Multi-scale topology optimization with shell and interface layers for additive manufacturing

Xu, Shuzhi; Liu, Ji‐Kai; Huang, Jiaqi; Zou, Bin; Ma, Yongsheng

doi:10.1016/j.addma.2020.101698

Cited by 19 publications

(11 citation statements)

References 62 publications

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“…where 𝜌 is a parameter related to the degree of aggregation of the maximum, and when 𝜌 → ∞, equality holds between Equations ( 11) and (23) and between Equations ( 12) and ( 24), respectively. The KS function has the property that convergence of the maximum value becomes slower for smaller values of 𝜌 and more unstable for larger values.…”

Section: Ks Functionmentioning

confidence: 99%

“…Gao et al presented a MATLAB code for concurrent multiscale optimization of 2D and 3D structures using a modified SIMP approach 22 . Xu et al presented a multiscale topology optimization method for lattice structure design with both shell and lattice‐lattice interface layers to enhance the structural aesthetical, mechanical, and manufacturability properties 23 . Especially on strength problem relating to the present research, Collet et al introduced stress responses within a topology optimization framework applied to the design of periodic microstructures 24 .…”

Section: Introductionmentioning

confidence: 99%

“…22 Xu et al presented a multiscale topology optimization method for lattice structure design with both shell and lattice-lattice interface layers to enhance the structural aesthetical, mechanical, and manufacturability properties. 23 Especially on strength problem relating to the present research, Collet et al introduced stress responses within a topology optimization framework applied to the design of periodic microstructures. 24 Coelho et al proposed a method to minimize the maximum von Mises stress in planar unit cells calculated by the homogenization method through shape and topology optimization.…”

Section: Introductionmentioning

confidence: 99%

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Shape optimization method for strength design problem of microstructures in a multiscale structure

TORISAKI

Shimoda

Ali

2022

Numerical Meth Engineering

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In this paper, we propose a solution to a shape optimization problem for the strength design of periodic microstructures in multiscale structures. Two maximum stress minimization problems are addressed: minimization of maximum microstructural stress and minimization of maximum macrostructural stress.The homogenization method is used to bridge the macrostructure and the microstructure and to calculate local microstructural stress. By replacing the maximum stress value with a Kreisselmeier-Steinhauser function, the difficulty of nondifferentiability of maximum stress is avoided. Each strength design problem is formulated as a distributed parameter optimization problem subject to an area constraint including the whole microstructure. The shape gradient functions for both problems are derived using Lagrange's undetermined multiplier method, the material derivative method, and the adjoint variable method. The H 1 gradient method is used to determine the unit cell shapes of the microstructure, while reducing the objective function and maintaining smooth design boundaries. In the numerical examples, the optimal shapes obtained for minimization of the maximum local stress of the microstructure and the macrostructure are compared and discussed. The results confirm the effectiveness of the microstructure shape optimization method for the two strength design problems of multiscale structures.

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Section: Ks Functionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Shape optimization method for strength design problem of microstructures in a multiscale structure

TORISAKI

Shimoda

Ali

2022

Numerical Meth Engineering

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“…26 Furthermore, Xu et al proposed a concurrent optimization method to place bonding materials between different microstructures to improve the manufacturability of multiscale structures. 27 Zhou et al proposed a novel multi-scale topology optimization method for the free-form surfaces consisting of micro-structured infills. 28 Zhou et al also proposed a topology optimization design of graded infills for 3D multi-scale structures.…”

Section: Introductionmentioning

confidence: 99%

Concurrent multiscale and multi‐material optimization method for natural vibration design of porous structures

Shimoda,

Fujita,

Al Ali

et al. 2024

Numerical Meth Engineering

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This paper proposes a concurrent multiscale optimization method of macrostructure topology and microstructure shapes for porous structures, aimed at maximizing a specified natural frequency. The multi‐material distribution of the macrostructure and the shape of the microstructures are optimized by topology and shape optimization, respectively. The homogenized properties of the porous materials are calculated using the homogenization method, and the homogenized elastic tensor and density are applied to the macrostructure. The optimum distribution of the porous material in the macrostructure is determined by a multi‐material topology optimization using the generalized solid isotropic material with penalization (GSIMP) method, which is a method to obtain multi‐material topology by implementing the successive binarization. The KS (Kreisselmeier–Steinhauser) function is introduced to solve the repeated natural frequencies issue that lies in the maximization of a specified natural frequency. An area‐constrained multiscale optimization problem is formulated as a distributed‐parameter optimization problem, and the sensitivity functions are derived using the Lagrange multiplier method and the adjoint variable method. Based on the obtained sensitivity functions, the design variables are updated using the H1 gradient method (i.e., a nonparametric shape/topology optimization method). The effectiveness of the proposed method for maximizing a specified natural frequency is confirmed through 2D and 3D numerical examples, in which the influences of sub‐regions of the macrostructure and anisotropic material of the microstructures are also investigated and the results are discussed.

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“…Most existing works alleviate this issue by an additional postprocessing step (smoothing) after optimization. [22][23][24][25][26][27][28][29] However, such post-processing can change the material properties since the optimized structure has been altered. In contrast, we parameterized the smoothing in the optimization loop.…”

Section: Introductionmentioning

confidence: 99%

Implicitly Represented Architected Materials for Multi‐Scale Design and High‐Resolution Additive Manufacturing

Rastegarzadeh

Wang

Huang

2023

Adv Materials Technologies

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Bio‐inspired structured materials have achieved unprecedented progress in realizing exceptional, effective properties. However, a rational design paradigm that enables both tailoring complex 3D architectures and manufacturing the engineered hierarchical structured materials is still missing. To bridge this gap, this study presents a holistic design‐through‐printing framework with implicitly represents cellular materials for high‐resolution structured materials design and manufacturing. Attributed to the parameterized implicit function‐based representation (FRep), the material's microstructures can be effectively controlled to tune the material properties (e.g., isotropic, orthotropic, and anisotropic) while enabling functional gradation in the multi‐scale hierarchical design. Given prescribed material properties in different applications, the proposed framework finds the optimal layout of microstructures with an adaptive cluster‐based topology optimization algorithm. The geometry frustration problem brought by the mixture of distinct microstructures is simultaneously addressed with a spatial gradation scheme in the optimization loop. Lastly, the FRep‐based architected material enables efficient geometry processing (e.g., slicing) for modern AM processes, thus facilitating the manufacturing of high‐resolution delicate designed materials. The proposed framework is scalable and adaptable to accomplish a broad spectrum of design demands in various applications.

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Multi-scale topology optimization with shell and interface layers for additive manufacturing

Cited by 19 publications

References 62 publications

Shape optimization method for strength design problem of microstructures in a multiscale structure

Shape optimization method for strength design problem of microstructures in a multiscale structure

Concurrent multiscale and multi‐material optimization method for natural vibration design of porous structures

Implicitly Represented Architected Materials for Multi‐Scale Design and High‐Resolution Additive Manufacturing

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