An investigation of thermoelastic behavior in periodic and functionally graded multilayered composite structures using tolerance modeling and finite element methods

In response to the increasing demand for accurate yet computationally efficient methods for analyzing modern composites under thermal loading, this study introduces a thermoelastic model for multicomponent, multilayer step-wise functionally graded materials (FGMs), based on the tolerance modeling approach. For the first time, the tolerance modeling method has been extended to the thermoelasticity equations of FGM structures comprising more than two components, which marks a clear departure from earlier studies mostly limited to two-component materials or, if for multi-component, then only for periodic structures. This extension enables a significantly more realistic representation of modern layered composites. Numerical verification of the model was performed using Mathematica and COMSOL Multiphysics, enabling assessment of both accuracy and predictive capability. Deviations from COMSOL-based reference results did not exceed 7 % for both periodic and step-wise FGM structures, confirming the high reliability of the approach. Unlike existing methods, which are often either oversimplified or extremely computationally demanding, the developed model provides a realistic description of structural behavior while requiring considerably less computational effort than classical finite element methods (FEM). The analysis has direct practical relevance to the design of components exposed to high thermal gradients, such as thermal shields in aerospace applications, layered partitions in energy-efficient buildings, and electronic device components. Accurate prediction of displacement and thermal stress distributions facilitates optimization of geometry and material layout, reducing stress concentrations and minimizing damage risk. A comparative analysis of analytical and numerical results under identical boundary conditions and geometries confirms that the tolerance model successfully captures the behavior of FGM structures while keeping computational costs low. The conclusions further indicate that ordered, symmetric layering reduces deformation, whereas asymmetry and abrupt material transitions lead to localized stress concentrations. The novel methodology not only broadens existing modeling capabilities but is also flexible and can be adapted to a wide spectrum of modern layered structures, enhancing its potential for practical engineering applications.