Equilibrium of prestressed networks

A general theory for small displacements superposed on finite deformations of elastic networks is presented. The network is regarded as a surface formed by two continuously distributed families of elastic fibres. The second variation of the potential energy is considered in detail and the Legendre-Hadamard inequality associated with a weak minimizer of the energy is examined. The theory is then specialized to the case of orthogonal fibres and applied to the solution of some simple problems.