An efficient multiscale optimization method for conformal lattice materials

Wu, Tongsuo; Shu, Li

doi:10.1007/s00158-020-02739-5

Cited by 8 publications

(4 citation statements)

References 46 publications

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“…The optimization algorithm necessitates the derivation of both the objective function and the constraint with respect to the design variable. In this article, the multi-material optimization problem is decoupled into a single-material optimization subproblem, so the solution method for the derivative is also the same as that for the single-material optimization method [43].…”

Section: Optimization Subproblem Formulationsmentioning

confidence: 99%

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Multi-Material Optimization for Lattice Materials Based on Nash Equilibrium

Xiao,

Hu,

2024

Applied Sciences

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Lattice materials are regarded as a new family of promising materials with high specific strength and low density. However, in the optimization of lattice materials, it is difficult in general to determine the material distribution in lattice structures due to the complex optimization formulations and overlaps between different materials. Thus, the article proposes to use the Nash equilibrium to address the multi-material optimization problem. Moreover, a suppression formula is investigated to tackle the issue of material overlapping. The proposed method is validated using a cantilever beam example, showing superior optimization results compared to single-material methods, with a maximum improvement of 20.5%. Moreover, the feasibility and stability of the approach are evaluated through L-shaped beam examples, demonstrating its capability to effectively allocate materials based on their properties and associated stress conditions within the design. Additionally, an MBB test demonstrates superior stiffness in the proposed optimized specimen compared to the unoptimized one.

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Section: Optimization Subproblem Formulationsmentioning

confidence: 99%

“…To illustrate the advantages of our method, we compare the performance results of using the single-material optimization method [43] (SMOM) and multi-material optimization method (MMOM) in this article. The example of the cantilever beam is shown in Figure 8.…”

Section: Cantilever Beammentioning

confidence: 99%

Multi-Material Optimization for Lattice Materials Based on Nash Equilibrium

Xiao,

Hu,

2024

Applied Sciences

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“…The structural weight was reduced while maintaining the lift. Li [7] presented a multiscale optimization method to solve size distribution problems in conformal lattice materials, and the design resulted in mechanical experiments on specimens fabricated by 3D printing. López [8] compared the structural designs derived from deterministic topology optimization and reliability-based topology optimization and proved that including uncertain data in the topology optimization can help to reduce the weight of the component.…”

Section: Introductionmentioning

confidence: 99%

Aeroelastic Topology Optimization of Wing Structure Based on Moving Boundary Meshfree Method

et al. 2022

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The increasing structural flexibility of large aircraft leads to significant aeroelastic effects. More efficient topology optimization techniques are required for the design to further take advantage of aeroelasticity and obtain lightweight structures. This paper proposes a moving boundary meshfree topology optimization that combines the Galerkin method of weighted residuals and non-uniform rational B-splines (NURBS). The solution domain is described by the control points of NURBS and its property is calculated adaptively with an integration subtraction technique. The minimal compliance is searched for using the globally convergent method of moving asymptotes (GCMMA) by designing the locations of control points as subject to volume and flux constraints. The method is first applied to a typical two-dimensional design example with symmetric boundary conditions. The results show that the shape constraints can be conveniently applied, and smoother boundaries are obtained with fewer parameters. Then, a three-dimensional wing structure with asymmetric boundary conditions is optimized. A three-dimensional flight load that combines the high-order-panel and meshfree methods is employed to calculate the elastic loads and update asymmetric external loads during the optimization process. The designed wing satisfies engineering requirements and the presented method can solve the practical topology optimization problems of three-dimensional structures.

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“…This has led to a wide range of applications ( [16,17]) including energy absorption ( [18]), heat exchangers ( [19]), and biomedical applications ( [20]). Current M-TO methods include clustering ( [21,15,22]), kriging ( [23]), multi-material ( [24]), conformal lattices ( [25]), etc. The advent of additive manufacturing has further spurned research in M-TO ([16]).…”

Section: Introductionmentioning

confidence: 99%

GM-TOuNN: Graded Multiscale Topology Optimization using Neural Networks

Chandrasekhar¹,

Sridhara²,

Suresh³

2022

Preprint

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Multiscale topology optimization (M-TO) entails generating an optimal global topology, and an optimal set of microstructures at a smaller scale, for a physics-constrained problem. With the advent of additive manufacturing, M-TO has gained significant prominence. However, generating optimal microstructures at various locations can be computationally very expensive. As an alternate, graded multiscale topology optimization (GM-TO) has been proposed where one or more pre-selected and graded (parameterized) microstructural topologies are used to fill the domain optimally. This leads to a significant reduction in computation while retaining many of the benefits of M-TO. A successful GM-TO framework must: (1) be capable of efficiently handling numerous pre-selected microstructures, (2) be able to continuously switch between these microstructures during optimization, (3) ensure that the partition of unity is satisfied, and (4) discourage microstructure mixing at termination. In this paper, we propose to meet these requirements by exploiting the unique classification capacity of neural networks. Specifically, we propose a graded multiscale topology optimization using neural-network (GM-TOuNN) framework with the following features: (1) the number of design variables is only weakly dependent on the number of pre-selected microstructures, (2) it guarantees partition of unity while discouraging microstructure mixing, and (3) it supports automatic differentiation, thereby eliminating manual sensitivity analysis. The proposed framework is illustrated through several examples.

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An efficient multiscale optimization method for conformal lattice materials

Cited by 8 publications

References 46 publications

Multi-Material Optimization for Lattice Materials Based on Nash Equilibrium

Multi-Material Optimization for Lattice Materials Based on Nash Equilibrium

Aeroelastic Topology Optimization of Wing Structure Based on Moving Boundary Meshfree Method

GM-TOuNN: Graded Multiscale Topology Optimization using Neural Networks

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