Meshfree Approach for the Torsional Analysis of Orthotropic and FGM Thin-Walled Open Sections

Abstract

The torsional study of different engineering sections made up of orthotropic and functionally graded material is presented in this paper. Prandtl's stress function approach is used for the formulation of governing differential equations. Thin plate spline (TPS) radial basis function-based collocation meshfree method is utilized for discretization and solution of the governing differential equations. A classical power law is considered for the modeling of FGM material. A computer program is developed for the solution of the discretized partial differential equations. To assess the efficacy and accuracy of the present mesh-free approach, a numerical example of an equilateral triangle is considered to conduct a convergence and accuracy test. Finally, the torsional stiffness and shear stress for the orthotropic and FGM sections of the equilateral triangle, L-section, and T-sections are computed. The novelty in the present meshfree methodology lies in the handling of the singular behavior of re-entrant corners. The effect of stress concentration can be seen at the re-entrant corners. The proposed methodology shows excellent performance in solving these types of torsion problems.