Thin Laminates with Homogeneous Elastic Properties

The analytic design of thin laminates is presented. The constitutive equation of a multilayer shell element of arbitrary construction is derived and reduced to the special cases of orthotropic and isotropic materials. The terms of the coefficient matrix are shown to be functions of the mechanical properties of each layer, as well as the lamination parameters, i.e., the number, thickness, and orientation of laminas. A comparison of the laminate's coefficient matrix with those of its homogeneous counterparts is made in order to deduce the mathematical relations which ensure homogeneous behavior. These relations contain lamination parameters only; the mechanical properties of each layer can thus be selected to obtain the optimum composite stiffness characteristics. Laminate configurations which satisfy the requirements for homogeneous elastic response are found by exact and approximate means. These results are useful in structural applications which call for orthotropic or isotropic material properties, or when a reliable stress analysis is mandatory.