Temperature rise caused by surface heating is responsible for thermal-related failures of heterogeneous material, such as composites and alloys, in manufacturing processes and tribology. This study presents a semi-analytical method (SAM) for temperature rise in a half plane involving dispersed inhomogeneities of arbitrary shape undergoing external heat load. Green functions and frequency response functions (FRFs) for subsurface heat flux induced by the applied heat load, as well as a set of formulas for influence coefficients correlating disturbed temperature rise and uniform eigen-temperature gradients inside a rectangular inclusion in a full plane, are derived. The rectangular inclusion solution in a full plane is treated as an elementary solution to solve disturbed temperature rise in a heterogeneous half plane involving arbitrarily shaped inhomogeneities, through implementing the equivalent inclusion method (EIM), the method of images and discretizing the total computation area into a good many rectangular elements with the same size. Results obtained by the SAM are consistent with those of the finite element method (FEM). Effects of inhomogeneity numbers, material properties, volume fractions, and velocities of the moving heat load on temperature rise are discussed in detail.

Transverse isotropy, a typical property of coating providing protection or lubrication for transmission parts, is different from isotropy focused in most of previous research, catching increasing attention in recent years. This study aims to make the lubricating contact behavior of transversely isotropic coating under different working conditions better understood, with the assistance of a proposed mixed elastohydrodynamic lubrication (EHL) model for a rigid ball in contact with transversely isotropic coating. Explicit analytical expressions of frequency response functions (FRFs) of the elastic field for transversely isotropic coating were derived, which could be used to work out surface/subsurface displacement and stress if surface pressure is known. The proposed EHL model for transversely isotropic coating was verified by comparing the film thickness and pressure distribution with those from literature by an uncoated model. Furthermore, the effects of coating elastic property, coating thickness, velocity, and load on lubrication performance and mechanical responses are investigated. In addition, the results under different coating parameters are also compared and discussed with those obtained by the Hamrock–Dowson equations to demonstrate the effectiveness of the latter. This investigation may provide a potential application for coating optimal design considering lubrication.

The magneto-electro-elastic (MEE) medium is a typical intelligent material with promising application prospects in sensors and transducers, whose thermal contact response is responsible for their sensitivity and stability. An effective thermal contact model between a moving sphere and a coated MEE medium with transverse isotropy is established via a semi-analytical method (SAM) to explore its thermal contact response. First, a group of frequency response functions for the magneto-electro-thermo-elastic field of a coated medium are derived, assuming that the coating is perfectly bonded to the substrate. Then, with the aid of the discrete convolution–fast Fourier transform algorithm and conjugate gradient method, the contact pressure and heat flux can be determined. Subsequently, the induced elastic, thermal, electric and magnetic fields in the coating and substrate can be obtained via influence coefficients relating the induced field and external loads. With the proposed method, parametric studies on the influence of the sliding velocity and coating property are conducted to investigate the thermal contact behavior and resulting field responses of the MEE material. The sliding velocity and thermal properties of the coating have a significant effect on the thermal contact response of the MEE material; the coupled multi-field response can be controlled by changing the coating thickness between ~0.1 a₀ and a₀.