Approximate torsional analysis of arbitrary trapezoidal bars by Kantorovich method

Several members in some structures tolerate torsional moment. Therefore, comprehending the torsional behavior of these members is essential. Investigating the torsional behavior of thin-walled sections and simple sections is possible by analytical and common numerical methods. The analysis and design of some structures with special sections (e.g., trapezoidal sections) in specific industries make it impossible to calculate these sections' responses using common methods. Therefore, the development of novel methods as alternative approaches seems very necessary. Due to the difficulty of analytical solution with asymmetric domains, semi-analytical and numerical methods are the most desirable alternatives. One of the proper methods for solving the boundary value problem is the vibrational methods. Moreover, the Kantorovich quasi-analytical method, an extension form of the Rayleigh-Ritz method, is an appropriate method for solving problems due to the lack of limitation in selecting the primary function for estimating boundary conditions. Therefore, the purpose of the present study is to develop the Kantorovich method to solve the governing equation of the torsion problem and estimate the warping and stress field of the arbitrary trapezoidal sections directly. Finally, the solution is compared with other existing methods to evaluate the accuracy of the Kantorovich method. The results indicate high precision and rapid convergence of this quasi-analytical method.