Shape optimization of thin-walled beam-like structures

This article presents a methodology for optimizing the shape of thin-walled structures having a beam-like dynamic behavior. The equivalent nominal beam characteristics (quadratic moments of inertia, torsional rigidity, etc.) of a refined finite element model are determined from a direct calculation based on explicit equations which are functions of the nodal coordinates defining the cross-sectional geometry. A subset of these coordinates is then taken as the design variables for a nonlinear optimization problem where new target physical properties are sought. A complementary model reduction procedure is introduced to improve the precision of the proposed method for beams with variable cross-section or topological accidents.