Analysis of Beam Bending with an Elliptical Cross-Section

Abstract

This paper calculates the stress function constants to determine and analyse the stress field of a beam with an elliptical cross-section under transverse loading. This was performed using linear elasticity principles. The Beltrami-Michell compatibility equations were used to derive the formulas used to calculate these parameters in the beam with the elliptical cross-section. This paper uses dimensionless analysis to comprehend the effect of each variable in the problem. The loading was applied at the centre of the right-end face of the elliptical beam. This loading configuration is the same as an existing linear elasticity problem; however, that problem models a cylindrical beam instead of an elliptical one. Thus, the existing parameters from the cylindrical model were used to verify the formulas, calculated in this paper, for the elliptical beam.

Analysis of Transverse Loading on a Beam Utilizing the Beltrami-Michell Equations

“…Beams with different cross-sections under transverse loading have been investigated by several researchers. The stress field of a beam with an elliptical crosssection was developed and presented in [3][4][5]. Study of a sandwich beam with a metallic foam core under transverse load was performed by Qin et al [6].…”