Fundamentals of thermoelasticity for curved beams

TL;DR

This paper provides a comprehensive mathematical analysis of thermoelastic curved beams, focusing on the interplay of mechanical forces and thermal effects within the Bresse model, and introduces new problem categories based on heat conduction laws.

Contribution

It offers an in-depth modeling framework for thermoelastic curved beams considering key forces and thermal couplings, and classifies various thermoelastic systems with new problem categories.

Findings

Detailed mathematical models of thermoelastic curved beams.

Classification of thermoelastic systems with different heat conduction laws.

Introduction of new problem categories based on thermal features.

Abstract

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 list of thermoelastic curved beam systems in various scenarios. We introduce new categories of problems that exhibit specific features from the thermal point of view.