Analysis for an infinite orthotropic elastic plane with a hole subjected to uniform heat flux

Abstract

A general solution is derived for the thermal stresses of an infinite orthotropic plane with a hole subjected to uniform heat flux. A dislocation method is applied to solve uniform heat flux problem, in which the orthotropic thermal conductivities and coefficients of thermal expansion are considered. The dislocation functions for stress analysis are also considered. The dislocations of displacements for the x and y directions due to the thermal stress and the elastic stress at infinity must be zero. Thus, the dislocation functions regarding elastic stress are determined. Then, the stress analysis is carried out by two methods, that is, methods due to the Riemann-Hilbert method and Cauchy integral method. These methods are completely different. It is confirmed that the stress functions achieved are identical. The final exact stress functions as a general solution are derived as a closed form. The stress components are represented by one complex variable. Therefore, the calculation of the stress components is simple. Arbitrarily shaped hole problem can be solved by exchanging the mapping function. As an example, an infinite plane with a square hole subjected to uniform heat flux is analyzed. The heat flux and stress distributions are shown.

Keywords:

• Cauchy integral
• heat flux
• irrational mapping function
• orthotropic elastic plane
• Riemann-Hilbert equation
• Schwarz-Christofell’s transformation
• temperature

Disclosure statement

No potential conflict of interest was reported by the authors.