DESIGN SENSITIVITY ANALYSIS OF NONLINEAR STRUCTURES IN REGULAR AND CRITICAL STATES

A general design sensitivity formulation is introduced for non-linear elastic structures reaching critical equilibrium states. A discretized formulation is considered first and the sensitivity analysis is discussed for regular and critical states including analysis of post-critical behavior. Next, a variational approach is presented for beam and surface structures for which,generalized stress and strain operator formulation is applied. The formulae for sensitivity of bifurcation loads are derived in terms of adjoint fields which are shown to be equivalent to post-buckling fields in the case of symmetric bifurcation.