In this paper sensitivity analysis for free form shells under static and free vibration loading is considered. The shell analysis is carried out with the nine-noded, degenerated, Huang-Ilinton shell element. The commonly used semi-analytical and finite difference methods are described in detail. Special attention is focused on the accuracy and performance when these methods are used. The distinction between the conventional semi-analytical and exact semi-analytical is made. Based on the exact semi-analytical concept, an alternative approach for sensitivity calculations for the element used here is also established. Several examples of sensitivity calculations show the difference in accuracy and speed obtained by the different schemes. Design variables that specify either the shape or thickness distribution within the structures are considered. The results obtained in the present paper justify the usage of the new semi-analytical method for sensitivity calculations for the type of shell element considered here.

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