Pith. sign in

REVIEW 3 major objections 3 minor 30 references

Topology Optimization of Leg Structures for Construction Robots Based on Variable Density Method

T0 review · 3 major / 3 minor · reviewed 2026-08-06 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read Topology optimization trims a construction robot leg by 7.92 percent of its mass while keeping it within strength and vibration limits.

desk verdict A competent but standard SIMP case study on a construction-robot leg; the static results are plausible, but the resonance claim is untestable because the operating frequency is never stated. read the letter →

arxiv 2507.16335 v1 pith:RZKD7XRG submitted 2025-07-22 cs.RO

Xiao Liu , Xianlong Yang , Weijun Wang , Wei Feng This is my paper · ORCID
classification cs.RO
keywords topologyoptimizationSIMPvariabledensitymethodlightweightdesignconstructionrobotlegstructurefiniteelementanalysismodal
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper aims to show that the heaviest segment of a construction robot's leg, the femur, can be made substantially lighter without sacrificing structural safety. Using the SIMP variable-density topology optimization method, the femur's mass is reduced by 19.45% and the whole leg's mass by 7.92% after the optimized geometry is reconstructed for manufacturability. Re-running finite element static and modal analyses on the rebuilt leg gives a maximum equivalent stress of 29.38 MPa, below the 138 MPa allowable stress, and a first natural frequency of 62.441 Hz, above the operating frequency. The central claim is that this optimize-reconstruct-verify workflow is a feasible path to lightweight legs for multi-legged construction robots.

What carries the argument

The load-bearing machinery is the SIMP (Solid Isotropic Material with Penalization) variable-density method, a density-based topology optimization in which each finite element's density is a design variable and a penalization factor pushes densities toward 0 or 1. The optimization minimizes structural compliance subject to a volume constraint, effectively redistributing material in the femur's side plates while excluding contact regions. The second mechanism is the reconstruction step: the raw optimization output, made of irregular mesh-like cells, is smoothed and symmetrized into a manufacturable model, and that rebuilt geometry is re-verified with the same static and modal analysis setup.

What would settle it

Build the reconstructed femur from 6061 aluminum alloy, apply the same 2400 N / 360 N·m support-phase loading in a physical test rig with the foot clamped, and measure the first resonance frequency; if the maximum measured stress exceeds 138 MPa or the first natural frequency falls at or below the drive frequency, the central claim would be refuted.

Watch

Extended reading notes

Core claim

The central result is that a SIMP-based topology optimization followed by manual secondary reconstruction can cut substantial mass from a construction robot's femur while keeping the leg within its strength and vibration limits. In the optimized supporting leg, maximum equivalent stress rises from 27.52 MPa to 29.38 MPa and maximum displacement from 0.67 mm to 0.78 mm, but both remain below allowable limits; the first natural frequency drops from 72.204 Hz to 62.441 Hz yet stays above the operating frequency, so resonance is considered unlikely. The mass reductions of 19.45% for the femur and 7.92% for the whole leg are presented as validation that the proposed strategy meets the lightweight design goal.

Load-bearing premise

The claim depends on the finite element model of the supporting leg, with the foot end fixed and a 2400 N vertical load and 360 N·m torque applied at the root joint, accurately representing real worst-case walking loads, and on the hand-smoothed reconstructed femur behaving in practice exactly as it does in simulation, with no physical prototype or test to confirm either.

Editorial extensions

If this is right

  • Achieving a 19.45% femur mass reduction and 7.92% total leg mass reduction means the same leg can carry the same rated payload with less self-weight.
  • The optimized leg's first natural frequency of 62.441 Hz remaining above the operating frequency implies that the lightweighting does not introduce a resonance risk during tripod-gait walking.
  • Because the maximum equivalent stress stays below the 138 MPa allowable stress, the mass-reduced femur is still rated for the 2400 N / 360 N·m support-phase loading.
  • The workflow can be applied to other heavy load-bearing members of mobile construction robots where design freedom exists, not only the femur.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The 19.45% mass reduction is computed on a hand-reconstructed geometry whose smoothed features may differ from the true optimum, so the real saving could be larger or smaller depending on how faithfully the reconstruction preserves the optimization's load paths.
  • Because no physical prototype was built or tested, the strongest untested link is whether the boundary condition of a fixed foot and a 2400 N / 360 N·m root load captures the impact and fatigue loads of walking on uneven construction terrain.
  • A direct extension would be to compare the SIMP result against other topology optimization methods on the same leg model, using stress, displacement, first natural frequency, and mass as common metrics.
  • The same workflow could be tested on the tibia segments and hip joints, where similar mass reductions might compound into a meaningfully lighter chassis.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 3 minor

Summary. The manuscript applies the SIMP (Solid Isotropic Material with Penalization) variable-density topology optimization method to the femur segment of a hexapod construction robot leg. The authors first perform static and modal finite element analyses (FEA) in ANSYS on the original leg, then optimize the femur's side plates for minimum compliance subject to a 50% volume constraint, manually reconstruct the resulting geometry, and re-analyze the optimized leg. They report a 19.45% reduction in femur mass and a 7.92% reduction in overall leg mass, with a maximum equivalent stress of 29.38 MPa (below an allowable stress of 138 MPa) and a first natural frequency of 62.441 Hz, which they claim remains above the operating frequency. The central conclusion is that the optimized leg meets strength and dynamic requirements while being significantly lighter.

Significance. If the claims are established, the paper offers a complete and practical workflow for lightweighting a load-bearing robot leg, combining topology optimization, geometry reconstruction, and FE verification. Strengths include a clearly stated load case (2400 N and 360 N·m, foot fixed), explicit material properties, and a quantitative reporting of mass and performance changes. However, the novelty is incremental: topology optimization of robot legs is already represented in the literature (e.g., Ref. [25]), and the paper's verification has gaps that prevent full confidence in the headline claims. Specifically, the dynamic acceptance criterion relies on an unquantified operating frequency, and the stress values are reported without mesh convergence evidence. These issues are fixable within the manuscript's scope, and their resolution would make the work a useful engineering case study.

major comments (3)
  1. [Sections 2.3 and 4.2] The conclusion that resonance is unlikely is stated relative to 'the operational frequency of the leg,' but no numerical value for this operating frequency is given anywhere in the manuscript. The first natural frequency drops from 72.204 Hz to 62.441 Hz after optimization (Tables 1 and 4), so the margin against the unspecified operating frequency is unknown. If the operating frequency or a harmonic is at or above 62.441 Hz, the optimized leg would fail the paper's own dynamic criterion. Please state the operating frequency or excitation bandwidth for the tripod gait and explicitly quantify the frequency margin before and after optimization.
  2. [Sections 2.2 and 4.1] The maximum equivalent stress values (27.52 MPa before and 29.38 MPa after optimization) are reported at joint regions that the authors describe as stress singularities, and no mesh convergence study is provided. Peak stresses at geometric singularities are mesh-dependent in finite element analysis, so the value 29.38 MPa is not established as a converged or physically meaningful quantity. The strength claim (stress remains below the 138 MPa allowable) is therefore not yet fully validated. Please include a mesh convergence study with at least two refinement levels and either report stresses at points away from the singularities or apply an appropriate stress-averaging/linearization procedure.
  3. [Section 3.4] The reconstructed femur geometry is obtained by manually 'smoothing and structural modifications' of the topology optimization result, but the manuscript does not quantify how the final geometry relates to the optimized density field or how much of the optimized load path is preserved. Because the reported mass reduction (19.45%) and the subsequent FEA results are based on this reconstructed model rather than on the raw optimization output, the reader cannot assess whether the reconstruction step, rather than the topology optimization itself, drives the reported outcomes. Please provide a quantitative comparison between the optimized density field and the reconstructed geometry, for example by reporting the retained volume fraction relative to the 50% target or the compliance of the reconstructed femur under the same loads.
minor comments (3)
  1. [Section 1 and Figure 1] The text states that a hexapod mobile chassis is 'shown in Figure 1,' but Figure 1 is captioned as the 'Flowchart of Leg Finite Element Analysis'; the actual figure of the hexapod robot appears to be missing, which makes the introductory motivation hard to follow.
  2. [Section 2.2 and 'Replication of Results'] Material properties are inconsistent: Section 2.2 gives density 2.77 g/cm³, Poisson's ratio 0.330, and elastic modulus 69.6 GPa, whereas the 'Replication of Results' section lists density 2.70 g/cm³, Poisson's ratio 0.33, and elastic modulus 69 GPa. Please harmonize these values.
  3. [Section 2.1] The mesh generation step is described only qualitatively; the element type and mesh size used in the ANSYS analyses are never stated. Specifying these parameters would improve reproducibility, especially because the authors claim in the 'Replication of Results' section that all mesh parameters are described in sufficient detail.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity found: SIMP optimization under a stated 50% volume constraint yields measured mass reductions, and structural performance is checked by independent post-optimization FEA; the unstated operating frequency is a verifiability gap, not a circular step.

full rationale

Walking the paper's derivation chain, I find no circular step. The inputs are stated independently: the 2400 N / 360 N·m load case follows from the robot's 400 kg capacity specification with a 1.2 safety factor (Section 2.2); the SIMP formulation (Eq. 4) minimizes compliance subject to a fixed 50% volume target on the femur side plates (Section 3.3), with contact regions excluded as non-optimizable; and the reconstructed geometry is weighed in SolidWorks (Table 2), so the 19.45% femur and 7.92% total-leg mass reductions are measured outcomes, not preset parameters relabeled as results. Performance validation is genuinely post hoc: the optimized model is re-imported into ANSYS under loads and boundary conditions identical to the pre-optimization analysis (Sections 4.1-4.2), and the resulting 29.38 MPa stress is compared with the independently stated 138 MPa allowable stress (yield 276 MPa divided by safety factor 2), while the natural-frequency check (62.441 Hz first mode, Table 4) is an independent modal analysis of the reconstructed geometry. No quantity is defined in terms of itself, no fitted parameter is renamed as a prediction, and none of the 29 references are authored by the present authors, so there is no self-citation chain to be load-bearing. Two flagged items affect verifiability rather than circularity: (1) Sections 2.3 and 4.2 assert that the natural frequencies are 'higher than the operational frequency of the leg' but never state that operating frequency's numerical value, making the resonance-safety claim untestable as written; and (2) the Replication of Results section lists material properties (2.70 g/cm3, 69 GPa) inconsistent with Section 2.2 (2.77 g/cm3, 69.6 GPa), and no mesh-convergence study or physical prototype test is reported. These are correctness and completeness risks, not circular ones: the optimized design's acceptability is not equated to its own inputs at any step of the derivation.

Assumptions & free parameters 5 free parameters · 6 assumptions · 0 invented entities

The analysis rests on standard FEA and SIMP assumptions, plus several domain choices: the 200 kg per-leg load, the 1.2 safety factor, the 50% volume target, and the restriction of optimization to the femur side plates. These are reasonable engineering inputs, but they are not derived from measured data or operational statistics. No new physical entities are introduced.

free parameters (5)
  • SIMP volume fraction target f = 0.5 (50% material volume reduction for femur side plates)
    Chosen design target in Section 3.3; it directly sets how much material is removed, so the reported mass reduction depends on this choice.
  • Load safety factor = 1.2
    Multiplies the 200 kg per-leg load to 2400 N in Section 2.2; not derived from load statistics.
  • Allowable stress safety factor = 2 (allowable stress 138 MPa)
    Set in Section 2.2; the performance check compares against this value.
  • SIMP penalization factor p = not reported (ANSYS default)
    Penalization factor in Eq. (4) influences the optimized layout but its value is not stated in the paper.
  • Mesh element type and size = not reported
    Mesh generation is mentioned in Section 2.1 but no element type, size, or convergence study is given, affecting stress values.
assumptions (6)
  • standard math SIMP density-based topology optimization model (Eq. 4) is valid for this structure
    Adopted from refs [28,29] in Section 3.2; no derivation is given.
  • domain assumption Worst-case single-leg load of 200 kg with 1.2 safety margin represents real operating conditions
    Section 2.2 assumes tripod gait with three supporting legs and takes one side leg to carry 200 kg.
  • domain assumption Fixing the foot end and applying loads at the distal root joint captures the support-phase stress state
    Section 2.2 states the foot is stationary during support; this boundary condition drives all stress results.
  • domain assumption ANSYS FEA results accurately represent the physical behavior of the as-manufactured leg
    No experimental validation is given; the optimized structure is validated only in simulation (Sections 4.1 and 4.2).
  • domain assumption Modal frequencies above an unspecified 'operating frequency' guarantee no resonance
    Sections 2.3 and 4.2 compare natural frequencies to an operating frequency that is never quantified.
  • ad hoc to paper Only the femur side plates are optimizable while vertical plates and contact regions are fixed
    Section 3.3 restricts the design domain; this choice shapes the resulting optimized topology.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Topology Optimization of Leg Structures for Construction Robots Based on Variable Density Method." pith.science (2026). https://pith.science/paper/RZKD7XRG

@misc{pith2026250716335,
  author       = {Pith},
  title        = {Pith review of: Topology Optimization of Leg Structures for Construction Robots Based on Variable Density Method},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/RZKD7XRG}},
  note         = {Machine review of arXiv:2507.16335}
}
read the original abstract

In complex terrain construction environments, there are high demands for robots to achieve both high payload capacity and mobility flexibility. As the key load-bearing component, the optimization of robotic leg structures is of particular importance. Therefore, this study focuses on the optimization of leg structures for construction robots, proposing a topology optimization strategy based on the SIMP (Solid Isotropic Microstructures with Penalization) variable density method along with a structural re-design approach. The design performance is comprehensively validated through finite element analysis using ANSYS. First, static and modal analyses are conducted to evaluate the rationality of the initial design. Then, topology optimization using the SIMP-based variable density method is applied to the femur section, which accounts for the largest proportion of the leg's weight. Based on iterative calculations, the femur undergoes secondary structural reconstruction. After optimization, the mass of the femur is reduced by 19.45\%, and the overall leg mass decreases by 7.92\%, achieving the goal of lightweight design. Finally, static and modal analyses are conducted on the reconstructed leg. The results demonstrate that the optimized leg still meets structural performance requirements, validating the feasibility of lightweight design. This research provides robust theoretical and technical support for lightweight construction robot design and lays a foundation for their efficient operation in complex construction environments.

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

30 extracted references · 22 canonical work pages

  1. [25]

    Lightweight design optimization for legs of bipedal humanoid robot,

    H. Ding, Z. Shi, Y . Hu, et al., “Lightweight design optimization for legs of bipedal humanoid robot,” Structural and Multidisciplinary Optimization, 2021, 64(4): 2749-2762. https://doi.org/10.1007/s00158-021-02968-2

    work page doi:10.1007/s00158-021-02968-2 2021

  2. [1]

    On-site autonomous construction robots: Towards unsupervised building,

    N. Melenbrink, J. Werfel, and A. Menges, “On-site autonomous construction robots: Towards unsupervised building,” Automation in Construction , 2020, 119: 103312. https://doi.org/10.1016/j.autcon.2020.103312

    work page arXiv 2020

  3. [2]

    Multidisciplinary design opti- mization in Architecture, Engineering, and Construction: a detailed review and call for collaboration,

    N. K. Muthumanickam, N. Brown, J. P. Duarte, et al., “Multidisciplinary design opti- mization in Architecture, Engineering, and Construction: a detailed review and call for collaboration,” Structural and Multidisciplinary Optimization , 2023, 66(11): 239. https://doi.org/10.1007/s00158-023-03673-y

    work page doi:10.1007/s00158-023-03673-y 2023

  4. [3]

    Recent advancements of robotics in construction,

    B. Xiao, C. Chen, and X. Yin, “Recent advancements of robotics in construction,”Automa- tion in Construction, 2022, 144: 104591. https://doi.org/10.1016/j.autcon.2022.104591

    work page arXiv 2022

  5. [4]

    Experimental and theoretical analysis on truss construc- tion robot: automatic grasping and hoisting of concrete composite floor slab,

    S. Tong, W. Xu, X. Zhang, et al., “Experimental and theoretical analysis on truss construc- tion robot: automatic grasping and hoisting of concrete composite floor slab,” Journal of Field Robotics, 2023, 40(2): 272-288. https://doi.org/10.1002/rob.22128

    work page doi:10.1002/rob.22128 2023

  6. [5]

    Automated wall-climbing robot for con- crete construction inspection,

    L. Yang, B. Li, J. Feng, et al., “Automated wall-climbing robot for con- crete construction inspection,” Journal of Field Robotics , 2023, 40(1): 110-129. https://doi.org/10.1002/rob.22119

    work page doi:10.1002/rob.22119 2023

  7. [6]

    Kinematic modeling and constraint analysis for robotic excavator operations in piling construction,

    D. Guan, N. Yang, J. Lai, et al., “Kinematic modeling and constraint analysis for robotic excavator operations in piling construction,” Automation in Construction , 2021, 126: 103666. https://doi.org/10.1016/j.autcon.2021.103666

    arXiv 2021

  8. [7]

    Hangrawler: Large-payload and high- speed ceiling mobile robot using crawler,

    R. Fukui, Y . Yamada, K. Mitsudome, et al., “Hangrawler: Large-payload and high- speed ceiling mobile robot using crawler,” IEEE Transactions on Robotics, 2020, 36(4): 1053-1066. https://doi.org/10.1109/TRO.2020.2973100 14

    work page arXiv 2020

Show all 30 references
  1. [8]

    Dynamic analysis of high precision construc- tion cable-driven parallel robots,

    V . Ferravante, E. Riva, M. Taghavi, et al., “Dynamic analysis of high precision construc- tion cable-driven parallel robots,” Mechanism and Machine Theory, 2019, 135: 54-64. https://doi.org/10.1016/j.mechmachtheory.2019.01.023

    2019 doi

  2. [9]

    Cable-driven parallel robot for cur- tain wall module installation,

    K. Iturralde, M. Feucht, D. Illner, et al., “Cable-driven parallel robot for cur- tain wall module installation,” Automation in Construction , 2022, 138: 104235. https://doi.org/10.1016/j.autcon.2022.104235

    2022

  3. [10]

    Current and Future Trends in Topology Optimization for Additive Manufacturing,

    J. Liu, A. T. Gaynor, S. Chen, et al., “Current and Future Trends in Topology Optimization for Additive Manufacturing,”Structural and Multidisciplinary Optimization, 2018, 57(6): 2457-2483. https://doi.org/10.1007/s00158-018-1994-3

    2018 doi

  4. [11]

    Optimization approach for the core structure of a wind turbine blade,

    I. Kuznetsov, V . Kozhin, A. Novokshenov, et al., “Optimization approach for the core structure of a wind turbine blade,” Structural and Multidisciplinary Optimization , 2024, 67(7): 108. https://doi.org/10.1007/s00158-024-03812-z

    2024 doi

  5. [12]

    Topology optimization of compliant mechanisms and structures subjected to design-dependent pressure loadings,

    Y . Lu and L. Tong, “Topology optimization of compliant mechanisms and structures subjected to design-dependent pressure loadings,” Structural and Multidisciplinary Optimization, 2021, 63: 1889-1906. https://doi.org/10.1007/s00158-020-02786-y

    2021 doi

  6. [13]

    An efficient method for shape and topology opti- mization of shell structures,

    T. Ho-Nguyen-Tan and H. G. Kim, “An efficient method for shape and topology opti- mization of shell structures,” Structural and Multidisciplinary Optimization , 2022, 65(4):

    2022

  7. [14]

    Stress uniformization using functionally graded materials,

    S. Sorohan and D. M. Constantinescu, “Stress uniformization using functionally graded materials,” The Romanian Journal of Technical Sciences. Applied Mechanics. , 2021, 66(2): 163-177

    2021

  8. [15]

    An explicit topology and thickness control approach in SIMP-based topology optimization,

    T. Zuo, H. Han, Q. Wang, et al., “An explicit topology and thickness control approach in SIMP-based topology optimization,” Computers & Structures , 2025, 307: 107631. https://doi.org/10.1016/j.compstruc.2024.107631

    2025

  9. [16]

    3D Structural Topology Optimization Using ESO, SESO and SERA: Comparison and an Extension to Flexible Mechanisms,

    H. L. Simonetti, V . S. Almeida, F. A. Neves, et al., “3D Structural Topology Optimization Using ESO, SESO and SERA: Comparison and an Extension to Flexible Mechanisms,” Applied Sciences, 2023, 13(10): 6215. https://doi.org/10.3390/app13106215

    2023 doi

  10. [17]

    Lightweight topology optimization of graded lattice structures with displacement constraints based on an independent continuous mapping method,

    N. Wei, H. Ye, X. Zhang, et al., “Lightweight topology optimization of graded lattice structures with displacement constraints based on an independent continuous mapping method,” Acta Mechanica Sinica, 2022, 38(4): 421352. https://doi.org/10.1007/s10409- 021-09047-x

    2022 doi

  11. [18]

    Icm Method for Topology Optimization of Multimaterial Continuum Structure with Displacement Constraint,

    H. Ye, Z. Dai, W. Wang, et al., “Icm Method for Topology Optimization of Multimaterial Continuum Structure with Displacement Constraint,” Acta Mechanica Sinica , 2019, 35(3): 552-562. https://doi.org/10.1007/s10409-018-0827-3 15

    2019 doi

  12. [19]

    Topology optimization of curved thick shells using level set method and non-conforming multi-patch isogeometric analy- sis,

    F. H. Scherer, M. Zarroug, H. Naceur, et al., “Topology optimization of curved thick shells using level set method and non-conforming multi-patch isogeometric analy- sis,” Computer Methods in Applied Mechanics and Engineering , 2024, 430: 117205. https://doi.org/10.1016/j.cma....

    2024

  13. [20]

    An effective phase field method for topology optimization without the curvature effects,

    W. Xie, Q. Xia, Q. Yu, et al., “An effective phase field method for topology optimization without the curvature effects,” Computers & Mathematics with Applications , 2023, 146: 200-212. https://doi.org/10.1016/j.camwa.2023.06.037

    2023 doi

  14. [21]

    A comprehensive review of explicit topology optimization based on moving morphable components (MMC) method,

    Z. Li, H. Xu, and S. Zhang, “A comprehensive review of explicit topology optimization based on moving morphable components (MMC) method,” Archives of Computational Methods in Engineering, 2024, 31(5): 2507-2536. https://doi.org/10.1007/s11831-023- 10053-8

    2024 doi

  15. [22]

    Topological derivative-based topology optimization of structures subject to self-weight loading,

    A. A. Novotny, C. G. Lopes, and R. B. Santos, “Topological derivative-based topology optimization of structures subject to self-weight loading,” Structural and Multidisci- plinary Optimization, 2021, 63: 1853-1861. https://doi.org/10.1007/s00158-020-02780-4

    2021 doi

  16. [23]

    Enhancing torsional stiffness of continuum robots using 3-D topology optimized flexure joints,

    Y . Sun and T. C. Lueth, “Enhancing torsional stiffness of continuum robots using 3-D topology optimized flexure joints,” IEEE/ASME Transactions on Mechatronics, 2023, 28(4): 1844-1852. https://doi.org/10.1109/TMECH.2023.3266873

    2023

  17. [24]

    A Topology Optimization Method of Robot Lightweight Design Based on the Finite Element Model of Assembly and Its Applications,

    L. Sha, A. Lin, X. Zhao, et al., “A Topology Optimization Method of Robot Lightweight Design Based on the Finite Element Model of Assembly and Its Applications,” Science Progress, 2020, 103(3): 2147483647. https://doi.org/10.1177/0036850420936482

    2020 doi

  18. [26]

    Topology optimization of multi-scale struc- tures: a review,

    J. Wu, O. Sigmund, and J. P. Groen, “Topology optimization of multi-scale struc- tures: a review,” Structural and Multidisciplinary Optimization , 2021, 63: 1455-1480. https://doi.org/10.1007/s00158-021-02881-8

    2021 doi

  19. [27]

    Larg: A lightweight robotic gripper with 3-d topology optimized adaptive fingers,

    Y . Sun, Y . Liu, F. Pancheri, et al., “Larg: A lightweight robotic gripper with 3-d topology optimized adaptive fingers,” IEEE/ASME Transactions on Mechatronics, 2022, 27(4): 2026-2034. https://doi.org/10.1109/TMECH.2022.3170800

    2022

  20. [28]

    Density-based topology optimization for 3D-printable building structures,

    G. Vantyghem, W. De Corte, M. Steeman, et al., “Density-based topology optimization for 3D-printable building structures,” Structural and Multidisciplinary Optimization , 2019, 60: 2391-2403. https://doi.org/10.1007/s00158-019-02330-7

    2019 doi

  21. [29]

    An improved multi-objective topology optimization model based on SIMP method for continuum structures including self-weight,

    S. Zhang, H. Li, and Y . Huang, “An improved multi-objective topology optimization model based on SIMP method for continuum structures including self-weight,”Structural and Multidisciplinary Optimization, 2021, 63: 211-230. https://doi.org/10.1007/s00158- 020-02685-2 16

    2021 doi

  22. [119]

    https://doi.org/10.1007/s00158-022-03213-0

    doi

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.