Modified element stacking method for multi-material topology optimization with anisotropic materials

Li, Daozhong; Kim, Il Yong

doi:10.1007/s00158-019-02372-x

Cited by 28 publications

(11 citation statements)

References 42 publications

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“…Combined with method of moving asymptotes (MMA) (Svanberg 1987) or globally convergent version of MMA (GCMMA) (Svanberg 2002(Svanberg , 2007 and sensitivity filtering technology, the optimization problem is able to be efficiently solved. For anisotropic material, SIMP can be transformed into solid anisotropic material with penalization (SAMP) by simply penalizing the elastic matrix (Sigmund and Torquato 1997;Li and Kim 2020). It should be noted that this paper assumes that overhanging features and support structures in SLA or SLM do not affect the mechanical properties of printed parts.…”

Section: Optimization Formulationmentioning

confidence: 99%

Multidisciplinary topology optimization incorporating process-structure-property-performance relationship of additive manufacturing

Yuan

Zhu

et al. 2021

Struct Multidisc Optim

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Multidisciplinary topology optimization (TO) for additive manufacturing (AM) exhibits unprecedented design and manufacturing freedom as an effective lightweight methodology. In order to fully utilize the AM advantages of materialized arrangement in spatial and voxel-by-voxel digitalized printing, multidisciplinary TO for AM requires a full understanding of the process-structure-property-performance (PSPP) relationship to establish the quantitative correlation of part property and multiple process factors, including laser-, process-, and material-related parameters. This study incorporates the PSPP relationships of laser sintered material with topology optimizer so as to provide a guideline for TO collaborative AM design. The proposed workflow involves mapping functions of PSPP relationships via a data-driven approach and then optimizes the multiple process parameters and structural topology by the gradientbased algorithm. Compared with conventional optimization approaches, three case-dependent optimizations demonstrate the effectiveness of the proposed approach yielding encouraging improvements of lightweight performance. The multidisciplinary TO can be generally applied to types of AM technologies, establishing a strong linkage of physical product and digital design.

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Section: Optimization Formulationmentioning

confidence: 99%

Multidisciplinary topology optimization incorporating process-structure-property-performance relationship of additive manufacturing

Yuan

Zhu

et al. 2021

Struct Multidisc Optim

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“…This is helpful for designers as they can get an idea of important load paths and key design areas from the initial phase. Most types of TO in continuum structures can be divided into four major categories: (1) Density-based methods, including the solid isotropic material with penalization (SIMP) interpolation scheme (Bendsøe and Sigmund, 1999; Zuo and Saitou, 2017; Li et al. , 2019); (2) boundary variation methods, including the level set and phase field methods (Wei and Wang, 2009; Van Dijk et al.…”

Section: Introductionmentioning

confidence: 99%

“…Thus, there has been an increased focus on developing multi-material topology optimization (MMTO) algorithms (Zuo and Saitou, 2017; Chu et al. , 2019; Li et al. , 2019).…”

Section: Introductionmentioning

confidence: 99%

Multi-material topology optimization considering natural frequency constraint

Shah

Pamwar

Sangha

et al. 2022

Self Cite

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PurposeThe purpose of this paper is to propose an effective and efficient numerical method that can consider natural frequency in multi-material topology optimization (MMTO) and which is scalable for complex three-dimensional (3D) problems.Design/methodology/approachThe optimization algorithm is developed by combining custom FORTRAN code for MMTO with the open-source software Mystran, which is used as a finite element analysis (FEA) solver. The proposed algorithm allows the designer to shift the fundamental frequency of the design beyond a defined frequency spectrum from the initial designing phase. The methodology is formulated in a smooth and differentiable manner, with the sensitivity expressions, required by gradient-based optimization solvers, presented.FindingsNatural frequency constraint has been successfully implemented into MMTO. The use of open-source software Mystran as an FEA solver in the algorithm provides ability to solve complex problems. Mystran offers powerful built-in functions for eigenvalue extraction using methods like Givens, modified Givens, inverse power and the Lanczos method, which provide the ability to solve complex models. The algorithm is successfully able to solve both two- and three-material MMTO jobs for two-dimensional and 3D geometries.Originality/valueNatural frequency constraint consideration into topology optimization is very challenging due to three common issues: localized eigenmodes, mode switching and high computational cost. The proposed algorithm addresses these inherent issues, implements natural frequency constraint to MMTO and solves for complex models, which is hardly possible using conventional methods.

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“…Peeters 17 used lamination parameters to define the material in the objective function. Finally, Li et al 31 used a homogenization approach for a set of material orientations to construct a multi-material TO.…”

Section: Introductionmentioning

confidence: 99%

Topological design using multivariate laminate stackings for tailored fiber placement

Schwingel

Middendorf

2022

Journal of Composite Materials

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In structural optimization of fiber-reinforced composites, unidirectional design material is normally applied due to its high anisotropy character. Using volume constraints to save weight often results in truss-like frameworks with defined tension and shear loaded areas, while the latter one is often neglected or improperly described with unidirectional material. Here, a method is proposed to extend the material design space to a continuously variable domain between UD and cross-ply laminates which is simultaneously optimized with topology. This allowed us to increase the design improvement and create smoother material distributions which is more beneficial for fiber placement technologies such as Tailored Fiber Placement. Parameter studies have been performed to investigate the effects of variable shear properties and different design spaces on the structural performance of the final designs, concluding with classical benchmarks to validate the proposed method.

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Modified element stacking method for multi-material topology optimization with anisotropic materials

Cited by 28 publications

References 42 publications

Multidisciplinary topology optimization incorporating process-structure-property-performance relationship of additive manufacturing

Multidisciplinary topology optimization incorporating process-structure-property-performance relationship of additive manufacturing

Multi-material topology optimization considering natural frequency constraint

Topological design using multivariate laminate stackings for tailored fiber placement

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