Flexural stiffness design by integer linear programming

Lamination parameters are linear in ply identity variables When we designed laminates in terms of lamination parameters, we exploited the linearity of the A and D matrices in these parameters. We could not optimize the angles, because the lamination parameters are not linear function of the angles. However, we will readily show that the lamination parameters are linear functions of ply identity variables. Hence, vibration frequencies and buckling loads are linear functions of ply identity variables.

In-plane lamination parameters.

Flexural lamination parameters Equation 8.2. For this application, it is convenient to count the plies from the nearest to the mid-plane. That is k=N/2 is the outer ply. Then Therefore, for fixed number of plies the lamination parameters are linear in terms of the ply identity design variables.

Maximizing buckling load for given thickness

Results

Constraint on no more than four contiguous plies

Minimum thickness design

Results: How would you estimate what is the maximum load that is reasonable ? (is 1.41 reasonable?)