Controlling thermal deformation by using laminated plates

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 combining layers of material with a positive thermal expansion coefficient with layers possessing a negative thermal expansion coefficient. For plates, an efficient reinforcement form for composite laminae is a plain weave. A three-layer plate 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 plate is demonstrated which can eliminate thermal curvature while matching a desired in-plane expansion (within sensible limits). The plate results are independent of the actual temperature values, within the limitations of steady-state heat transfer and constant material properties.