340 / 2019-09-30 22:30:11

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

Topology Optimization,Moving Morphable Components,Thin-walled Cross Section,Moment of Inerita,Stamping Process

结构优化与结构行为分析 > 结构优化与拓扑优化

Thin-walled structures, which are usually manufactured by stamping and spot-welding processes of metal sheets, can be described by thin-walled beams. Due to the high stiffness-to-mass ratio, thin-walled beams have been extensively applied in various engineering structures. The design of cross-sectional shape can be conducted by using traditional topology optimization (TO) methods at the conceptual design stage. Nevertheless, these methods can not obtain the optimized results with the thin-walled features from stamping process and were inefficient in conceptual design because of the huge design variables. TO methods based on Moving morphable components (MMC), which can directly establish the link between optimization model and computer-aided-design on the basis of explicit boundary geometric information in the optimized results, was innovatively proposed in recently. Therefore, this paper proposes a thin-walled cross-sectional design method using the MMC approach to improve efficiency and manufacturability. To acquire the thin-walled structure with high stiffness-to-mass ratio, the cross-sectional area is selected as objective function, and the cross-sectional bending and torsional moments of inertia are selected as constraints. Especially, the torsional moment of inertia and bending moments of inertia are detailedly listed based on MMC approach. The bending moment of inertia is derived by Euler-Bernoulli beam theory and the torsional moment of inertia is calculated by using the finite element method. Moreover, the sensitivities of area, bending moments of inertia and torsional moment of inertia with respect to an arbitrary geometry parameters are derived by using MMC approach, respectively. Three numerical examples, which consider the pure shear, the pure bending and the combined conditions, respectively, demonstrate the effectiveness and accuracy of this method. Besides, the optimized results by cleaning-up are equivalent to the thin-walled cross sections of single-cell, three-cell and four-cell, respectively. According to the numerical examples, the design of thin-walled cross section using MMC approach has two advantages at the conceptual design stage. On the one hand, the manufacturability is improved because the optimized possess distinctly thin-walled features and satisfy stamping process. On the other hand, the computational efficiency is remarkably improved and the development cycles of thin-walled beams have been greatly shortened because of fewer design variables.