A Thermo-Mechanical Analysis of Isotropic and Composite Beams via Collocation with Radial Basis Functions

Abstract

In this article, the mechanical behavior of beams subjected to thermal loads is investigated. The temperature field is obtained by exactly solving Fourier's heat conduction equation and it is considered as an external load within the mechanical analysis. Several higher-order beam models as well as Timoshenko's classical theory 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 nucleal form that does not depend upon the displacements’ expansion order. The latter can be regarded as a free parameter of the formulation. A meshless strong-form solution based upon collocation with Wendland's radial basis functions is adopted. Isotropic and laminated orthotropic beams are investigated. Results are validated toward an analytical Navier-type solution and three-dimensional FEM results. It is shown that good accuracy can be obtained.