Three-dimensional stress analysis of orthotropic curved tubes-part 1: Single-layer solution

In this paper (Part 1), a new displacement-based method is proposed to investigate orthotropic curved tubes subjected to pure bending moment. A displacement approach of Toroidal Elasticity is chosen to analyze orthotropic curved tubes with a single layer. The governing equations are developed in three toroidal coordinates system. The method of successive approximation is used to find the general solution. Then, the governing equations are decomposed into different orders, based on a small parameter. The formulas for calculating different order displacement components are derived. The accuracy of the proposed method is subsequently verified by comparing the numerical results obtained using the proposed method with finite element method (FEM), stress-based Toroidal Elasticity and Lekhnitskii solution. The results show good correspondence. The proposed method provides advantages in terms of computational time compared to FEM.