Tailoring thermal deformation by using layered beams

In application, many thin structural components such as beams, plates and shells experience a through-thickness temperature variation. This temperature variation can produce both an in-plane expansion and an out-of-plane (bending) curvature. Given that these thin components interact with or connect to other components, we often wish to minimize the thermal deformation or match the thermal deformation of another component. This is accomplished by combining layers of material with a positive thermal expansion coefficient with layers possessing a negative thermal expansion coefficient. A three-layer beam is demonstrated which can eliminate thermal curvature while lowering in-plane expansion or can match a desired in-plane expansion while lowering thermal curvature. A five-layer beam is demonstrated which can eliminate thermal curvature while matching a desired in-plane expansion. The beam results are independent of the actual temperature values, within the limitations of steady-state heat transfer and constant material properties.