This paper presents explicit formulas for shape sensitivity analysis of thin shell structures. The curvature distribution is the design to be determined. The thin-shell theory employed is the general Koiter model in the Cartesian coordinates. For the shape sensitivity formulation, both the direct differentiation method and the material derivative concept have been used. The two formulations are shown to be equivalent. A computer program based on these formulations has been developed and applied to examples. The shape sensitivity results obtained have been compared to those obtained by finite differencing. © 1992.
Lee, S. S., & Kwak, B. M. (1992). Shape sensitivity analysis of thin-shell structures. Finite Elements in Analysis and Design, 10(4), 293–305. https://doi.org/10.1016/0168-874X(92)90017-7