General solutions for thermopiezoelectrics with various holes under thermal loading

A survey of new integral equations in plane elasticity crack problem

The two-dimensional thermal stress problem is one of the important problems in the field of solid mechanics. In this paper, the complex variable method for solving this kind of problem is stated. The basic equations of complex variable functions in conjunction with a rational mapping function are considered. The formulation of the rational mapping function and its accuracy are indicated. The general solutions for the external force, displacement, and mixed boundary value problems under uniform heat flux and under a point heat source are stated. The Green's functions for a point heat source and sink are suggested for the three kinds of boundary value problems. The equation to obtain the stress intensity factor for the crack problems and the stress intensity of debonding for a partially debonded rigid inclusion are shown. The interaction problem between a hole and a line crack under uniform heat flux is analyzed.

Complex Variable Method for Thermal Stress Problem

Heat conduction and thermal stress induced by an electric current in an infinite thin plate containing an elliptical hole with an edge crack

In two-dimensional thermoelasticity, Green's functions of the external force boundary value problem are derived for an infinite plane with an arbitrary shaped hole under adiabatic and isothermal boundary conditions subjected to heat sources in two cases as follows. One is the case ofa heat source and a heat sink arbitrarily located within the plane, the other is the case of a heat source arbitrarily located within the plane and a heat sink at infinity. Complex stress functions, temperature function, a rational mapping function, and the thermal dislocation method are used for the analysis. In analytical examples, distributions of temperature, heat flux, and stresses are shown for an infinite plane with a rectangular hole under adiabatic and isothermal boundary conditions.

Green's Function for a Heat Source in an Infinite Region With an Arbitrary Shaped Hole

Analyses of thermal stress, heat flux, and temperature distributions are carried out for an infinite plate with a cracked circular hole under uniform heat flux in any direction. The stress intensity factor and the singularity of the heat flux at the crack tip are also obtained. The rational mapping function and the dislocation method are used for the analyses. The closed solutions are obtained for the temperature and thermal stress analyses.

Thermal stresses of a cracked circular hole due to uniform heat flux

The general solution of the displacement boundary value problem is obtained for an infinite plate with an arbitrary shaped hole under uniform heat flux in any direction. The complex stress functions, the dislocation method, and a rational mapping function are used and the closed solution is obtained. An infinite plate with a circular hole and a slit is analyzed under the condition of the constrained displacements. The singularity at the tip of the slit of the constrained displacement is investigated

Akinori Tomida

Papers

Thermal stresses of a cracked circular hole due to uniform heat flux

Solution of displacement boundary value problem under uniform heat flux