QUALITATIVE PROPERTIES OF OPTIMAL DESIGN OF NONHOMOGENEOUS STRUCTURES SUBJECT TO THE ACTION OF ACOUSTIC WAVES

One of the fundamental issues of the optimal design of structures is the limiting performance analysis, i.e., the investigation of the limiting potentials for improving the structure by choosing its configuration so as to attain the global extremum (as a rule, minimum) of an objective function. In the variational formulation, the limiting performance analysis involves the determination of all globally optimal designs. Numerical optimization techniques based on the necessary optimality conditions associated with nonlocal variations of control variables allow one to construct more effective solutions than the methods based on local variations of an admissible solution [1-3]. However, as is case for methods using local variations, the effectiveness of determination of all globally optimal designs of laminated structures depends on the number of extrema of the performance index with respect to control variables. Numerical experiments show that the number of designs satisfying the necessary optimality conditions in the problems of design of laminated structures subject to acoustic wave excitations is rather large. Therefore, the determination of all laminated structure designs demonstrating the limiting performance characteristics faces considerable computational difficulties.