Abstract:
Based on the interdependent relation between the torsion angle and the generalized warp displacement, cubic polynomials are used to interpolate the displacement fields of the restrained torsion and to formulate the restrained torsion element. High similarities are found between the interdependent interpolation element of restrained torsion and the Timoshenko beam element, such as the interdependent relation between the generalized displacements, shape functions, stiffness matrix coefficients, and equivalence of non-nodal loads. Based on the post-processing results, a separation algorithm for the secondary moment and free torque is proposed for the finite element, which improves the computing functions and facilitates the stress calculation of cross-section. Results of example demonstrate that the interdependent interpolation element depends on the mesh density to improve the calculating accuracy, but obtains an excellent convergence. Under the mesh density condition of the example, there are errors of less than 0.12% for torsion angle, generalized warp displacement, free torsion moment and secondary moment, and error of 4.55% for bimoment. If the mesh density is refined, the error of bimoment is reduced to 1.17%. Compared with those existing elements, the properties of the present element have been improved.