Controlling thermal deformation and stresses in laminated structures

Under a through-thickness temperature variation, thin structural elements such as beams, plates and shells usually react by producing deformations composed of (in-plane) expansion and (out-of-plane) bending. These deformations can distort the structure and cause stresses when its parts expand unequally. By symmetrically laminating laminae possessing a negative axial coefficient of thermal expansion (CTE) with laminae having a positive CTE, these deformations can be minimized or matching with the deformation of other components.; A three-layer beam or plate is demonstrated which can eliminate thermal curvature while lowering in-plane thermal expansion or can match a desired in-plane expansion (including zero CTE) while lowering thermal curvature. A five-layer beam or plate is demonstrated which can eliminate thermal curvature and match a desired in-plane expansion (within limits). Solutions are given in terms of layer thickness ratio. The results are independent of the actual temperatures, within the limitation of steady-state heat transfer and constant material properties. These design conditions can also be used to control or tailor the thermally induced stresses within the laminated structure.; An additional design parameter is the fiber volume fraction (V{dollar}sb{lcub}rm f{rcub}).{dollar} For a three-layer beam of (composite/metal/composite), the thickness ratio to meet thermal curvature stable (TCS) design requirement and the CTE of the beam are relatively insensitive to V{dollar}sb{lcub}rm f{rcub}{dollar} at higher V{dollar}sb{lcub}rm f{rcub}.{dollar} At lower V{dollar}sb{lcub}rm f{rcub},{dollar} the in-plane thermal expansion can be further reduced at the expanse of increased composite layer thickness.; Compared to an homogeneous (metal which was used in the laminated structure) structural element with identical flexural stiffness or compliance, the layered structure has the advantage of lower thickness and weight, higher in-plane stiffness, fundamental vibration frequency and critical thermal buckling temperature. When material properties are considered to be functions of temperature, a layered structure with zero thermal curvature or matched in-plane expansion may still be constructed. The solution using temperature-dependent properties is compared to that for constant properties for a three layer system. The penalty for assuming constant properties is assessed. The time-dependent temperature profile is also discussed.; The results of a sensitivity study show that variations in the thermal conductivity ratios have very little effect on the effective CTE of the laminates; they have little effect on the thermal curvature of a five-layer laminate and three-layer laminate with a negative CTE center layer. For three-layer laminates, the thermal curvature is more sensitive to variations in the layer thickness ratio than to variation in the property ratios. For five-layer laminates, the in-plane expansion is seen more sensitive to variations in the relative thickness and properties of the second layer to the third layer than that of the first layer to the third layer. For the example laminates, it is seen that those with a positive CTE center layer have a little better control of the thermal deformation. It is also observed that the thermal deformation of the laminated plates are less sensitive to uncertainty of the laminae properties and thickness to that of the beams.