Thick isotropic curved tubes: three-dimensional stress analysis

Abstract

While the structural analysis of straight beams is straightforward, the behavior of curved beams is more complex to predict. In the present work, a displacement approach of toroidal elasticity is used to analyze thick isotropic curved tubes subjected to axial load, torque, and bending moment. The governing equations are developed in a toroidal coordinate. The method of successive approximation is used to obtain the general solution. The accuracy of the present methodology is tested comparing the numerical results with those obtained by finite element method (FEM) and stress-based toroidal elasticity (SBTE). The proposed methodology is computationally cost-effective, and its results reveal good agreements with FEM and SBTE results. Finally, several numerical examples of stress distributions in thick isotropic curved tubes under axial load, torque, and bending moment are presented. By using the present methodology, displacements as well as stresses are obtained which are important information for fracture analysis.