Topology optimization of thin-walled cross section using moving morphable components approach

Thin-walled beams are extensively applied in the engineering structures, in which the conceptual design of cross-sectional shape and topology is the most important issue. Traditional topology optimization methods cannot easily obtain the thin-walled features. Therefore, a thin-walled cross-sectional design method using the moving morphable components (MMC) approach is proposed in this paper. To acquire a thin-walled structure with a high stiffness-to-mass ratio, the cross-sectional area is defined as the objective function, and the cross-sectional bending and torsional moments of inertia are selected as constraints. The bending and torsional moments of inertia in arbitrary domain are both solved by using the finite element method. In addition, the sensitivities of cross-sectional area, bending moments of inertia, and torsional moment of inertia with respect to geometrical parameters of components are derived in the MMC framework, respectively. To demonstrate the effectiveness and accuracy of this method, numerical examples are given to consider the torsional, the bending, and the combined conditions, respectively. By post-process, the obtained thin-walled features can be further transformed into stamping sheets.