Shape optimization of shells and locking

In the present paper, the significance of a reliable finite element formulation in the optimization process is discussed. First, analytical sensitivities for a shell element based on the DSG concept are derived. Due to its simplicity, efficiency and the possibility to compute sensitivities analytically, the DSG method turns out to be perfectly well-suited for shape optimization. The effects of locking on shape optimization of shells are studied by numerical experiments using a standard displacement shell formulation and the DSG method. It is shown that locking phenomena may affect the optimum not only quantitatively, but also qualitatively.