Topology optimization of conformal structures on manifolds using extended level set methods (X-LSM) and conformal geometry theory

Ye, Qian; Guo, Yang; Chen, Shikui; Lei, Na; Gu, Xianfeng

doi:10.1016/j.cma.2018.08.045

Cited by 44 publications

(18 citation statements)

References 60 publications

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“…Therefore, other deformations such as out of plane bending, the membrane, and shear deformations are not considered, but will be in the future. A possible direction to solve these problems is to develop similar objective functions as [29] did for other boundary conditions. A physical platform is also planned to develop for studying the specification of load and verifying the fabricated results.…”

Section: Resultsmentioning

confidence: 99%

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Customization and topology optimization of compression casts/braces on two-manifold surfaces

Zhang

Kwok

2019

Computer-Aided Design

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This paper applies the topology optimization (TO) technique to the design of custom compression casts/braces on two-manifold mesh surfaces. Conventional braces or casts, usually made of plaster or fiberglass, have the drawbacks of being heavy and unventilated to wear. To reduce the weight and improve the performance of a custom brace, TO methods are adopted to optimize the geometry of the brace in the three-dimensional (3D) space, but they are computationally expensive. Based on our observation that the brace has a much smaller thickness compared to other dimensions and the applied loads are normal forces, this paper presents a novel TO method based on thin plate elements on the two-dimensional manifold (2-manifold) surfaces instead of 3D solid elements. Our working pipeline starts from a 3D scan of a human body represented by a 2-manifold mesh surface, which is the base design domain for the custom brace. Similar to the concept of isoparametric representation, the 3D design domain is mapped onto a two-dimensional (2D) parametric domain. An Finite Element Analysis (FEA) with bending moments is performed on the parameterized 2D design domain, and the Solid Isotropic Material with Penalization (SIMP) method is applied to optimize the pattern in the parametric domain. After the optimized cast/brace is obtained on the 2-manifold mesh surface, a solid model is generated by our design interface and then sent to a 3D printer for fabrication. Compared with the optimization method with solid elements, our method is more efficient and controllable due to the high efficiency of solving FEA in the 2D domain.

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Section: Resultsmentioning

confidence: 99%

“…A recent work [29] proposed a TO framework for 2-manifold surfaces. In their work, they theoretically proved the validity of the idea of solving TO problem on 2-manifold surface.…”

Section: Structural Analysis and Optimizationmentioning

confidence: 99%

Customization and topology optimization of compression casts/braces on two-manifold surfaces

Zhang

Kwok

2019

Computer-Aided Design

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“…Implementing topology optimization on 2-manifolds can be helpful to enhance the freedom of structural design, where a 2-manifold is a topological space with its arbitrary interior point having a neighborhood homeomorphic to a sub-region of R 2 and it can be used to describe a structural surface or a material interface. Related researches have been implemented for the structural design on 2-manifolds based on the conformal geometry theory [40,41], layouts on surfaces for shell structures [51][52][53][54][55], and material interfaces for stiffness and multi-material structures [42][43][44][45][46][47][48][49][50], fluid-structure interaction [56][57][58], energy absorption [59], cohesion [60] and actuation [61].…”

Section: Introductionmentioning

confidence: 99%

Topology optimization on two-dimensional manifolds

Deng

Liu

Korvink

2020

Computer Methods in Applied Mechanics and Engineering

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This paper implements topology optimization on two-dimensional manifolds. In this paper, the material interpolation is implemented on a material parameter in the partial differential equation used to describe a physical field, when this physical field is defined on a two-dimensional manifold; the material density is used to formulate a mixed boundary condition of the physical field and implement the penalization between two different types of boundary conditions, when this physical field is defined on a threedimensional domain with its boundary conditions defined on the two-dimensional manifold corresponding a surface or an interface of this three-dimensional domain. Based on the homeomorphic property of two-dimensional manifolds, typical two-dimensional manifolds, e.g., sphere, torus, Möbius strip and Klein bottle, are included in the numerical tests, which are provided for the problems on fluidic mechanics, heat transfer and electromagnetics.

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“…Such convergence issues were examined by [15][16][17][18], but the examples provided only extend these successful techniques to 2-D problems, without introducing complexities such as composite materials and shell elements. The challenge of performing topology optimization using shell elements was also tackled [19,20] as a separate issue. For example, [19] uses a commercial software, Abaqus, to perform sizing optimization of a bumper shell finite element model.…”

mentioning

confidence: 99%

“…Nevertheless, [19] mentions that this is the first work that shows results for non-linear sizing of shell thicknesses using adjoint sensitivities and including the simultaneous modeling of three non-linearities: large deformations, plasticity, and contact. A different study [20] uses the level-set method, which allows for formation of cutouts, to optimize shell structures, but the examples provided do not include geometrical or material non-linearities. Finally, topology optimization problems including composite materials were analyzed [21,22] using numerical homogenization.…”

mentioning

confidence: 99%

Topology and Shape Optimization of Ultrathin Composite Self-Deployable Shell Structures with Cutouts

Ferraro

Pellegrino

2021

AIAA Journal

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The paper presents topology optimization studies of selfs-deployable joints in thin-walled tubular structures. The joints are made entirely of ultra-thin, fiber reinforced composite materials. The objective of this research is to strategically position cutouts on the joints so that they can fold without failing, while maximizing the deployed bending stiffness. The optimal shape and position of cutouts are the results of concurrent topology optimization of these composite, thin-shell joints with geometrical non-linearities, due to their folding and self-deployable nature. Numerical methods to accurately detect failure are implemented and results from a novel level-set method for topology optimization are compared to results from classical parametric optimization and preliminary designs based on physical intuition.

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Topology optimization of conformal structures on manifolds using extended level set methods (X-LSM) and conformal geometry theory

Cited by 44 publications

References 60 publications

Customization and topology optimization of compression casts/braces on two-manifold surfaces

Customization and topology optimization of compression casts/braces on two-manifold surfaces

Topology optimization on two-dimensional manifolds

Topology and Shape Optimization of Ultrathin Composite Self-Deployable Shell Structures with Cutouts

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