C.K. Chao

On the general treatment of multiple inclusions in antiplane elastostatics

This article provides an explicit general solution of an infinitely extended plate containing any number of circular inclusions under antiplane deformation. The derived solution of the present heterogeneous problem associated with multiple inclusions is obtained in terms of the corresponding homogeneous solution by a simple algebraic substitution. This is accomplished by the technique of analytical continuation and the method of successive approximations. A rapidly convergent series solution either in the matrix or in the inclusions, which is expressed in terms of an explicit general term involving the complex potential of the corresponding homogeneous problem, is derived in an elegant form. The present derived solution can also be applied to the inclusion problem with straight boundaries. Numerical examples of three circular inclusions embedded in an infinite matrix, in a half-plane matrix, and in a strip are discussed in detail and displayed in graphic form. Interaction of a crack with multiple circular inclusions is also considered.

Green's Functions for a Point Heat Source in Circularly Cylindrical Layered Media

Within the framework of the linear theory of thermoelasticity, the problem of circularly cylindrical layered media subjected to an arbitrary point heat source is considered and solved in this paper. Based on the method of analytical continuation in conjunction with the alternating technique, the solutions to heat conduction and thermoelasticity problems for a three-phase multilayered cylinder are first derived. A rapid convergent series solution for both the temperature and stress functions, which is expressed in terms of an explicit general term of the complex potential of the corresponding homogeneous problem, is obtained in an elegant form. Numerical results are provided for some particular examples to investigate the effect of material combinations on the interfacial stresses.

Mixed boundary-value problems of two-dimensional anisotropic thermoelasticity with elliptic boundaries

Abstract The two-dimensional mixed boundary-value problems for an anisotropic thermoelastic body containing an elliptic hole boundary are considered in this paper. By using the formalism of Stroh [Phil. Mag. 7, 625–646], the approach of analytic function continuation and the technique of conformal mapping, a unified analytical solution for elliptic hole boundaries and for general anisotropic thermoelastic media is provided. As an application, two typical examples associated with mixed boundary-value problems are solved completely. One is an indentation problem over an elliptic hole boundary, the other is a partially reinforced elliptic hole under a remote uniform heat flow. Both the contact stress under the rigid stamp and the bonded stress along the reinforced segment are studied in detail and shown in graphic form.

Stress Analysis of an Infinite Plate with a Coated Elliptic Hole Under a Remote Uniform Heat Flow

A thermoelastic solution to a coated elliptic hole embedded in an infinite matrix subjected to a remote uniform heat flow is provided in this article. Based on the technique of conformal mapping and the method of analytical continuation in conjunction with the alternating technique, the general expressions of the temperature and stresses in the coated layer and the matrix are derived explicitly in a series form. Some numerical results are provided to investigate the effects of the material combinations and geometric configurations on the interfacial stresses. It is found that a coated layer has a strong effect on thermal stresses of the problem with an elliptic hole embedded in an infinite plate.

Rigid stamp indentation for a thermoelastic half-plane

Abstract A problem for the thermoelastic half-plane indented by a rigid punch of various shapes is solved explicitly in this paper by the method of analytical continuation. The effects of applied loadings, the profile of the punch and material properties on the contact stress under the punch face are studied in detail and shown in graphic form. A rigid punch of three different profiles with or without friction is considered under the complete or incomplete indentation condition.

Thermal stresses induced by a remote uniform heat flow interacting with two circular inclusions

ABSTRACT An analytical solution to two circular inclusions embedded in an infinite plate subjected to a remote uniform heat flux is provided in this article. Based on the method of analytical continuation and the technique of conformal mapping, the general expressions of the temperature and stresses are derived explicitly in a series form. Since our derived series solutions are expressed in terms of the material parameters, the present results are available for the case of even two circular inclusions are getting closer. For a limiting case, when two circular inclusions are set apart sufficiently, the derived analytical solutions are reduced to those of the corresponding single inclusion problem. Numerical results of interfacial stresses are performed and displayed in graphic form. It is interesting to see that both the normal and shear interfacial stresses experience a big jump across the point nearest to the neighboring inclusion, when the distance of two circular inclusions is sufficiently small.

Interaction between a Nonuniformly Coated Circular Inclusion and a Remote Uniform Heat Flow

This article presents an analytical solution for plane thermoelasticity problems of a nonuniformly coated circular inclusion under a remote uniform heat flow. Based on the technique of conformal mapping and the method of analytical continuation in conjunction with the alternating technique, the general expressions of the temperature, displacements and stresses for three dissimilar media are derived explicitly in a series form. For a limiting case that the thickness of the interphase layer is uniform, the derived analytical solutions are reduced to those of the corresponding circularly cylindrical layered media problem. Numerical results of interfacial stresses are carried out and displayed in graphic form.

Thermodynamic Derivation in Magneto-Electro-Elasticity

Magneto-electro-elastic materials constitute important elements of smart structures. Based on thermodynamics within isothermal linear process and isentropic linear process, the mathematical derivation of magneto-electro-elasticity is established in this work. The Helmholtz free energy density, internal energy density and enthalpy density are applied to solve the problem. It is important to mention that constant pressure specific heat and constant volume specific heat play a remarkable role in thermodynamic analysis of magneto-electro-elasticity. Overall, this study has successfully derived a theoretical framework in solving basic problems of thermodynamics and magneto-electro-elasticity.

Heterogeneous Problems in Plane Thermoelasticity

Within the framework of the linear theory of thermoelasticity, the heterogeneous problem associated with multiple inclusions, circularly cylindrical layered media and plane layered media is considered and solved in this paper. The number of inclusions and layers is arbitrary and the system is subjected to arbitrary loading (singularities). The solutions to heat conduction (or antiplane deformation) and thermoelasticity problems are derived by the heterogenization technique that allows us to write down the solution explicitly in terms of the solution of a corresponding homogeneous problem subjected to the same loading. A rapid convergent series solution for both the temperature (or antiplane displacement) and stress functions, which is expressed in terms of an explicit general term of the complex potential of the corresponding homogeneous problem, is obtained in an elegant form. Numerical results are provided for some particular examples to investigate the effect of material combinations and geometrical configurations on the interfacial stresses.