Determination of the shear correction factors of complex plane sections for the bending of beams and application to airfoils

• Published in: Indian journal of physics Vol. 96; no. 8; pp. 2457 - 2466
• Main Authors: Zefouni, Omar, Kirad, Abd-el-Kader
• Format: Journal Article
• Language: English
• Published: New Delhi Springer India 01.07.2022; Springer Nature B.V
• Subjects: Aeronautics; Astrophysics and Astroparticles; Bending; Exact solutions; Original Paper; Physics; Physics and Astronomy; Shear forces; Stiffness matrix; Shear correction factors; Shear stress; Geometrical characteristics; Deflection; Shear area; Airfoil
• ISSN: 0973-1458; 0974-9845
• DOI: 10.1007/s12648-021-02207-w

In this paper, a numerical program to calculate shear correction factors of complex plane sections in the case of deformation of simple bending beams with moderate dimensions is developed. Shear force influences the deflection calculation that becomes non-negligible. The elementary stiffness matrix of the finite element will be modified or become dependent on some shear correction factors of the section. It is then useful to find for each section its shear correction factors given their importance in practice. In the literature, exact analytical solutions only exist for some simple geometric shapes such as circular and rectangular sections, hence the interest in orienting our investigations towards numerical solutions for other complex sections used in aeronautics. The program has been validated by the numerical convergence results toward those obtained for circular and rectangular sections whose exact solutions are displayed. It should be noted that the relative error for a high discretization tends toward zero. Given their various applications in aeronautics as well as in industrial mechanics, the aerodynamic profiles are the subject of this numerical investigation.