Abstract
A class of distributed-parameter optimal design problems is treated, in which the design variable appears as a coefficient in a partial differential operator. Formal sensitivity analysis techniques that are in common use in the engineering literature are studied and made technically precise. Operator theoretic techniques and Frechet differentiation theory are employed to develop a rigorous sensitivity analysis for static and vibrating elastic structures. Two examples involving fourth-order ordinary and partial differential operators, commonly encountered in treating beam and plate elements, are analyzed.
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