Feasible region in general design space of lamination parameters for laminated composites

In the classical lamination theory and the first-order shear deformation theory, the stiffnesses of laminated composites can be expressed as linear functions of 12 lamination parameters. A method is presented for determining the feasible region in general design space of 12 lamination parameters. In some optimization problems, the local optimum can be avoided by using lamination parameters instead of layer angles and thicknesses. Thus, the lamination parameters are useful design variables in the layup optimization for mechanical properties of laminated composites. To perform the layup optimization, the feasible region of the lamination parameters needs to be known. The lamination parameters are functionals of the distribution function of fiber orientation angles through the thickness. In the determination of the feasible region, the laminate configurations are not restricted. In the method, a variational approach is applied to find the boundary of the feasible region in the general design space of 12 lamination parameters. The feasible region for any set of lamination parameters can be also obtained. With use of the method, the feasible regions in four different design spaces are examined as an example. The reliability and the validity of the method are confirmed.