Abstract:
The major three methods can be used to solute the torsion bars’torsion problem. One is the boundary element method and the finite element method that is based on the warping function of torsion theory, the others are numerical solution based on the thinwall theory and the finite element method based on the torsion stress function of torsion theory. According to stress function theory of torsion bars with arbitrary cross section, a functional equivalent to the torsion’s differential equation and definite condition was discussed and improved, finite element formulas were deduced to solute the torsion stress function for multi-connected section, the boundary condition of single warping-displacement value was changed to concentrated force loaded on boundary nodes. The condition that the stress function must be constant value on each hole boundary was satisfied by using master-slave node method, so the torsion stress function with arbitrary multi-connected complex section could be obtained directly by finite element method, and the torsion constant was solved by integrating from the torsion stress function. Examples verified the feasibility and validity of this method.
