Shape derivative of the energy functional for the bending of elastic plates with thin defects

The paper deals with an equilibrium problem for a homogeneous isotropic elastic plate with a thin rigid inclusion and interfacial crack. We provide an explicit formula for the first shape derivative of the energy functional in the direction of a given vector field by means of a volume integral. For specific examples of the vector field, we derive some representations of the formula in terms of path-independent contour integrals.