EXACT FINITE ELEMENT FORMULATION FOR COUPLED FLEXURAL-LATERAL-TORSIONAL-WARPING STATIC ANALYSIS OF THIN-WALLED ASYMMETRIC SHEAR DEFORMABLE MEMBERS

Abstract

Abstract

A super-convergent finite beam element is developed for the coupled flexural-lateral-torsional-warping static analysis of thin-walled beams with asymmetric open sections subjected to general loading. The present formulation is based on a generalized Timoshenko-Vlasov beam theory and fully captures the effects of shear deformation, the St. Venant and warping torsion as well as the coupling between bending and torsion due to the nonsymmetry of the cross-section. A family of exact shape functions is derived based on the closed form solution of the coupled equilibrium static equations. The exact shape functions developed are then employed to formulate the stiffness matrix and the energy equivalent load vector. The beam element developed has two-nodes and six degrees of freedom per node and is able to fully capture the flexural-torsional coupling. In order to demonstrate the exactness and efficiency of the element, comparisons are provided against other established finite element solutions under Abaqus. The element is shown to be free from discretization errors encountered under other interpolation schemes and yields results in excellent agreement with those based on other finite element solutions at a fraction of the computational and modeling cost.https://jer.ly/PDF/Vol-32-2021/JER-02-32-Abstract.php?f=a