Solution of Torsion of Beams with Non-Circular Cross-Sections with numerical methods

Abstract

This thesis deals with the torsion of beams with non-circular cross-section. The differential equation of the torsion is derived and discretized with finite element method and boundary element method. Examples of these methods are shown on one-dimensional and also two-dimensional cases. The derived theory is illustrated on two-dimensional examples. The author’s software was developed to solve torsion with finite element method as well as boundary element method using membrane analogy. Results of the software TorPy are verified with available analytical solution and more complicated cases are compared with commercial software Ansys.