On the plane theory of microthermoelasticity for transversely isotropic bodies with voids

The paper considers a two-dimensional static case of microthermoelasticity for transversely isotropic bodies with voids. The corresponding linear system of equations is divided into two parts: a system of equations for the components of the displacement vector, the temperature change, and the change in the volum fraction of voids, and a system of equations that includes the components of the microtemperature vector and the temperature change. The second of these systems is independent of the first and is solved independently in advance. The resulting solution is then taken into account when solving the first system of equations. Both systems are written in complex form, and their general solutions are represented using analytic functions of a complex variable and solutions of the Helmholtz equations. The constructed general solution makes it possible to solve boundary problems analytically. As an example, an exact solution is given for a circle with a temperature source in the center.