Thermal Stresses in an Anisotropic Plate Disturbed by an Insulated Elliptic Hole or Crack

Abstract

The solutions presented in the literature for the thermal stresses under uniform heat flow disturbed by an insulated elliptic hole are for an isotropic or orthotropic medium. However, the solution for the latter cannot be specialized to the former due to the repeated eigenvalue of the elastic constants of isotropic materials, which also restricts the application to other degenerate materials. Based upon the Stroh formalism, a simple and compact version of general solutions for plane anisotropic thermoelasticity is given in this paper. Some new identities concerning the eigenvalues and eigenvectors are developed, which are the keys for the present solutions to be valid in any kind of anisotropic materials including degenerate materials. The hoop stress around the elliptic hole is given in an explicit form. The effect of geometry, heat flow, elastic and thermal anisotropy, and heat conductivity can then be studied. The solutions for the crack problem are obtained by setting the minor axis of the ellipse approach to zero. The stress intensity factors, crack opening displacement, and strain energy release rate are expressed in terms of the fundamental elasticity matrix L and thermal vector γ˜2* introduced in this paper. The validity of the fully open crack assumption is also discussed.