Calculation of viscoelastic rods of non-circular cross section for free torsion

Abstract

Aim. The article aims to present a solution to a resolving equation for determining the stress-strain state of a rod of non-circular cross-section under torsion, taking into account the material creep. Methods. The solution is based on the hypotheses introduced by Saint-Venant when considering an elastic rod. Finally, the problem is reduced to a second-order differential equation in terms of the stress function. The solution of this equation is performed using the finite element method in combination with the Euler method. Results. The work presents resolving equations for a triangular finite element. The solution of a test problem for a polymer rod of rectangular cross-section is given, the material of which adheres to the nonlinear Maxwell-Gurevich equation. Graphs of changes in time of the relative twisting angle, as well as the maximum values of tangent stresses, are presented. Conclusion. It is established that the stresses in the rod are not constant over time. The tangent stresses in the rod during creep initially decrease followed by a return to the elastic solution.

Keywords

• creep
• torsion
• deplanation
• finite element method
• poisson equation