Controlling thermal deformation by using functionally graded materials

Many thin structural components such as beams, plates, and shells experience a through-thickness temperature variation. This temperature variation can produce thermal deformation containing both an in-plane expansion component as well as an out-of-plane (bending) curvature component. For use in engineering structures, we often wish to minimize the thermal deformation of a component or to match it to the thermal deformation of another component. This can be accomplished by using a composite whose fibers have a negative axial thermal expansion coefficient. By varying the fiber volume fraction within a symmetric laminated beam to create a functionally graded material (FGM), certain thermal deformations can be controlled or tailored. Specifically, a beam can be designed which does not curve under a steady-state through-thickness temperature variation. This result is independent of the actual temperature values, within the limitation of constant material properties of the constituents. The beam can also be designed to match or eliminate an in-plane expansion coefficient, or to match a desired axial stiffness.