Weight minimization of orthotropic flat panels subjected to a flutter speed constraint

Abstract

This paper deals with the minimum weight design of orthotropic panels subjected to a supersonic flutter speed constraint and to a system of uniform in-plane loadings. In approaching the problem, use is made of the methods of optimal control theory of distributed parameter systems. This leads to a set of necessary optimality conditions that, together with a supplementary condition ensuring that the flutter speed of the optimal panels coincides with the constrained one, constitute the governing optimality equations of the problem. An alternative form of the optimality equations is derived and a symmetry property of the optimal thickness distribution is placed in evidence. Numerical solutions are obtained via Galerkin's procedure, providing rough estimates of the optimal panel design. The results also show the influence of some important parameters, such as orthotropy ratio, in-plane loading, aspect ratio, and support conditions.