Shear Stress Analysis of a Square Shaft by Triangular and Rectangular Elements

The torsion of a square shaft is a unique two – dimensional problem because the value of field variable is specified around the entire boundary. Most physical problems have a mixture of boundary conditions. That is to say that the values of field variable are specified on part of the boundary, and values related to the derivatives are specified on other parts of the boundary. This shaft has four axes of symmetry; therefore, only one – eighth of the cross – section needs to be analyzed. This fractional portion was divided into different grid sizes by two – dimensional elements. To say explicitly, the present work focuses on the shear stress analysis of a square shaft by linear triangular and bilinear rectangular elements. In addition, one – fourth of the cross – section has also been considered and discretized by rectangular elements for performing the stress analysis. The nodal displacements were evaluated by considering different mesh sizes of the finite element (FE) model of the given physical structure. Furthermore, the shear stress and torque values of the square shaft were also calculated for each element of the FE grids. Keywords - Square Shaft, Shear Stress, Triangular and Rectangular Elements, FE Grids