Modeling the warping displacements for discontinuously varying arbitrary cross-section beams

In this paper, we propose a new and efficient warping displacement model to ensure the continuity of warping in beams with discontinuously varying arbitrary cross-sections. We briefly review the formulation of the continuum mechanics based beam finite elements allowing warping displacements. We then propose three basis warping functions: one free warping function and two interface warping functions. The entire warping displacement field is constructed by a combination of the three basis warping functions with warping degrees of freedom (DOFs). We also propose a new method to simultaneously calculate the free warping function and the corresponding twisting center. Based on this method, the interface warping functions and the twisting centers at the interface cross-sections are obtained by solving a set of coupled equations at the interface of two different cross-sections. Several beam problems with discontinuously varying cross-sections are numerically solved. The effectiveness of the proposed model is demonstrated by comparing the numerical results with those obtained by refined solid and shell finite element models.