# Bending Behavior of Fiber Metal Laminate Plates Under Thermo-Mechanical Loads

## TL;DR

This paper presents an analytical model to study how fiber metal laminate plates bend under combined thermal and mechanical loads.

## Contribution

The study introduces an exact analytical model using 3D thermo-elasticity theory and a modified superposition principle for modulus degradation.

## Key findings

- Analytical solutions show good agreement with FE results, with relative errors under 2%.
- The modified superposition principle reduces discrepancies in thermo-mechanical performance predictions.
- Temperature and lamina number significantly affect stresses and displacements in FML plates.

## Abstract

An exact analytical model based on three-dimensional (3D) thermo-elasticity theory is developed to investigate the bending behavior of fiber metal laminate (FML) plates under thermo-mechanical load. The temperature-dependent properties and the orthotropy of the component materials are considered in this model. The analytical model is based on the heat conduction theory and thermoelasticity theory, and the solutions are determined by employing the Fourier series expansion, the state space approach and the transfer matrix method. Comparison study shows that the FE results are generally in good agreement with the present analytical solutions, exhibiting relative errors of less than 2%, except in the regions near the upper and lower surfaces. The present solution is close to the experimental values for the laminated plate within the linear range, with errors less than 10%. The decoupling analysis indicates that the thermo-mechanical performance of FML plates no longer strictly adheres to the traditional superposition principle, with errors reaching 30.39%. A modified principle accounting for modulus degradation is introduced to address this discrepancy. Furthermore, parametric studies reveal that the temperature and the lamina number have significant effect on the stresses and displacements of the FML plate.