Solution of Torsion of Beams with Non-Circular Cross-Sections in Python

Abstract

TUTIASHVILI, T. Solution of Torsion of beams with Non-Circular Cross- Sections in Python. VŠB-Technical University of Ostrava, Faculty of Mechanical Engineering, Department of Applied Mechanics, 2016, 75 p. Head of thesis: Markopoulos, A. This thesis deals with unconstrained torsion of prismatic beams. Original 3 dimensional problem is simplified to 2 dimensional due to free warping (technique known as membrane analogy). Followed equilibrium equation is solved by Finite Element Method in own library written in Python. The quality of the solution is validated for the cases of cross-sections with known analytical solution. The work includes derivation of stiffness matrix and right-hand side for 3 and 4-nodes planar elements. These elements are implemented in own library written in Python in which most of numerical results were performed.