The sufficient conditions for an extremum in problems of optimizing the shapes of elastic plates
The problems of selecting the thickness distributions of elastic plates in order to maximize the fundamental free vibrations frequency, as well as to minimize the strain potential energy, are considered. Necessary and sufficient conditions are obtained for a weak local extremum in such optimal design problems. These conditions retain their form even for reciprocal problems: minimization of plate weight when there are constraints on the fundamental frequency or the strain potential energy. The conditions obtained include an integral estimate on the maximum growth of second derivatives of the thickness distributions that satisfy the necessary extremum conditions.
maximize the fundamental free vibrations frequency
scientific article; zbMATH DE number 3976549
scientific article