# Nonlocal integral thermoelasticity: a thermodynamic framework for functionally graded beams

## TL;DR

This paper develops a thermodynamically consistent nonlocal integral model for functionally graded beams under thermal and mechanical loads, revealing complex behaviors influenced by nonlocality and temperature effects at small scales.

## Contribution

It introduces a novel stress-driven integral formulation for thermoelastic analysis of functionally graded beams, incorporating thermodynamic consistency and boundary conditions.

## Key findings

- Nonlocality and temperature significantly affect beam behavior.
- Complex structural responses occur in nonisothermal indeterminate problems.
- The model captures the shift of the neutral surface due to thermal effects.

## Abstract

An effective nonlocal integral formulation for functionally graded Bernoulli-Euler beams in nonisothermal environment is developed. Both thermal and mechanical loadings are accounted for. The proposed model, of stress-driven integral type, is shown to be governed by a thermodynamically consistent differential problem with proper constitutive boundary conditions. The new thermoelastic strategy is illustrated by investigating a set of examples. It is demonstrated that in nonisothermal statically indeterminate problems rather complex structural behaviours can appear and that both the shift of the neutral surface and nonlocality have a dominating influence at small-scales.