Reinforced mindlin plates with extremal stiffness

For a prescribed area fraction of stiffeners, we characterize the set of stiffener reinforced Mindlin plates with extremal overall stiffness. The method rests upon the derivation of optimal bounds of the Hashin-Shtrikman type. Our method is distinct from the usual Hashin-Shtrikman approach. We make use of the underlying variational structure behind the Hashin-Shtrikman method to show that the use of a comparison material is redundant. We do this by proceeding directly and express the equilibrium equations in terms of positive definite integral operators. The positivity of the operators is used to obtain a new Hilbert space variational principle for the effective stiffness. The associated bounds are shown to be realized by effective rigidities associated with hierarchical laminar arrangements of stiffeners. © 1997 Elsevier Science Ltd