Transverse and torsional shear stresses in prismatic bodies having inhomogeneous material properties using a new 2D stress function

Abstract

We introduce a new formulation to concurrently calculate torsional and transverse shear stresses in prismatic beams with homogeneous or inhomogeneous material properties. This new formulation is generated using kinematic assumptions for the torsion problem and using a new stress function for the transverse shear problem that accounts for Poisson effects. The effect of gradients in material properties is captured explicitly as body forces. The results using this new formulation are compared to full three-dimensional solutions and show good agreement (l2 error metric in the order of 10-4), while both modeling and computational costs are significantly lower. The numerical implementation of this new formulation can be used to analyze stresses in arbitrary cross sections ranging from structural members (civil) to long bones (biomechanics) with either homogeneous or inhomogeneous material properties.