A new displacement-based solution for thick isotropic curved tubes

•The displacement-based Toroidal Elasticity (DBTE) is employed.•The DBTE has the advantage of yielding the displacements and the stresses.•The input for the modeling is really simple, easy to use and fast to run.•High efficiency in terms of computational time is obtainable.

Simple beam theories may be applied to straight structures, while the behavior of curved structures subjected to mechanical loadings is complex. In the present study, a displacement approach of Toroidal Elasticity is chosen to analysis thick isotropic curved tubes under pure bending moments. The governing equations are developed in a toroidal coordinate system. The method of successive approximation is used to find the general solution. The accuracy of the presented method is subsequently verified by comparing the results with finite element method (FEM) and stress-based Toroidal Elasticity (SBTE). The results show good agreement. Also, high efficiency in terms of computational time is shown when the presented method is used as compared with FEM (ANSYS). Finally, several numerical examples of stress distributions in the thick isotropic curved tube subjected to pure bending are presented and discussed.