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.
Bibliographical noteFunding Information:
This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT and Future Planning (No. 2011-0014387 ).
All Science Journal Classification (ASJC) codes
- Civil and Structural Engineering
- Modelling and Simulation
- Materials Science(all)
- Mechanical Engineering
- Computer Science Applications