Accurate Solution for Orthotropic Beams with Continuously Variable Cross Sections

Abstract

Orthotropic materials and components are widely used in various engineering fields, such as aerospace, energy, infrastructure, and water conservancy projects. The orthotropic components such as slabs and beams cannot be investigated accurately by using traditional beam theory because it is unable to take more elastic constants into account. The precise stress distribution of orthotropic simply supported beams of any thickness is determined in this article. Meanwhile, all undetermined coefficients of the stress function are derived by performing a Fourier sine series expansion upon the bottom and top surfaces of the beam. It shows that the resolution corresponds well with the numerical analysis findings from the finite element method. It indicates rapid convergence and can obtain high-precision and high stress analysis results, which has a good application prospect in engineering.