Shape sensitivity analysis and optimal design of disks and plates with strong discontinuities of kinematic fields

Abstract Disks, plates or beams subjected to loading and initial strains or displacements are assumed to be composed of portions interconnected by hinge or slip and dilatancy lines admitting discontinuities in displacements or slopes. The shape of such lines and their stiffness properties are subjected to variation. The sensitivity analysis is first discussed for an arbitrary functional of generalized stress, strain, displacement and boundary traction. The variation of complementary and potential energies is considered as a particular case of a general derivation for sensitivity. The optimal design problem is then considered and the relevant optimally conditions are derived. The general theory is illustrated by examples of sensitivity analysis and optimal design with respect to shape, position and stiffness of discontinuity lines for disks, plates and beams. Numerical aspects of sensitivity analysis are also discussed.