Level set-based topology optimization for compliance and stress minimization of shell structures using trimmed quadrilateral shell meshes

Ho-Nguyen-Tan, Thuan; Kim, Hyun‐Gyu

doi:10.1016/j.compstruc.2021.106695

Cited by 16 publications

(6 citation statements)

References 40 publications

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“…In [74], the optimization of elastoplastic and incompressible media was made possible by employing a mixed finite-element discretization scheme. Recently, the same optimization formulations were solved using the BESO method for linearly elastic materials in [82,83] and the LSM for shell structures in [84]. Notably, [71] by Da and Chen represents the first work that systematically analyzes the effects of stress-based designs on fracture resistance properties (see Fig.…”

Section: Stress-based Approachesmentioning

confidence: 99%

Topology Optimization to Fracture Resistance: A Review and Recent Developments

Yvonnet,

2024

Arch Computat Methods Eng

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Topology Optimization (TO) methods for fracture resistance offer new possibilities for designing stronger structures or materials with lower masses than conventional designs. This article presents an overview of topology optimization techniques for fracture resistance, from pioneering works to the most recent developments at the time of writing. We first review stress-based methods, which were the forerunners of crack resistance methods, producing optimal designs that prevent any damage or crack initiation. Other works followed, taking into account the presence of defects or cracks in structures, but using classical approaches aimed at minimizing compliance in an elastic framework. TO methods for fatigue damage are also an important branch of these approaches and are reviewed. We then present more recent methodologies, including non-linear effects in structural design, such as plasticity and damage. Finally, we describe the latest methods of TO design for fracture resistance, including an explicit description of crack propagation during loading, from initiation to failure of structures and materials. In particular, the design of two-phase materials that are more resistant to cracking and that can be manufactured by 3D printing is discussed. The article concludes with some challenges and promising avenues for the coming years in this field.

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Section: Stress-based Approachesmentioning

confidence: 99%

Topology Optimization to Fracture Resistance: A Review and Recent Developments

Yvonnet,

2024

Arch Computat Methods Eng

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“…However, due to the use of the element density in Eq. ( 24), optimal configurations of CCF-reinforced composite structures exhibit rough boundaries [42,47], which cannot provide accurate structural boundaries. As described in section 2, in the two-material topology optimization process of CCF-reinforced composite structures, the structural boundaries of the resin material and fiber reinforcement are represented by the zero-contour of level set functions.…”

Section: Generation Of Stl Modelsmentioning

confidence: 99%

“…As described in section 2, in the two-material topology optimization process of CCF-reinforced composite structures, the structural boundaries of the resin material and fiber reinforcement are represented by the zero-contour of level set functions. To accurately represent the structural boundary of an optimal design, the cutting method, presented in two of the authors' works [42,[46][47][48][49][50], is used. In this method, the zero-contour of level set functions k,i .…”

Section: Generation Of Stl Modelsmentioning

confidence: 99%

“…During the optimization process, the reaction-diffusion equation is solved by utilizing topological sensitivity fields, which are employed to update the level set functions. At the zero-surface (in 3D) or zero-contour (in 2D) of level set functions, one of the authors used the cutting method [42,43] to generate optimal designs with clear structural boundaries. Using the triangulation scheme, these configurations are directly translated into STL models, which are compatible with the printing process.…”

Section: Introductionmentioning

confidence: 99%

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Coupling design and fabrication of continuous carbon fiber-reinforced composite structures using two-material topology optimization and additive manufacturing

Ho,

Nguyen,

et al. 2024

Int J Adv Manuf Technol

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This study presents an integration of the level set-based two-material topology optimization method and the additive manufacturing technique for the design and fabrication of continuous carbon fiber (CCF)-reinforced composite structures. Firstly, optimal configurations of the resin material and fiber reinforcement are obtained to maximize the structural stiffness under desired volume constraints using the two-material topological optimization. After that, the level set-based cutting mesh method and triangulation scheme are employed to interpret these 1 ManuscriptClick here to access/download;Manuscript;IJAMT.tex Click here to view linked References topological designs into stereolithography (STL) models with clear structural boundaries for the manufacturing. A customized pre-processing strategy is used to accurately determine the fiber placement regions from the optimal designs. Topological results are then fabricated using the CCF-based 3D printing method with prepreg carbon fibers. Subsequently, the performance of printed CCF-reinforced composite structures is investigated, using different resin materials: Esun polylactic acid (EPLA) and polyamide 12 with 10% carbon fiber (PA12 10CF).Experimental results indicate a significant increase in stiffness and strength of composite structures with fiber reinforcements for all resin materials, with an increase of 315% for EPLA and 234% for PA12 10CF. Additionally, the CCFreinforced composite structures made of PA12 10CF exhibit superior stiffness compared to those made of EPLA with a double increment. The microstructural characteristics of damaged regions are examined using scanning electron microscope (SEM) images, which provide valuable insights into the behavior of resin and fiber materials.

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“…However, the original SIMP method can suffer from drawbacks such as instability problems, checkerboard patterns, mesh dependency, and grayscales. To prevent those drawbacks, the level set method, in particular, the one via solving the reaction diffusion equation (RDE), has been proposed by Yamada et al (2010) and has since emerged as an attracting alternative for various topology optimization problems (Choi et al 2011;Otomori et al 2012;Yamada et al 2013;Fujii et al 2013;Lu et al 2013;Yaji et al 2014;Isakari et al 2014;Jing et al 2015;Yaji et al 2015;Otomori et al 2015;Isakari et al 2017;Emmendoerfer et al 2019;Nguyen et al 2020;Zhang et al 2020;Kim et al 2020;Gao et al 2021;Kubo et al 2021;Li et al 2021;Zhuang et al 2021;Jung et al 2021;Ho-Nguyen-Tan and Kim 2022). The enhanced smoothness and stability of the RDE-based level set method can be attributed to the introduction of a fictitious interfacial energy.…”

Section: Introductionmentioning

confidence: 99%

A time-saving FEM-based approach for structural topology optimization with exact boundary representation

Cui

Takahashi

Matsumoto

2022

Mechanical Engineering Journal

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A time-saving finite element method (FEM) based approach for structural topology optimization with exact boundary representation is proposed in this work. The optimization process consists of two loops. The first loop adopts a fixed and fairly coarse mesh. Afterwards, the second loop reconstructs the material domain and hence the boundary representation becomes exact. A novelty of this work is that our two-loop approach is realized with the domain reconstruction (not just remeshing). The convergence of the second loop is only made possible by imposing the volume constraint in an exact fashion. The proposed approach can save a substantial amount of computational time while allowing the exact representation of boundary (no grayscale throughout the second loop). For the two-loop approach, its computational time can be reduced to merely 13.6% of that for the single loop approach. The optimized structure is also found independent of mesh size. In addition, the two-loop approach resolves the issue of a deteriorated connectivity of the reconstructed domain Ω once the constrained volume is set extremely small.

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Level set-based topology optimization for compliance and stress minimization of shell structures using trimmed quadrilateral shell meshes

Cited by 16 publications

References 40 publications

Topology Optimization to Fracture Resistance: A Review and Recent Developments

Topology Optimization to Fracture Resistance: A Review and Recent Developments

Coupling design and fabrication of continuous carbon fiber-reinforced composite structures using two-material topology optimization and additive manufacturing

A time-saving FEM-based approach for structural topology optimization with exact boundary representation

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