On Further Developments of Feasible Region of Lamination Parameters for Symmetric Composite Laminates

Abstract

Usage of lamination parameters for design of composite laminates significantly reduces the complexity of the optimisation problem and also allows gradient based methods to effectively be used in design. Lamination parameters are trigonometric functions of the stacking sequence of the laminate and are related to each other by a set of nonlinear constraints which define their feasible region. The feasibility constraints have been derived for in-plane or out-of-plane lamination parameters separately. In the previous work by the authors, a set of nonlinear expressions were derived for two in-plane and two out-of-plane lamination parameters and were used for design of orthotropic variable angle tow laminates. In the present work, feasibility constraints are derived for a symmetric laminate which are functions of four in-plane and four out-of-plane lamination parameters. These nonlinear constraints were derived using the Cauchy-Schwarz inequality and algebraic identity relations between in-plane, coupling and out-of-plane lamination parameters. The significance of the constraints in accurately defining the feasible region for different lamination parameters of a symmetric laminate is studied. Further, the derived nonlinear constraints are then used in the design of symmetrical variable angle tow laminate for maximising shear buckling performance.