the analytical solution, 3D FE solution, and other state-of-the-art methods. The static behavior of the beams is shown to be significantly influenced by the NUW effects especially in the vicinity of beam boundaries.