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

TL;DR

This work develops a three-dimensional dual-reciprocity inclusion-based boundary element method (DR-iBEM) to analyze transient and time-harmonic heat transfer in bi-layered composites containing ellipsoidal inhomogeneities. It combines bimaterial Green's functions with Eshelby-inspired eigen-field representations (ETG and EHS) to enforce interfacial continuity without interior meshing, enabling efficient boundary-only simulations and reduced system size. The approach is validated against FEM for both homogeneous bimaterials and inhomogeneous configurations, and extended to functionally graded materials to study gradation effects on average and local thermal fields. The results demonstrate robust accuracy, substantial computational savings, and applicability to FGMs with complex microstructures.

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.

Figures (11)

• Figure 1: Schematic illustration of a bi-layered composites system composed of two dissimilar jointed blocks with same length $l_a$ and width $l_b$, but different heights at $h_1$ and $h_2$, respectively. Multiple ($N^I$) ellipsoidal subdomains $\Omega^I$ are embedded in the bi-layered composites, which exhibit thermal conductivity $K^I$ and specific heat $C_p^I$, and they can be handled as equivalent inclusions with continuously distributed ETG and EHS.
• Figure 2: Variation and comparison of (a) temperature and (b) heat flux along the centerline $x_3 \in [-0.5, 0.5]$ m evaluated by the bimaterial dual-reciprocity boundary integral equations (DR-BIEs) and the finite element method (FEM) at time $t = 2, 4, 6$ s.
• Figure 3: Variation and comparison of (a) temperature and (b) heat flux at field point (0.5, 0.5, $x_3$) ($x_3 = 0.5, 0.25, 0, -0.25, -0.5$ m) evaluated by the bimaterial dual-reciprocity boundary integral equations (DR-BIEs) and the finite element method (FEM), when time $t \in [0, 6]$ s.
• Figure 4: Variation and comparison of (a) temperature and (b) heat flux caused by two spherical inhomogeneities ($\textbf{a}^1 = \textbf{a}^2 = (0.1, 0.1, 0.1)$ m) along the centerline $x_3 \in [-0.5, 0.5]$ m evaluated by the dual-reciprocity inclusion-based boundary element method (DR-iBEM) with three order of eigen-fields and the finite element method (FEM) at time $t = 3, 6$ s.
• Figure 5: Variation and comparison of (a) temperature and (b) heat flux caused by two spheroidal inhomogeneities ($\textbf{a}^1 = \textbf{a}^2 = (0.2, 0.2, 0.1)$ m) along the centerline $x_3 \in [-0.5, 0.5]$ m evaluated by the dual-reciprocity inclusion-based boundary element method (DR-iBEM) with three order of eigen-fields and the finite element method (FEM) at time $t = 3, 6$ s.