Conditions of Single-Valuedness of Rotation and Displacements for Non-Homogeneous Materials in Plane Thermoelasticity

Abstract

The conditions of single-valuedness of rotation and displacements in the multiply connected regions for non-homogeneous materials are discussed theoretically by using the stress function. As an example of a multiply connected region, we have considered the steady thermal stresses in a functionally graded hollow circular body with an eccentric outer circular boundary. The material properties are expressed by the power law of the radius of the inner circle. The inner boundary conditions are satisfied strictly, whereas the outer boundary conditions are satisfied numerically using a point-matching method. Steady thermal stresses in the body are shown for ZrO₂/Ti-6Al-4 V functionally graded materials (FGMs). The results were verified by comparing with those of a functionally graded hollow circular cylinder.

Keywords:

• Conditions of single-valuedness
• Functionally graded materials (FGMs)
• Non-homogeneous materials
• Steady thermal stresses
• Stress function method