Peng-Fei Hou

Three-Dimensional Steady-State General Solution for Isotropic Thermoelastic Materials with Applications I: General Solutions

Three general solutions of the three-dimensional steady-state governing equations of isotropic thermoelastic materials are derived in this article. For this object, two displacement functions are first introduced to simplify the govering equation. Then, using the differential operator theory, three general solutions can be expressed in terms of two functions, one satisfies a harmonic equation and the other satisfies a six-order partial differential equation. By virtue of Almansis theorem, three general solutions can be further transferred to two general solutions, which are expressed in terms of three harmonic functions. At last, one more relatively completed general solution expressed in four harmonic functions is obtained by superposing the two general solutions. The proposed general solutions are simple in form and hence they may bring more convenience to certain boundary problems. As two examples, the fundamental solutions for both a point heat source in the interior of infinite thermoelastic body and a point heat source on the surface of semi-infinite thermoelastic body are presented by virtue of the obtained general solutions.

Three-Dimensional Fundamental Solution for Transversely Isotropic Electro-Magneto-Thermo-Elastic Materials

Fundamental solutions play an important role in the analyses of coupled fields in electro-magneto-thermo-elastic material. However, most works available on this topic address the case of uniform temperature. Based on the compact general solution of transversely isotropic electro-magneto-thermo-elastic material, which is expressed in harmonic functions, and employing the trial-and-error method, the three-dimensional fundamental solution for a steady point heat source in an infinite transversely isotropic electro-magneto-thermo-elastic material is presented by five newly induced harmonic functions. Numerical results are given graphically by contours.

2D General Solution and Fundamental Solution for Orthotropic Electro-Magneto-Thermo-Elastic Materials

The 2D general solution for the plane problem of electro-magneto-thermo-elastic materials is derived in terms of five harmonic functions using strict differential operator theory for the case of distinct material eigenvalues. Based on the obtained general solution, the 2D fundamental solution for a steady point heat source in an infinite and a semi-infinite magneto-electro-thermo-elastic plane is obtained by virtue of the trial-and-error method.

Green’s function for a line heat source acting on the surface of a coated isotropic thermoelastic material

Abstract Two-dimensional Green’s function, for a line heat source acting on the surface of a coated isotropic thermoelastic material, is investigated in this paper to improve the understanding of interface mechanisms of coating/substrate system. The coating and substrate are modeled as infinite layer and semi-infinite substrate respectively. They are perfectly bonded or are in smooth contact at the interface. Based on the two-dimensional general solution of isotropic thermoelastic materials expressed by harmonic functions, the corresponding harmonic functions with undetermined constants for coating and semi-infinite substrate are constructed, respectively. The thermoelastic field can be obtained by substituting the harmonic function into the general solution. The constants can be determined by the free surface boundary conditions and interface continuous conditions between the coating and the semi-infinite substrate. Numerical results are exhibited in the form of contours and some valuable conclusions for interface effect, interface shear debonding and coating tensile failure are presented.

Two-dimensional Green's functions for fluid and thermoelastic two-phase plane

The two-dimensional Greens functions for a steady-state line heat source in the interior of fluid and thermoelastic two-phase plane are derived in this paper. By virtue of the compact two-dimensional general solutions which are expressed in harmonic functions, four newly introduced harmonic functions with undetermined constants are constructed. Then, all the thermoelastic components in the fluid and thermoelastic two-phase plane can be derived by substituting these harmonic functions into the corresponding general solutions. And the undetermined constants can be obtained by the corresponding conditions of compatibility, boundary and equilibrium. Numerical results are given graphically by contours.