Design Sensitivity Analysis in Structural Mechanics. III. Effects of Shape Variation

The dependence of static response and eigenvalues on the shape of plates and plane elastic solids is characterized. Shape of elastic bodies is taken as the design variable. The material derivative idea of continuum mechanics is used to obtain expressions for directional derivatives of displacement fields and eigenvalues with respect to a transformation function that defines a shape variation. The result is used to obtain explicit and computable expressions for variations of integral functionals that arise in structural optimization problems.