A Thermal Stress Analysis of Three-Dimensional Beams by Refined One-Dimensional Models and Strong Form Solutions

Abstract

This paper investigates the mechanical behaviour of three-dimensional beams subjected to thermal stresses.The temperature field is obtained by exactly solving Fourier's heat conduction equation and, as classically done by a staggered solution approach, it is considered as an external load within the mechanical analysis.Several higher-order beam models are derived thanks to a compact notation for the a-priori approximation of the displacement field upon the cross-section.The governing differential equations and boundary conditions are obtained in a compact nuclearform using the Principle of Virtual Displacement.The final form does not depend upon the order of approximation of the displacement fieldover the cross-section (this latter being a free parameter of the proposed modelling approach).The obtained problem is solved by means of two strong form solutions: an analytical Navier-type solution andpoint collocation (using Wendland's radial basis functions).Isotropic, functionally graded and laminated beams are considered.Results are validated towards three-dimensional FEM solution obtained by ANSYS.The proposed models yield accurate results characterised by smooth stresses thanks to the used solution methods.Furthermore, computational costs are very attractive when compared to the reference three-dimensional solutions.