In this paper a unified shape optimum design scheme, combining the material derivative and boundary parametrization is presented to find the optimal cross-sectional shapes of elastic hollow bars. Performance criteria can be the bending stiffness, the torsional rigidity, or the weight of the bar. The existence of a keyway (an example of geometric irregularity) can be considered as well. Material property can be either isotropic or anisotropic. Various numerical examples have been provided to show the validity of the presented approach.

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