A unified framework for full-parameter concurrent topology optimization of thin-walled stiffened structures

TY - JOUR

T1 - A unified framework for full-parameter concurrent topology optimization of thin-walled stiffened structures

AU - Ji, Wei

AU - Bai, Yingchun

AU - Lin, Cheng

AU - Cui, Xiangyang

AU - Sun, Fengchun

N1 - Publisher Copyright: © 2026 Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

PY - 2026/5/1

Y1 - 2026/5/1

N2 - Traditional topology optimization methods for thin‑walled stiffened structures focus primarily on stiffener layout and topology. The thin wall is typically treated as a non‑design domain, which restricts design freedom. To overcome this limitation, this paper proposes a full-parameter concurrent topology optimization method for thin‑walled stiffened structures, in which stiffener topology, thin-wall shape, and thin-wall thickness are co-designed. A unified modeling framework is established to describe thin walls and stiffeners via density filtering method. For thin‑wall modeling, a novel two‑step anisotropic‑isotropic filtering and projection scheme is developed by incorporating thin-wall thickness variables to characterize non‑uniform-thickness thin-wall shape. For stiffener modeling, an anisotropic filtering and projection scheme describes variable‑height features, while an improved maximum‑length‑scale constraint prevents material aggregation. In addition, a material interpolation scheme links the density variables to the physical finite‑element model, and a concurrent optimization framework updates the stiffener topology, thin‑wall shape, and thin-wall thickness variables simultaneously. Sensitivities of compliance, volume fraction and maximum-length-scale constraint with respect to design variables are derived and used within the method of moving asymptotes (MMA) to efficiently solve the optimization model. The proposed method is systematically validated through several 3D numerical examples, including practical engineering applications such as a vehicle motor‑mounting bracket and an EV’s casting frontal member.

AB - Traditional topology optimization methods for thin‑walled stiffened structures focus primarily on stiffener layout and topology. The thin wall is typically treated as a non‑design domain, which restricts design freedom. To overcome this limitation, this paper proposes a full-parameter concurrent topology optimization method for thin‑walled stiffened structures, in which stiffener topology, thin-wall shape, and thin-wall thickness are co-designed. A unified modeling framework is established to describe thin walls and stiffeners via density filtering method. For thin‑wall modeling, a novel two‑step anisotropic‑isotropic filtering and projection scheme is developed by incorporating thin-wall thickness variables to characterize non‑uniform-thickness thin-wall shape. For stiffener modeling, an anisotropic filtering and projection scheme describes variable‑height features, while an improved maximum‑length‑scale constraint prevents material aggregation. In addition, a material interpolation scheme links the density variables to the physical finite‑element model, and a concurrent optimization framework updates the stiffener topology, thin‑wall shape, and thin-wall thickness variables simultaneously. Sensitivities of compliance, volume fraction and maximum-length-scale constraint with respect to design variables are derived and used within the method of moving asymptotes (MMA) to efficiently solve the optimization model. The proposed method is systematically validated through several 3D numerical examples, including practical engineering applications such as a vehicle motor‑mounting bracket and an EV’s casting frontal member.

KW - Concurrent topology optimization

KW - Full-parameter modeling

KW - Maximum-length-scale constraint

KW - Non‑uniform-thickness thin wall

KW - Thin-walled stiffened structures

KW - Variable-height stiffener

UR - https://www.scopus.com/pages/publications/105034192166

U2 - 10.1016/j.cma.2026.118850

DO - 10.1016/j.cma.2026.118850

M3 - Article

AN - SCOPUS:105034192166

SN - 0045-7825

VL - 453

JO - Computer Methods in Applied Mechanics and Engineering

JF - Computer Methods in Applied Mechanics and Engineering

M1 - 118850

ER -