This paper provides a thorough investigation of a heat conduction problem that pertains to tolerance modelling in layered materials made up of multiple components. These media are functionally graded materials and thus have varying properties that affect their effectiveness. The proposed equations explain the conduction of heat in layered composites. The formulation involves partial differential equations, which utilise smooth and slowly varying functions. Notably, an extension of the unified tolerance modelling procedure is presented generalising existing models for two-component step-wise functionally graded materials (FGMs). This extension allows for the analysis of specific issues related to heat conduction in multi-component stratified composites with a transversal gradation of effective properties. This is the most important novelty achievement of the present paper because it will contribute to advancing knowledge and allows researchers, engineers, and practitioners to use the method in a broader context, addressing a more extensive set of real-world situations not limited to the number of component materials.

本文对与由多个组件组成的层状材料的公差建模相关的热传导问题进行了彻底的研究。这些介质是功能分级材料，因此具有影响其有效性的不同特性。所提出的方程解释了层状复合材料中的热传导。该公式涉及偏微分方程，它利用平滑且缓慢变化的函数。值得注意的是，提出了统一公差建模程序的扩展，概括了两组分逐步功能梯度材料（FGM）的现有模型。该扩展允许分析与具有有效性能横向梯度的多组分分层复合材料中的热传导相关的具体问题。这是本文最重要的新颖性成就，因为它将有助于推进知识的发展，并允许研究人员、工程师和从业者在更广泛的背景下使用该方法，解决更广泛的现实世界情况，而不仅限于数量的组成材料。