AN EFFICIENT FINITE ELEMENT OF TORSIONAL DYNAMIC ANALYSIS FOR OPEN THIN-WALLED BEAMS UNDER TORSIONAL EXCITATIONS

Abstract

ABSTRACT

A super-convergent finite beam element formulation is developed for the torsional-warping dynamic coupled analysis of thin-walled open doubly symmetric beams under various harmonic torsional and warping moments. The dynamic equations of motion and related boundary conditions for torsional warping coupled response were derived in previous study. The finite element formulation is based on a generalized Vlasov-Timoshenko beam theory, and accounts for shear deformation effects due to non-uniform warping. It is also capturing the effects of axial constant static forces on the natural torsional frequencies, quasi-static and steady state dynamic responses. A family of shape functions is developed based on the exact solution of the coupled equations and are then used to formulate a beam finite element. The new two-nodded beam element with four degrees of freedom per element successfully captured the coupled torsional-warping quasi-static and steady state dynamic responses of open thin-walled beams under various harmonic torsional and warping moments. It is also used to extract the coupled torsional-warping natural frequencies and mode shapes from the dynamic analysis of the structural member. The present beam element is demonstrated to be free from discretization errors occurring in conventional finite element solutions. The applicability of the finite beam element is verified through several numerical examples. The numerical results based on the present finite element solution are found to be in excellent agreement with those based on exact and Abaqus finite element solutions available in the literature at a small fraction of the computational and modelling cost involved.