Shape sensitivity analysis of elastic shells with cracks

This study concerns the application of shape sensitivity analysis as a systematic methodology to determine the energy relase rate of cracked shells, within the framework of a linear elastic approach that takes into account the effect of transverse shear deformation. This methodology and the direct method of shape sensitivity analysis is applied to shells with an arbitrary middle surface and leads to an explicit general expression for the shape sensitivity of the total potential strain energy. In elastic shells with cracks, crack initiation is simulated by a change of shape characterized by a suitable tangential velocity distribution over the middle surface of the shell. In this case, a useful expression of energy release rate is expressed in terms of the strain-stress state and the adopted shape change velocity field. Finally, shape sensitivity analysis is applied to the circular cylindrical shell and thus the condition of null divergence of the corresponding Eshelby tensor is verified.