Approximate Feasible Regions for Lamination Parameters

This is the authors' abstract. We don't add key points for this paper.

Lamination parameters represent the laminate lay-up configuration in a compact form. According to their definitions, lamination parameters are related and cannot be arbitrarily selected. The region which defines physically meaningful lamination parameters is called the feasible lamination parameters region. In order to formulate a typical structural design problem using lamination parameters, the feasible domain for the particular set of lamination parameters is required. Such a domain is known to be convex and is available in closed form only for a limited number of combinations of the lamination parameters. In the present study, we exploit the convexity of these feasible regions and outline a numerical approach using successive convex hull approximations. In the successive convex hull approximation we refine the feasible region by increasing number of layers as well as number of possible fiber orientation angles. In this process, the volume of the feasible domain is monitored to measure the convergence of the approach. The final approximation is presented in the form of linear inequality constraints (hyperplanes) that can be included in typical structural optimization problems as side constraints. The major advantage of such a methodology is that this approximation needs to be done only once and the resulting set of constraints can be stored and reused for any other structural optimization problem. First, numerical results are compared for the cases where exact definitions exist for feasible domains. Next we apply the present approach to sets of lamination parameters for which exact definitions for feasible regions do not exist and compare our results with approximate results using other methods already available in the literature.