Fundamentals of thermoelasticity for curved beams

The purpose of this paper is twofold. Firstly, we conduct an in-depth analysis of mathematical modeling concerning thermal-mechanical curved beams, by taking into consideration three primary forces widely accepted in the literature: axial load, shear force, and bending moment. Additionally, we examine their appropriate thermal couplings, shedding light on the intricate interplay between stress-strain relationships and temperature variations. This analysis is situated within the well-recognized context of the Bresse governing model for arched beams. Secondly, drawing upon distinguished constitutive laws for heat flux of conduction, we compile a comprehensive catalog of thermoelastic curved beam systems in various scenarios. We introduce new categories of problems that exhibit specific features from the thermal point of view.