Transient thermal analysis of a bi-layered composites with the dual-reciprocity inclusion-based boundary element method

TL;DR

This paper introduces a boundary element method for analyzing transient and harmonic thermal behaviors in bi-layered composites with inhomogeneities, offering an efficient alternative to FEM with verified accuracy.

Contribution

It develops a dual-reciprocity boundary element method that models transient thermal problems in bi-layered composites without interface continuity equations, improving computational efficiency.

Findings

Method accurately predicts transient thermal responses.

Numerical results agree with finite element method.

Application to graded materials demonstrates versatility.

Abstract

This paper proposes a single-domain dual-reciprocity inclusion-based boundary element method (DR-iBEM) for a three-dimensional fully bonded bi-layered composite embedded with ellipsoidal inhomogeneities under transient/harmonic thermal loads. The heat equation is interpreted as a static one containing time- and frequency-dependent nonhomogeneous source terms, which is similar to eigen-fields but is transformed into a boundary integral by the dual-reciprocity method. Using the steady-state bimaterial Green's function, boundary integral equations are proposed to take into account continuity conditions of temperature and heat flux, which avoids setting up any continuity equations at the bimaterial interface. Eigen-temperature-gradients and eigen-heat-source are introduced to simulate the material mismatch in thermal conductivity and heat capacity, respectively. The DR-iBEM algorithm is particularly suitable for investigating the transient and harmonic thermal behaviors of bi-layered composites and is verified by the finite element method (FEM). Numerical comparison with the FEM demonstrates its robustness and accuracy. The method has been applied to a functionally graded material as a bimaterial with graded particle distributions, where particle size and gradation effects are evaluated.