Numerical computation of shear stress in a complex cross section subjected to a shear force and application to airfoils

¹ Department of Mechanical Engineering, Faculty of Technology, University of Blida 1, BP 270, Blida 09000, Algeria
² Aircraft Laboratory, Institute of Aeronautics and Space Studies, University of Blida 1, BP 270, Blida 09000, Algeria
³ University of Blida 1, BP 270, 09000 Q.A. Blida, Algeria
⁴ Aeronautical Sciences Laboratory, Institute of Aeronautics and Space Studies, University of Blida 1, BP 270, Blida 09000, Algeria

^a Corresponding author: z_toufik270169@yahoo.fr

Received: 12 July 2015
Accepted: 3 December 2015

Abstract

The aim of this work is to develop a new numerical computational program for determining the distribution of the shear stress in a complex cross section subjected to the application of a shear force and applications to airfoils, in light to determine the position and the value of the maximum stress, and consequently the determination of the shape factor seen their practical importance. In the general case, there may be two shear forces along the two principal axes of inertia, and consequently two shape factors can be found from those two directions. The calculation of the geometric characteristics of the section is necessary in this case. The discretization is based on the development of a new technique by dividing the upper part of the section in adjacent triangles common at a point to determine the static moment of this part and the length of the band width. The validation of the program is certified by the convergence of the numerical accurate results to those for the circular section. The exact solution exists for the circle. In this case, the relative error for high discretization approaches to zero. The application will be for airfoils, considering their practical interests in the fields of aeronautics and industrial mechanics.