Design/Control Optimization of Cross‐Ply Laminates Under Buckling and Vibration

Abstract

The optimal layer thicknesses and optimal feedback control function are determined for a symmetric, cross‐ply laminate. The objectives of the optimization are to maximize the biaxial buckling load (design objective) and to minimize the dynamic response to external disturbances (control objective) subject to a constraint on the expenditure of control energy. The design/control problem is formulated as a multiobjective optimization problem by employing a performance index that combines the design and control objectives in a weighted sum. Numerical results are given for a laminate made of an advanced composite material. Comparisons of controlled and uncontrolled laminates as well as optimally designed and nonoptimal laminates indicate the benefits of treating the design and control problems in unified formulation. The implications of solving these two problems are discussed. The values of optimal design and control variables are given for a number of problem parameters.