Sensitivity Analysis of Fibre-Reinforced Composites with Interphase Unilateral Constraints

Abstract

In the past decade computational methods for Design Sensitivity Analysis (D.S.A.), i.e. for determining variations occurring in the behaviour of mechanical models in consequence of modifications of their control parameters, have made a considerable progress in the contexts of optimisation and inverse problems in Structural Mechanics, also in relation to non-linear problems characterized, for instance, by geometrical [1] or material nonlinearities [2]. Sensitivities for non-linear systems have been obtained also in the presence of unilateral constraints or unilateral constitutive equations, such as the classical incremental elasto-plastic relationships. In these cases non-linear and non-differentiable problems have to be dealt with and only directional sensitivities can be obtained. Moreover, standard finite difference approaches, although easier to use, can produce totally erroneous results [2][3].