Plane Thermal Stress at an Insulated Hole Under Uniform Heat Flow in an Orthotropic Medium

Abstract

When a uniform heat flow in an infinite orthotropic solid is disturbed by the presence of a long circular insulated cavity, local intensification of the temperature gradient occurs in the neighborhood of the cavity. This report describes a study of the stress field induced by the temperature distribution. The linear plane (plane stress or plane strain) thermoelastic problem is solved by using the complex variable technique. The analysis may also be used for other steady-state thermal stress problems in an orthotropic medium.

Piezothermoelastic analysis of a piezoelectric material with an elliptic cavity under uniform heat flow

“…Since the roots of dz P a ad1 a 0 and dz s ad1 s 0 are located inside the unit circle, the transformations (30) and (31) are oneto-one outside the hole and 1 a C 1 s j j C e i5 r when z p a and z s are on the elliptic boundary, in which 5 is de®ned in (18). On the other hand, the mapping of the region X c inside the ellipse is done by considering a straight line C 0 along x 1 and of length 2…”

“…It is a fundamental problem concerning thermal stress concentration, and has been well studied for pure elastic materials [8,18,19]; it has not been solved yet for piezoelectric materials, according to the available literature. This problem is studied here.…”

“…By letting b 3 0 in (18), the problem discussed before becomes an in®nite piezoelectric domain with a slit crack of length 2a. In this case, (30) and (31) are reduced to…”

A new solution for thermopiezoelectric solid with an insulated elliptic hole

“…In this context, Florence and Goodier [1'2] studied the thermal stresses for an isotropic elastic medium containing a circular or an ovaloid hole by the method of Muskhelishvili [3]. Using the complex variable technique, Chen [4] investigated the orthotropic elastic medium with a circular or an elliptic hole, and obtained a solution in complex form for the hoop stress around the hole. With respect to anisotropic elastic materials, based on the Stroh formalism and conformal mapping, Hwu [5] obtained the stress formulation for an anisotropic elastic plate with an elliptic hole subjected to remote uniform heat flow in x2-direction.…”

Green function and its application for a piezoelectric plate with various openings

“…Thermal stress in an isotropic medium containing an insulated oval hole was studied in [4]. Based on the complex variable method, the problem for orthotropic medium with a circular or elliptic hole was studied, and a complex form solution for the hoop stress at the hole was obtained in [5]. Treated in [6] was the compressibility of holes by way of conformal mapping of a hole onto a unit circle.…”