Shape Sensitivity by Finite Elements*

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Abstract
An analytical approach for performing shape sensitivity analysis of structural response requires a knowledge of derivatives of loads, stress, and stiffness matrices of the finite elements of the model, with respect to parameters that control structural shape. This paper presents a new method for computing such derivatives. It uses either first-order Taylor series expansions or the material derivative of continuum mechanics in order to establish equations that are satisfied by shape derivatives of structural displacements. When discretized, these equations provide the mathematical structure for the derivatives that are needed. A shape optimal design problem is presented to demonstrate the effectiveness of the new method. The formulation is general and could be applied in a variety of other fields; in fracture mechanics, for instance.

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