Torsional stress in non-circular cross sections by the finite element method

The presented work is used to develop a new numerical calculation program to determine the torsional stress in simply connected non-circular cross sections of a beam subjected to a constant torque using the finite element method. The method used is the finite element quadrilateral element with four nodes. The boundary conditions are of Dirichlet. In applications for torsion usually formulas and results for the circular section are used, although the section in the case of type real and not circular. This is due to lack of form for non-circular sections in general. Each section has its own form of the twist angle and strain which is different from one section to another. This formula is connected with the polar moment of inertia if the section is circular and different if the section is not circular. Hence, our interest is directed toward calculating polar moment of inertia and constant torque if the section is not circular. The results presented are chosen for simple sections for comparison and other complex shapes such as airfoil having a physical and practical interest. A calculation error between the theoretical results and the calculated results is done in this context.