Explicit layout optimization of complex rib-reinforced thin-walled structures via computational conformal mapping (CCM)

Jiang, Xudong; Huo, Wendong; Liu, Chang; Du, Zongliang; Zhang, Xiaoyu; Li, Xiao; Guo, Xu

doi:10.1016/j.cma.2022.115745

Cited by 13 publications

(1 citation statement)

References 49 publications

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“…A limit load numerical analysis was conducted to study the rib forms in the continuous and discontinuous regions of a structure and find the rational ribs that provided the most effective reinforcement to the structure [17]. By integrating surface cutting optimization and a multi-patch stitching scheme on the parametric space, an explicit layout optimization method was developed to design rib-reinforced thin-walled structures with complex geometries [18]. How to find the most effective and reasonable reinforcement type of structure and realize the lightweight design of a structure is a crucial problem that urgently needs to be solved [19].…”

Section: Introductionmentioning

confidence: 99%

Rib Reinforcement Bionic Topology Optimization under Multi-Scale Cyclic Excitation

Xiao

Zhu

et al. 2023

Mathematics

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Thin-walled structures have problems such as low stiffness, large deflection, and vibration. The layout of rib reinforcement in thin-walled structures plays a vital role in providing structural strength and rigidity and reducing structural weight. A multi-scale bionic topology optimization method with a cyclic variable load is proposed in this paper to optimize dynamic flexibility by simulating the growth law of leaf vein formation and distribution. A material interpolation method is adopted to penalize the material attributes of rib reinforcement according to their thickness, based on polynomial interpolation. Combined with the layout of rib reinforcement and SIMP, the mathematical model of rib reinforcement layout optimization with cyclic variable loading is proposed, and the sensitivity of thin-walled dynamic flexibility to the rib reinforcement thickness is analyzed. Two typical examples of thin-walled structures are presented to validate the proposed method. Considering the impact effect of multi-scale cyclic loads such as wind speed, pressure, and raindrops acting on the leaf vein, the natural frequencies of bionic topological structures of heart-shaped and elliptical leaf veins are increased by 63.44% and 47.2%, respectively. Considering the change in radial thickness, the mass of the automotive door inner panel with a bionic topological structure increased by 3.2%, the maximum stress value was reduced by 1.4% and 36.8%, and deformation was reduced by 37.6% and 27.1% under the anti-concave and sinking conditions, respectively. Moreover, the first-order natural frequency of the automotive door’s inner panel with a bionic topological structure increased to 30.45%, 3.7% higher than the original.

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Section: Introductionmentioning

confidence: 99%

Rib Reinforcement Bionic Topology Optimization under Multi-Scale Cyclic Excitation

Xiao

Zhu

et al. 2023

Mathematics

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Towards closed-walled designs in topology optimization using selective penalization

Rieser

Zimmermann

2023

Struct Multidisc Optim

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Abstract3D topology optimization using a density approach with penalization usually produces truss-like, open-walled structures. The coarser the mesh, the smaller the volume fraction, and the faster the penalization is increased, the more pronounced this effect tends to be. However, closed-walled designs are often more efficient and have other beneficial properties. For instance, closed walls can contribute to achieving self-supporting designs for additive manufacturing that potentially require fewer sacrificial support structures than truss-like designs. This paper presents a two-step optimization procedure for generating closed-walled designs using coarse meshes. The first step takes the usual Eulerian approach of performing a SIMP-based topology optimization on a fixed mesh. To keep thin geometrical features, like walls with a thickness below element size, penalization is switched off deliberately where the formation of such features is detected. Adopting a Lagrangian description, intermediate densities still present in the optimized design are subsequently eliminated in a second step by shrinking each element according to its density. By analogy with volumetric thermal contraction, this is accomplished by solving a fictitious thermo-elastic problem where the temperature has been replaced by a density expression. The outcome is a morphed mesh with a somewhat smoothed surface and a volume close to the specified material volume limit. This body-fitted representation of the design considerably simplifies the final conversion into a manufacturable CAD-type geometry. The two-step optimization procedure is applied to a cantilever, a torsion rod, and a disk reinforcement benchmark problem. Optimized designs are closed-walled and show very good agreement to those found for much finer meshes. Problem-specific stiffness improvements over truss-like designs between $$6\%$$ 6 % and almost $$30\%$$ 30 % were achieved and confirmed the findings previously reported by other authors.

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Shell topology optimization based on level set method

Kobayashi,

Nomura,

Zhou

et al. 2024

Struct Multidisc Optim

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Explicit layout optimization of complex rib-reinforced thin-walled structures via computational conformal mapping (CCM)

Cited by 13 publications

References 49 publications

Rib Reinforcement Bionic Topology Optimization under Multi-Scale Cyclic Excitation

Rib Reinforcement Bionic Topology Optimization under Multi-Scale Cyclic Excitation

Towards closed-walled designs in topology optimization using selective penalization

Shell topology optimization based on level set method

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