Structural topology optimization with smoothly varying fiber orientations

Schmidt, Martin-Pierre; Couret, Laura; Gout, Christian; Pedersen, Claus

doi:10.1007/s00158-020-02657-6

Cited by 68 publications

(14 citation statements)

References 26 publications

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“…Using these variables means once again that the design space is redundant, as any set of two values having the same ratio will correspond to the same orientation. Using these variables also helps reducing the observed dependency on initial orientations, as in Schmidt et al (2020).…”

Section: Avoiding Local Minimamentioning

confidence: 99%

A well connected, locally-oriented and efficient multi-scale topology optimization (EMTO) strategy

Duriez

Morlier

Charlotte

et al. 2021

Struct Multidisc Optim

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Multi-scale topology optimization (a.k.a. micro-structural topology optimization, MTO) consists in optimizing macro-scale and micro-scale topology simultaneously. MTO could improve structural performance of products significantly. However, a few issues related to connectivity between micro-structures and high computational cost have to be addressed, without resulting in loss of performance. In this paper, a new efficient multi-scale topology optimization (EMTO) framework has been developed for this purpose. Connectivity is addressed through adaptive transmission zones which limit loss of performance. A pre-computed database of micro-structures is used to speed up the computing. Design variables have also been chosen carefully and include the orientation of the micro-structures to enhance performance. EMTO has been successfully tested on two-dimensional compliance optimization problems. The results show significant improvements compared to mono-scale methods (compliance value lower by up to 20% on a simplistic case or 4% on a more realistic case), and also demonstrate the versatility of EMTO.

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Section: Avoiding Local Minimamentioning

confidence: 99%

A well connected, locally-oriented and efficient multi-scale topology optimization (EMTO) strategy

Duriez

Morlier

Charlotte

et al. 2021

Struct Multidisc Optim

View full text Add to dashboard Cite

show abstract

“…Most researches focus on the simultaneous optimization of 2D components for minimizing the compliance of structure (Hoglund and Smith, 2016;Tong et al, 2017;Boddeti et al, 2018;Kim et al, 2020Kim et al, , 2021Ding and Xu, 2021;Li et al, 2021;Chu et al, 2021). There are also some topology optimization methods for 3D FRC structures (Jiang et al, 2019;Schmidt et al, 2020;Jantos et al, 2020;Fedulov et al, 2021;Jung et al, 2022).…”

Section: Introductionmentioning

confidence: 99%

Strength-constrained simultaneous optimization of topology and fiber orientation of fiber-reinforced composite structures for additive manufacturing

Yang

Wang

2022

Advances in Structural Engineering

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Additive manufacturing (AM) enables flexible fabrication of lightweight fiber-reinforced composite (FRC) structures with topological optimized geometries and fiber orientations. However, premature failure may occur if the manufactured FRC structure is not properly designed against stress distribution. The present study develops a strength-constrained optimization algorithm by considering the 3D printed filament embedded with fiber to be orthotropic material. The Tsai–Wu criterion is incorporated in the topological and fiber orientation optimization process. The element density and the fiber angle are formulated as design variables to simultaneously optimize the distribution of matrix and fiber. Meanwhile, both design variables are filtered to prevent checkerboard patterns of matrix elements and to ensure the continuity of fiber angle. A P-norm approach combined with an adaptive normalization scheme is employed to achieve the global strength constraint and reduce the difference between the P-norm value and the actual maximum Tsai–Wu value. Sensitivity analysis of objective function and strength-constraint conditions with respect to design variables is carried out and it serves as a basis for the method of moving asymptotes. Topological optimization of three typical numerical examples under different loading conditions are conducted and the effectiveness of the proposed method is validated. 73.7% decrease in maximum Tsai–Wu value of the optimized L-shaped beam as well as a slight increase (∼0.2%) in compliance are obtained in comparison with the compliance-based design result.

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“…is determined for each location in space (e.g., on a voxel grid). Similarly, almost all existing methods for optimizing carbon fiber composites focus on the spatially-varying fiber direction field, then use variants of greedy extraction or ODE solvers to extract the fiber paths themselves [Schmidt et al 2020;Wang et al 2021].…”

Section: Introductionmentioning

confidence: 99%

More Stiffness with Less Fiber: End-to-End Fiber Path Optimization for 3D-Printed Composites

Sun¹,

Roeder²,

Xue³

et al. 2022

Preprint

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In 3D printing, stiff fibers (e.g., carbon fiber) can reinforce thermoplastic polymers with limited stiffness. However, existing commercial digital manufacturing software only provides a few simple fiber layout algorithms, which solely use the geometry of the shape. In this work, we build an automated fiber path planning algorithm that maximizes the stiffness of a 3D print given specified external loads. We formalize this as an optimization problem: an objective function is designed to measure the stiffness of the object while regularizing certain properties of fiber paths (e.g., smoothness). To initialize each fiber path, we use finite element analysis to calculate the stress field on the object and greedily "walk" in the direction of the stress field. We then apply a gradient-based optimization algorithm that uses the adjoint method to calculate the gradient of stiffness with respect to fiber layout. We compare our approach, in both simulation and real-world experiments, to three baselines: (1) concentric fiber rings generated by Eiger, a leading digital manufacturing software package developed by Markforged, ( 2) greedy extraction on the simulated stress field (i.e., our method without optimization), and (3) the greedy algorithm on a fiber orientation field calculated by smoothing the simulated stress fields. The results show that objects with fiber paths generated by our algorithm achieve greater stiffness while using less fiber than the baselines-our algorithm improves the Pareto frontier of object stiffness as a function of fiber usage. Ablation studies show that the smoothing regularizer is needed for feasible fiber paths and stability of optimization, and multi-resolution optimization help reduce the running time compared to single-resolution optimization.CCS Concepts: • Applied computing → Computer-aided manufacturing.

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Structural topology optimization with smoothly varying fiber orientations

Cited by 68 publications

References 26 publications

A well connected, locally-oriented and efficient multi-scale topology optimization (EMTO) strategy

A well connected, locally-oriented and efficient multi-scale topology optimization (EMTO) strategy

Strength-constrained simultaneous optimization of topology and fiber orientation of fiber-reinforced composite structures for additive manufacturing

More Stiffness with Less Fiber: End-to-End Fiber Path Optimization for 3D-Printed Composites

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