This paper presents a linear elasticity solution for determining the response of composite tubes subjected to a circumferential temperature gradient of the form ΔTo+ ΔT1 cos(θ). The temperature does not vary with distance along the tube nor through the wall. Temperature-independent material properties are assumed and a displacement approach is used. The results are limited to tubes with the fibers in each layer oriented axially or circumferentially, so-called cross-ply tubes. It is shown that for both single layer and multiple layer tubes, one constant characterizes overall bending of the tube and one constant characterizes overall axial deformation. Numerical results show that fiber orientation strongly influences the stresses in a single layer tube. When the fibers are aligned axially, all components of stress in the tube are small. When the fibers are aligned circumferentially, the hoop stress becomes large. This is due to the large difference between the radial and circumferential coefficients of thermal expansion when the fibers are oriented circumferentially. Also, for a single layer tube constructed of a material with no thermal expansion in the axial direction, the overall change of length of the tube due to the temperature gradient will be zero only if the material is transversely isotropic. However, even if the material is transversely isotropic, the tube will still experience overall bending.
Control of biaxial strain in single-layer molybdenite using local thermal expansion of the substrate
