Optimal design and control of composite laminated plates with various boundary conditions using various plate theories

Abstract

The optimal control problem of minimizing the dynamic response of anisotropic symmetric or antisymmetric composite laminated rectangular plates with various boundary conditions is presented using various plate theories. The objective of the present control problem is to minimize the dynamic response of the plate with minimum possible expenditure of force. The dynamic response of the structure comprises a weight sum of the control objective (the total vibrational energy) and a penalty functional of the control force. In addition to the active control, the layer thickness and the orientation angle of the material fibers are taken as optimization design variables. The explicit solutions for the optimal force and controlled deflections are obtained in forms of double series using the Liapunov–Bellman theory. The effectiveness of the proposed control and the behavior of the controlled structure are investigated. Various numerical results including the effect of boundary conditions, number of layers, anisotropy ratio, aspect ratio, and side-to-thickness ratio on the control process for symmetric and antisymmetric laminates are presented.