Pith. sign in

REVIEW 3 major objections 2 minor 91 references

Isogeometric multi-patch shell analysis using the Geometry + Simulation Modules

T0 review · 3 major / 2 minor · reviewed 2026-08-05 · deepseek-v4-flash

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

Pith's one-line read G+Smo now offers integrated, extendable modules for multi-patch isogeometric shell analysis.

desk verdict Can't actually review this one—the supplied full text is a different paper; from the abstract alone it reads as an honest software-description paper, but the load-bearing claims need the real manuscript. read the letter →

arxiv 2508.10648 v1 pith:ZMHFI2AC submitted 2025-08-14 math.NA cs.NA

Hugo M. Verhelst , Angelos Mantzaflaris , Matthias Möller This is my paper
classification math.NAcs.NA MSC 65D0765N3074K25
keywords isogeometricanalysisKirchhoff-Loveshellsmulti-patchG+Smopenaltycouplingunstructuredsplinesgoal-orientederrorestimationwrinkling
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 describes the design and implementation of three new modules in the G+Smo library that together enable isogeometric Kirchhoff-Love shell analysis on multi-patch geometries. The modules provide penalty-based patch coupling, unstructured spline constructions, goal-oriented error estimation, structural analysis algorithms, and wrinkling modeling for hyperelastic membranes. The claim is that these components form a versatile, fast, off-the-shelf ecosystem with a simple interface, ready for extension in future research. A sympathetic reader would care because it lowers the barrier to using spline-based shell analysis in engineering practice, while keeping the door open for new material laws and discretizations.

What carries the argument

The central mechanism is the integration of three software modules within G+Smo: (1) a Kirchhoff-Love shell module that uses high-continuity spline bases to eliminate rotation unknowns, (2) a structural analysis module that treats algorithms as black-box functions over the shell model, and (3) an unstructured spline construction module that provides arbitrary-continuity basis functions across patches. Together they enable penalty-based multi-patch coupling, goal-oriented error estimation, and wrinkling simulation. The key design choice is the modular separation of geometry, discretization, and analysis algorithms, so that material laws and solver procedures can be swapped without rewriting t

What would settle it

Run the new modules on a standard multi-patch shell benchmark, such as a pinched cylinder with a non-matching patch interface, using the library's default settings; if the computed displacement or stress fails to converge to the reference solution as the mesh is refined, or if the penalty parameter must be tuned case-by-case to achieve the reported accuracy, then the central claim of a fast, off-the-shelf, parameter-free ecosystem is falsified.

Watch

Extended reading notes

Core claim

The paper's central claim is that the three new G+Smo modules—a Kirchhoff-Love shell module, a structural analysis module, and an unstructured spline module—provide a coherent and extensible software environment for solving multi-patch shell problems. By exploiting the arbitrary continuity of spline bases, the Kirchhoff-Love formulation avoids rotational degrees of freedom, reducing the number of unknowns. Patch coupling is handled through penalty methods and unstructured splines, and the same modules supply goal-oriented error estimators, several structural analysis algorithms, and advanced wrinkling models. The paper argues that this integration yields fast solvers with a simple interface,

Load-bearing premise

The load-bearing premise is that the underlying numerical methods—penalty patch coupling, unstructured spline continuity, goal-oriented error estimation, and hyperelastic wrinkling algorithms—were correctly implemented and validated in the predecessor publications, and that their integration into the new modules does not degrade their behavior; if that prior validation is missing or the integration changes results, the claim of a reliable off-the-shelf tool collapses.

Editorial extensions

If this is right

  • Engineers can set up multi-patch shell simulations with spline-based IGA without implementing the Kirchhoff-Love formulation themselves.
  • The penalty and unstructured-spline patch couplings allow models with non-matching or non-conforming patches, simplifying CAD-to-analysis workflows.
  • Goal-oriented error estimators give users targeted mesh refinement indicators, reducing computational cost for quantities of interest.
  • The structural analysis module's black-box function design permits drop-in implementation of new analysis procedures (e.g., buckling, vibration, wrinkling) without altering the core shell solver.
  • Base material law implementations make it straightforward to experiment with new constitutive models in the same shell environment.

Reading between the lines

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

  • The supplied manuscript text is from a different work, so the implementation details and numerical validations described in the abstract are not inspectable here; the pith is therefore an integration claim that depends on the companion publications for evidence.
  • The modular architecture suggests the penalty coupling and unstructured spline constructions could be reused for other multi-patch problem types, such as plates or volumetric solids, not just shells.
  • A natural testable extension is to benchmark the new modules against established shell benchmarks (pinched cylinder, Scordelis-Lo roof, hemispherical shell) using default settings, to quantify the 'off-the-shelf' speed and accuracy claim.
  • The black-box structural analysis interface could enable automatic differentiation or adjoint-based sensitivity analysis with minimal changes, a possibility the paper does not discuss.
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 / 2 minor

Summary. The manuscript as supplied cannot be assessed as the paper it claims to be. The abstract of arXiv:2508.10648 announces an implementation of isogeometric Kirchhoff–Love shells within the G+Smo software library, claiming three new modules for shell analysis, structural analysis, and unstructured spline constructions, and asserting that the paper demonstrates a versatile ecosystem with fast off-the-shelf solvers and a simple interface. However, the full text provided is the unrelated experimental fluid-dynamics paper arXiv:2508.10647, 'Dynamic Stall Characteristics and Modelling of Time-Varying Pitching Kinematics' by Rezapour and Mulleners. That text contains no equations, derivations, benchmarks, code, or discussion relevant to G+Smo, isogeometric analysis, shell mechanics, penalty coupling, or wrinkling. The central claim of the abstract is therefore unsupported by any reviewable material.

Significance. The stated result, if properly supported, would be of practical significance to the isogeometric analysis community: a modular, extensible, open-source implementation of Kirchhoff–Love shells with penalty-based multi-patch coupling, goal-oriented error estimation, and wrinkling modeling would lower the barrier to using IGA for shell problems and would complement the authors' prior method papers. The design goals mentioned in the abstract—base material laws, black-box structural-analysis functions, and standardized unstructured-spline construction—are sensible software-engineering objectives. However, none of these contributions can be evaluated from the submitted manuscript. There are no machine-checked proofs, reproducible code artifacts, parameter-free derivations, or falsifiable numerical predictions in the reviewable material. The significance of the claimed software ecosystem is therefore entirely conditional on external prior publications that are not available in this submission.

major comments (3)
  1. [Full text / arXiv metadata] The full text supplied for arXiv:2508.10648 is actually the unrelated paper arXiv:2508.10647, 'Dynamic Stall Characteristics and Modelling of Time-Varying Pitching Kinematics' by Rezapour and Mulleners. It contains no mention of G+Smo, isogeometric analysis, Kirchhoff–Love shells, penalty coupling, unstructured splines, error estimators, or wrinkling. The abstract's central claim that this paper demonstrates an extensible G+Smo shell ecosystem therefore has no supporting content in the manuscript. This is a load-bearing mismatch, not a presentation issue.
  2. [Abstract, last paragraph] The abstract explicitly states that the paper 'accompanies multiple previous publications and elaborates on the design of the software used in these papers, rather than the novelty of the methods presented therein.' This is an explicit limitation: the paper's own claim is one of integration and usability, yet none of the integration is described. There are no equations, no benchmark tables, no convergence studies, no code examples, and no performance measurements in the submitted material, so the asserted 'fast off-the-shelf solvers with a simple interface' are not demonstrated here.
  3. [All sections / absent content] Because the full text is an experimental fluid-dynamics paper, there is no derivation or numerical result to check. The claimed dependencies on prior validation are not documented within the manuscript itself; no references to the previous G+Smo publications are present in the supplied text. The central claim of a usable, validated ecosystem cannot be checked and is not supported by the reviewable material. This is not a matter of a contested derivation or a missing benchmark that a revision could locally fix; the entire claimed subject matter is absent.
minor comments (2)
  1. [Header / metadata] The arXiv identifier in the full text header is 2508.10647, which does not match the claimed submission 2508.10648. The metadata should be corrected and the correct full text should be attached if a revision/resubmission is intended.
  2. [Nomenclature and figures] The nomenclature, figures, and experimental setup in the supplied full text are entirely irrelevant to the claimed paper; they describe a water-channel pitching-airfoil experiment. This is not a clarity issue in the shell-analysis presentation because no such presentation exists.

Circularity Check

0 steps flagged · score 0.0 of 10

No circular derivation found: the submitted full text is an unrelated paper, and the G+Smo abstract explicitly defers to prior publications, which is a support gap rather than circularity.

full rationale

The claimed paper (arXiv:2508.10648) is an isogeometric multi-patch shell software paper. Its abstract does not present a mathematical derivation chain; it describes software modules and explicitly states that the paper 'accompanies multiple previous publications and elaborates on the design of the software used in these papers, rather than the novelty of the methods presented therein.' No equations, fitted parameters, or predictions are made in the abstract, so there is no equation-level reduction to test. The supplied full text is entirely unrelated (arXiv:2508.10647, a dynamic-stall study), so no in-scope derivation chain from the actual G+Smo paper is available. The abstract's reliance on prior publications is a limitation in evidentiary support, not a circular step: citing one's own prior method papers is normal when those papers contain independent benchmarks, and the present text does not attempt to rename a fitted quantity as a prediction. The mismatch between the abstract and the submitted full text is a manuscript/support issue, not a circularity defect. Therefore no circularity is identified.

Assumptions & free parameters 0 free parameters · 2 assumptions · 0 invented entities

The paper is a software design paper, so it introduces no new physical entities and no fitted parameters. Its central claim rests on the adequacy of existing shell theory and numerical coupling methods, which are treated as assumptions in the abstract.

assumptions (2)
  • domain assumption Kirchhoff-Love shell theory is adequate for the thin-shell applications targeted by the modules.
    The entire shell module is framed around the advantage of Kirchhoff-Love shells in isogeometric analysis; the abstract does not justify this modeling choice because it is inherited from prior literature.
  • domain assumption Penalty-based patch coupling and unstructured spline constructions provide sufficiently accurate and stable multi-patch discretizations for the module to be useful.
    The abstract lists these as enabling mechanisms for multi-patch shell analysis, but presents no convergence or stability evidence in the reviewable material.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Isogeometric multi-patch shell analysis using the Geometry + Simulation Modules." pith.science (2026). https://pith.science/paper/ZMHFI2AC

@misc{pith2026250810648,
  author       = {Pith},
  title        = {Pith review of: Isogeometric multi-patch shell analysis using the Geometry + Simulation Modules},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/ZMHFI2AC}},
  note         = {Machine review of arXiv:2508.10648}
}
read the original abstract

Isogeometric Analysis (IGA) bridges Computer-Aided Design (CAD) and Finite Element Analysis (FEA) by employing splines as a common basis for geometry and analysis. One of the advantages of IGA is in the realm of thin shell analysis: due to the arbitrary continuity of the spline basis, Kirchhoff-Love shells can be modeled without the need to introduce unknowns for the mid-plane rotations, leading to a reduction in the number of unknowns. In this paper, we provide the background of an implementation of Isogeometric Kirchhoff--Love shells within the Geometry + Simulation Modules (G+Smo). This paper accompanies multiple previous publications and elaborates on the design of the software used in these papers, rather than the novelty of the methods presented therein. The presented implementation provides patch coupling via penalty methods and unstructured splines, goal-oriented error estimators, several algorithms for structural analysis and advanced algorithms for the modeling of wrinkling in hyperelastic membranes. These methods are all contained in three new modules in G+Smo: a module for Kirchhoff-Love shells, a module for structural analysis, and a module for unstructured spline constructions. As motivated in this paper, the modules are implemented to be compatible with future developments. For example, by providing base implementations of material laws, by using black-box functions for the structural analysis module, or by providing a standardized approach for the implementation of unstructured spline constructions. Overall, this paper demonstrates that the new modules contribute to a versatile ecosystem for the modeling of multi-patch shell problems through fast off-the-shelf solvers with a simple interface, designed to be extended in future research.

Discussion (0). Sign in to comment.

Reference graph

Works this paper leans on

91 extracted references · 56 canonical work pages

  1. [1]

    Infill Optimization for Additive Manufacturing -- Approaching Bone-like Porous Structures

    barticle Hughes , T.J.R. , Cottrell , J.A.A. , Bazilevs , Y. : Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement . Comput. Methods Appl. Mech. Eng. 194 ( 39-41 ), 4135 -- 4195 ( 2005 ) 10.1016/j.cma.2004.10.008 https://arxiv.org/abs/1608.04366 arXiv:1608.04366 barticle

    work page Pith review arXiv 2005

  2. [2]

    , Martin , T

    barticle Cohen , E. , Martin , T. , Kirby , R.M. , Lyche , T. , Riesenfeld , R.F. : Analysis-aware modeling: Understanding quality considerations in modeling for isogeometric analysis . Computer Methods in Applied Mechanics and Engineering 199 ( 5 ), 334 -- 356 ( 2010 ) 10.1016/j.cma.2009.09.010 barticle

    work page doi:10.1016/j.cma.2009.09.010 2010

  3. [3]

    Geometric Numerical Integration for Complex Dynamics of Tethered Spacecraft

    barticle Bazilevs , Y. , Calo , V.M.M. , Cottrell , J.A.A. , Evans , J.A.A. , Hughes , T.J.R.J.R. , Lipton , S. , Scott , M.A.A. , Sederberg , T.W.W. : Isogeometric analysis using T-splines . Computer Methods in Applied Mechanics and Engineering 199 ( 5-8 ), 229 -- 263 ( 2010 ) 10.1016/j.cma.2009.02.036 https://arxiv.org/abs/1010.1724 arxiv:1010.1724 barticle

    work page Pith review arXiv 2010

  4. [4]

    , Chanon , O

    botherref Buffa , A. , Chanon , O. , V \'a zquez , R. : Adaptive Analysis-Aware Defeaturing. arXiv (2022). 10.48550/arXiv.2212.05183 botherref

    arXiv doi:10.48550/arxiv.2212.05183 2022

  5. [5]

    , Chanon , O

    barticle Buffa , A. , Chanon , O. , V \'a zquez , R. : Analysis-aware defeaturing: Problem setting and a posteriori estimation . Mathematical Models and Methods in Applied Sciences 32 ( 02 ), 359 -- 402 ( 2022 ) 10.1142/S0218202522500099 barticle

    work page doi:10.1142/s0218202522500099 2022

  6. [6]

    , J \"u ttler , B

    barticle Giannelli , C. , J \"u ttler , B. , Speleers , H. : THB-splines : The truncated basis for hierarchical splines . Computer Aided Geometric Design 29 ( 7 ), 485 -- 498 ( 2012 ) 10.1016/J.CAGD.2012.03.025 barticle

    doi:10.1016/j.cagd.2012.03.025 2012

  7. [7]

    , J \"u ttler , B

    barticle Giannelli , C. , J \"u ttler , B. , Kleiss , S.K. , Mantzaflaris , A. , Simeon , B. , S peh , J. : THB-splines : An effective mathematical technology for adaptive refinement in geometric design and isogeometric analysis . Computer Methods in Applied Mechanics and Engineering 299 , 337 -- 365 ( 2016 ) 10.1016/J.CMA.2015.11.002 barticle

    doi:10.1016/j.cma.2015.11.002 2016

  8. [8]

    , Chen , F

    barticle Deng , J. , Chen , F. , Li , X. , Hu , C. , Tong , W. , Yang , Z. , Feng , Y. : Polynomial splines over hierarchical T-meshes . Graphical Models 70 ( 4 ), 76 -- 86 ( 2008 ) 10.1016/j.gmod.2008.03.001 barticle

    work page doi:10.1016/j.gmod.2008.03.001 2008

Show all 91 references
  1. [9]

    , Lyche , T

    barticle Dokken , T. , Lyche , T. , Pettersen , K.F. : Polynomial splines over locally refined box-partitions . Computer Aided Geometric Design 30 ( 3 ), 331 -- 356 ( 2013 ) 10.1016/j.cagd.2012.12.005 barticle

    2013 doi

  2. [10]

    , Gantner , G

    barticle Buffa , A. , Gantner , G. , Giannelli , C. , Praetorius , D. , V \'a zquez , R. : Mathematical Foundations of Adaptive Isogeometric Analysis . Archives of Computational Methods in Engineering 29 ( 7 ), 4479 -- 4555 ( 2022 ) 10.1007/s11831-022-09752-5 barticle

    2022 doi

  3. [11]

    , Ambati , M

    barticle Proserpio , D. , Ambati , M. , De Lorenzis , L. , Kiendl , J. : A framework for efficient isogeometric computations of phase-field brittle fracture in multipatch shell structures . Computer Methods in Applied Mechanics and Engineering 372 , 113363 ( 2020 ) 10.1016/j.c...

    2020

  4. [13]

    , Patton , A

    barticle Greco , L. , Patton , A. , Negri , M. , Marengo , A. , Perego , U. , Reali , A. : Higher order phase-field modeling of brittle fracture via isogeometric analysis . Engineering with Computers 40 ( 6 ), 3541 -- 3560 ( 2024 ) 10.1007/s00366-024-01949-5 barticle

    2024 doi

  5. [14]

    , Maggiorelli , E

    botherref Greco , L. , Maggiorelli , E. , Negri , M. , Patton , A. , Reali , A. : AT1 Fourth-Order Isogeometric Phase-Field Modeling of Brittle Fracture. arXiv (2025). 10.48550/arXiv.2501.16968 botherref

    2025 doi arXiv

  6. [15]

    , Schmidt , R

    barticle Kiendl , J. , Schmidt , R. , W \"u chner , R. , Bletzinger , K.U. : Isogeometric shape optimization of shells using semi-analytical sensitivity analysis and sensitivity weighting . Computer Methods in Applied Mechanics and Engineering 274 , 148 -- 167 ( 2014 ) 10.1016...

    2014 doi

  7. [16]

    , Morganti , S

    barticle Xu , F. , Morganti , S. , Zakerzadeh , R. , Kamensky , D. , Auricchio , F. , Reali , A. , Hughes , T.J.R. , Sacks , M.S. , Hsu , M.-C. : A framework for designing patient-specific bioprosthetic heart valves using immersogeometric fluid-structure interaction analysis ....

    2018 doi

  8. [17]

    , Benson , D

    bchapter Hartmann , S. , Benson , D. , Nagy , A. : Isogeometric analysis with LS-DYNA . In: Journal of Physics : Conference Series , vol. 734 , p. 032125 . IOP Publishing , ??? ( 2016 ) bchapter

    2016

  9. [18]

    , Hartmann , S

    bchapter Leidinger , L.F. , Hartmann , S. , Rorris , L. , Breitenberger , M. , Bauer , A.M. , W \"u chner , R. , Bletzinger , K.-U. , Duddeck , F. , Song , L. : Connecting Design and Analysis : Explicit Isogeometric Analysis using ANSA and LS-DYNA . In: 8th Before Reality Conf...

    2019

  10. [19]

    , Bucher , P

    botherref Ferr \'a ndiz , V.M. , Bucher , P. , Zorrilla , R. , Rossi , R. , Warnakulasuriya , S. , Cornejo , A. , jcotela , Roig , C. , Celigueta , M.A. , Maria , J. , tteschemacher , Mas \'o , M. , Casas , G. , N \'u \ n ez , M. , Dadvand , P. , Latorre , S. , Pouplana , I. ,...

    2023

  11. [20]

    , Rossi , R

    barticle Dadvand , P. , Rossi , R. , O \ n ate , E. : An Object-oriented Environment for Developing Finite Element Codes for Multi-disciplinary Applications . Archives of Computational Methods in Engineering 17 ( 3 ), 253 -- 297 ( 2010 ) 10.1007/s11831-010-9045-2 barticle

    2010 doi

  12. [21]

    , Collier , N

    barticle Dalcin , L. , Collier , N. , Vignal , P. , C \^o rtes , A.M.A. , Calo , V.M. : PetIGA : A framework for high-performance isogeometric analysis . Computer Methods in Applied Mechanics and Engineering 308 , 151 -- 181 ( 2016 ) barticle

    2016

  13. [22]

    , Andrej , J

    barticle Anderson , R. , Andrej , J. , Barker , A. , Bramwell , J. , Camier , J.-S. , Cerveny , J. , Dobrev , V. , Dudouit , Y. , Fisher , A. , Kolev , T. , Pazner , W. , Stowell , M. , Tomov , V. , Akkerman , I. , Dahm , J. , Medina , D. , Zampini , S. : MFEM : A modular fini...

    2021 doi

  14. [23]

    , Bazilevs , Y

    barticle Kamensky , D. , Bazilevs , Y. : tIGAr : Automating isogeometric analysis with FEniCS . Computer Methods in Applied Mechanics and Engineering 344 , 477 -- 498 ( 2019 ) 10.1016/J.CMA.2018.10.002 barticle

    2019 doi

  15. [24]

    , Zwieten , J

    botherref Zwieten , G. , Zwieten , J. , Hoitinga , W. : Nutils. Zenodo (2022). 10.5281/zenodo.6006701 botherref

    2022 doi

  16. [25]

    : A new design for the implementation of isogeometric analysis in Octave and Matlab : GeoPDEs 3.0

    barticle V \'a zquez , R. : A new design for the implementation of isogeometric analysis in Octave and Matlab : GeoPDEs 3.0 . Computers & Mathematics with Applications 72 ( 3 ), 523 -- 554 ( 2016 ) 10.1016/j.camwa.2016.05.010 barticle

    2016 doi

  17. [26]

    , Langer , U

    barticle J \"u ttler , B. , Langer , U. , Mantzaflaris , A. , Moore , S.E. , Zulehner , W. : Geometry + Simulation Modules : Implementing Isogeometric Analysis . PAMM 14 ( 1 ), 961 -- 962 ( 2014 ) 10.1002/pamm.201410461 barticle

    2014 doi

  18. [27]

    : An overview of geometry plus simulation modules

    bchapter Mantzaflaris , A. : An overview of geometry plus simulation modules . In: Mathematical Aspects of Computer and Information Sciences : 8th International Conference , MACIS 2019, Gebze , Turkey , November 13 15, 2019, Revised Selected Papers 8 , pp. 453 -- 456 . Springe...

    2019

  19. [28]

    , Hadjout , S

    bchapter G \"u c l \"u , Y. , Hadjout , S. , Ratnani , A. : PSYDAC : A high-performance IGA library in Python . In: 8th European Congress on Computational Methods in Applied Sciences and Engineering ( 2022 ) bchapter

    2022

  20. [29]

    o lz , J. , Harbrecht , H. , Kurz , S. , Multerer , M. , Sch \

    barticle D \"o lz , J. , Harbrecht , H. , Kurz , S. , Multerer , M. , Sch \"o ps , S. , Wolf , F. : Bembel: The fast isogeometric boundary element C ++ library for Laplace , Helmholtz , and electric wave equation . SoftwareX 11 , 100476 ( 2020 ) 10.1016/j.softx.2020.100476 barticle

    2020

  21. [30]

    , Hirschler , T

    bchapter Duval , A. , Hirschler , T. , Cornejo Fuentes , J.E. , Guerder , M. , Elguedj , T. : YETI : YET another Iga code . In: IGA 2023 , Lyon, France ( 2023 ) bchapter

    2023

  22. [31]

    , M \"o ller , M

    bchapter Verhelst , H.M. , M \"o ller , M. , Den Besten , J.H. , Vermolen , F.J. , Kaminski , M.L. : Equilibrium Path Analysis Including Bifurcations with an Arc-Length Method Avoiding A Priori Perturbations . In: Lecture Notes in Computational Science And Engineering , vol. 1...

    2021 doi

  23. [32]

    , M \"o ller , M

    barticle Verhelst , H.M. , M \"o ller , M. , Den Besten , J.H. , Mantzaflaris , A. , Kaminski , M.L. : Stretch- Based Hyperelastic Material Formulations for Isogeometric Kirchhoff Love Shells with Application to Wrinkling . Computer-Aided Design 139 , 103075 ( 2021 ) 10.1016/j...

    2021

  24. [33]

    , Verhelst , H.M

    barticle Farahat , A. , Verhelst , H.M. , Kiendl , J. , Kapl , M. : Isogeometric analysis for multi-patch structured Kirchhoff Love shells . Computer Methods in Applied Mechanics and Engineering 411 , 116060 ( 2023 ) 10.1016/j.cma.2023.116060 barticle

    2023

  25. [34]

    , Takacs , T

    barticle Weinm \"u ller , P. , Takacs , T. : Construction of approximate C1 bases for isogeometric analysis on two-patch domains . Computer Methods in Applied Mechanics and Engineering 385 , 114017 ( 2021 ) 10.1016/J.CMA.2021.114017 https://arxiv.org/abs/2103.02980 arxiv:2103....

    2021

  26. [35]

    , Takacs , T

    barticle Weinm \"u ller , P. , Takacs , T. : An approximate C1 multi-patch space for isogeometric analysis with a comparison to Nitsche 's method . Computer Methods in Applied Mechanics and Engineering 401 , 115592 ( 2022 ) 10.1016/j.cma.2022.115592 barticle

    2022

  27. [36]

    , Besten , J.H.D

    botherref Verhelst , H.M. , Besten , J.H.D. , M \"o ller , M. : An Adaptive Parallel Arc-Length Method . arXiv (2023). 10.48550/arXiv.2303.01075 botherref

    2023 doi arXiv

  28. [37]

    , Mantzaflaris , A

    botherref Verhelst , H.M. , Mantzaflaris , A. , M \"o ller , M. , Besten , J.H.D. : Goal- Adaptive Meshing of Isogeometric Kirchhoff-Love Shells . arXiv (2023). 10.48550/arXiv.2307.08356 botherref

    2023 doi arXiv

  29. [38]

    , Weinm \"u ller , P

    botherref Verhelst , H.M. , Weinm \"u ller , P. , Mantzaflaris , A. , Takacs , T. , Toshniwal , D. : A Comparison of Smooth Basis Constructions for Isogeometric Analysis. arXiv (2023). 10.48550/arXiv.2309.04405 botherref

    2023 doi arXiv

  30. [39]

    , Möller , M

    botherref Verhelst , H.M. , Möller , M. , Den Besten , J.H. : A wrinkling model for general hyperelastic materials based on tension field theory 441, 117955 10.1016/j.cma.2025.117955 botherref

    2025

  31. [40]

    , J \"u ttler , B

    barticle Farahat , A. , J \"u ttler , B. , Kapl , M. , Takacs , T. : Isogeometric analysis with C1-smooth functions over multi-patch surfaces . Computer Methods in Applied Mechanics and Engineering 403 , 115706 ( 2023 ) 10.1016/j.cma.2022.115706 barticle

    2023

  32. [41]

    : The openNURBS Initiative

    botherref Associates , R.M.. : The openNURBS Initiative . https://www.rhino3d.com/features/developer/opennurbs/ botherref

  33. [42]

    , Giannelli , C

    bchapter Bracco , C. , Giannelli , C. , Gro mann , D. , Imperatore , S. , Mokri s , D. , Sestini , A. : THB-Spline Approximations for Turbine Blade Design with Local B-Spline Approximations . In: SEMA SIMAI Springer Series vol. 29 , pp. 63 -- 82 . Springer, Cham , ??? ( 2022 )...

    2022 doi

  34. [43]

    , Yu , Y.Y

    botherref Ji , Y. , Yu , Y.Y. , Wang , M.Y. , Zhu , C.G. : Constructing high-quality planar NURBS parameterization for isogeometric analysis by adjustment control points and weights . J. Comput. Appl. Math. 396 (2021) 10.1016/j.cam.2021.113615 botherref

    2021

  35. [44]

    , Wang , M.Y

    barticle Ji , Y. , Wang , M.Y. , Pan , M.D. , Zhang , Y. , Zhu , C.G. : Penalty function-based volumetric parameterization method for isogeometric analysis . Comput. Aided Geom. Des. 94 , 1 -- 21 ( 2022 ) 10.1016/j.cagd.2022.102081 barticle

    2022

  36. [45]

    , M \" o ller , M

    barticle Hinz , J. , M \" o ller , M. , Vuik , C. : Elliptic grid generation techniques in the framework of isogeometric analysis applications . Comput. Aided Geom. Des. 65 , 48 -- 75 ( 2018 ) 10.1016/j.cagd.2018.03.023 barticle

    2018 doi

  37. [46]

    , Jaeschke , A

    barticle Hinz , J. , Jaeschke , A. , M \" o ller , M. , Vuik , C. : The role of PDE-based parameterization techniques in gradient-based IGA shape optimization applications . Comput. Methods Appl. Mech. Eng. 378 , 113685 ( 2021 ) 10.1016/j.cma.2021.113685 barticle

    2021

  38. [47]

    , Moreland , K

    bchapter Fabian , N. , Moreland , K. , Thompson , D. , Bauer , A.C. , Marion , P. , Gevecik , B. , Rasquin , M. , Jansen , K.E. : The paraview coprocessing library: A scalable, general purpose in situ visualization library . In: 2011 IEEE Symposium on Large Data Analysis and V...

    2011

  39. [48]

    : Optimal quadrature for univariate and tensor product splines

    barticle Johannessen , K.A. : Optimal quadrature for univariate and tensor product splines . Computer Methods in Applied Mechanics and Engineering 316 , 84 -- 99 ( 2017 ) 10.1016/j.cma.2016.04.030 barticle

    2017 doi

  40. [49]

    , Jacob , B

    botherref Guennebaud , G. , Jacob , B. , et al.: Eigen v3. http://eigen.tuxfamily.org (2010) botherref

    2010

  41. [50]

    : Yixuan/Spectra (2023) botherref

    botherref Qiu , Y. : Yixuan/Spectra (2023) botherref

    2023

  42. [51]

    , Bletzinger , K.-U

    barticle Kiendl , J. , Bletzinger , K.-U. , Linhard , J. , W \"u chner , R. : Isogeometric shell analysis with Kirchhoff Love elements . Computer Methods in Applied Mechanics and Engineering 198 ( 49-52 ), 3902 -- 3914 ( 2009 ) 10.1016/J.CMA.2009.08.013 barticle

    2009 doi

  43. [52]

    : Isogeometric analysis and shape optimal design of shell structures

    botherref Kiendl , J. : Isogeometric analysis and shape optimal design of shell structures. PhD thesis, Technische Universit\"at M\"unchen (2011) botherref

    2011

  44. [53]

    , Hsu , M.-C

    barticle Kiendl , J. , Hsu , M.-C. , Wu , M.C.H. , Reali , A. : Isogeometric Kirchhoff Love shell formulations for general hyperelastic materials . Computer Methods in Applied Mechanics and Engineering 291 , 280 -- 303 ( 2015 ) 10.1016/J.CMA.2015.03.010 barticle

    2015 doi

  45. [54]

    , Liguori , F

    barticle Leonetti , L. , Liguori , F. , Magisano , D. , Garcea , G. : An efficient isogeometric solid-shell formulation for geometrically nonlinear analysis of elastic shells . Computer Methods in Applied Mechanics and Engineering 331 , 159 -- 183 ( 2018 ) 10.1016/j.cma.2017.1...

    2018 doi

  46. [55]

    , Day , A.S

    botherref Otter , J.R.H. , Day , A.S. : Tidal Computations . The Engineer (1960) botherref

    1960

  47. [56]

    : Computations for prestressed concrete reactor pressure vessels using dynamic relaxation

    barticle Otter , J.R.H. : Computations for prestressed concrete reactor pressure vessels using dynamic relaxation . Nuclear Structural Engineering 1 ( 1 ), 61 -- 75 ( 1965 ) 10.1016/0369-5816(65)90097-9 barticle

    1965 doi

  48. [57]

    , Cassell , A.C

    barticle Otter , J.R.H. , Cassell , A.C. , Hobbs , R.E. , Poisson : D ynamic R elaxation . Proceedings of the Institution of Civil Engineers 35 ( 4 ), 633 -- 656 ( 1966 ) 10.1680/iicep.1966.8604 barticle

    1966

  49. [58]

    , Rio , G

    barticle Rodriguez , J. , Rio , G. , Cadou , J.M. , Troufflard , J. : Numerical study of dynamic relaxation with kinetic damping applied to inflatable fabric structures with extensions for 3D solid element and non-linear behavior . Thin-Walled Structures 49 ( 11 ), 1468 -- 147...

    2011 doi

  50. [59]

    , Estiri , H

    barticle Rezaiee-Pajand , M. , Estiri , H. : Geometrically nonlinear analysis of shells by various dynamic relaxation methods . World Journal of Engineering 14 ( 5 ), 381 -- 405 ( 2017 ) 10.1108/WJE-10-2016-0109 barticle

    2017 doi

  51. [60]

    : Explicit finite-difference methods in geomechanics

    botherref Cundall , P. : Explicit finite-difference methods in geomechanics. Proc. 2nd Int. Cof. Num. Meth. Geomech., ASCE, New York, 132--150 (1976) botherref

    1976

  52. [61]

    : Form-finding and analysis of prestressed nets and membranes

    barticle Barnes , M.R. : Form-finding and analysis of prestressed nets and membranes . Computers & Structures 30 ( 3 ), 685 -- 695 ( 1988 ) 10.1016/0045-7949(88)90304-5 barticle

    1988 doi

  53. [62]

    : Form Finding and Analysis of Tension Structures by Dynamic Relaxation

    barticle Barnes , M.R. : Form Finding and Analysis of Tension Structures by Dynamic Relaxation . International Journal of Space Structures 14 ( 2 ), 89 -- 104 ( 1999 ) 10.1260/0266351991494722 barticle

    1999 doi

  54. [63]

    : Automated Dynamic Relaxation Solution Algorithms for Compliant Systems

    bbook Shugar , T.A. : Automated Dynamic Relaxation Solution Algorithms for Compliant Systems . Naval Civil Engineering Laboratory , ??? ( 1990 ) bbook

    1990

  55. [64]

    , Khan , A.I

    barticle Topping , B.H.V. , Khan , A.I. : Parallel computation schemes for dynamic relaxation . Engineering Computations 11 ( 6 ), 513 -- 548 ( 1994 ) 10.1108/02644409410799407 barticle

    1994 doi

  56. [65]

    , Bertoldi , K

    barticle Taylor , M. , Bertoldi , K. , Steigmann , D.J. : Spatial resolution of wrinkle patterns in thin elastic sheets at finite strain . Journal of the Mechanics and Physics of Solids 62 , 163 -- 180 ( 2014 ) 10.1016/J.JMPS.2013.09.024 barticle

    2014 doi

  57. [66]

    : A method for the automatic evaluation of the dynamic relaxation parameters

    barticle Papadrakakis , M. : A method for the automatic evaluation of the dynamic relaxation parameters . Computer Methods in Applied Mechanics and Engineering 25 ( 1 ), 35 -- 48 ( 1981 ) 10.1016/0045-7825(81)90066-9 barticle

    1981 doi

  58. [67]

    , Wittek , A

    barticle Joldes , G.R. , Wittek , A. , Miller , K. : Real-time nonlinear finite element computations on GPU - application to neurosurgical simulation . Computer Methods in Applied Mechanics and Engineering 199 ( 49 ), 3305 -- 3314 ( 2010 ) 10.1016/j.cma.2010.06.037 . Publisher...

    2010 doi

  59. [68]

    , Wittek , A

    barticle Joldes , G.R. , Wittek , A. , Miller , K. : An adaptive dynamic relaxation method for solving nonlinear finite element problems. application to brain shift estimation . International Journal for Numerical Methods in Biomedical Engineering 27 ( 2 ), 173 -- 185 ( 2011 )...

    2011 doi

  60. [69]

    , Persson , K

    barticle Alic , V. , Persson , K. : Form finding with dynamic relaxation and isogeometric membrane elements . Computer Methods in Applied Mechanics and Engineering 300 , 734 -- 747 ( 2016 ) 10.1016/j.cma.2015.12.009 . Publisher: Elsevier B.V. barticle

    2016 doi

  61. [70]

    : Dynamic Relaxation

    bbook Underwood , P. : Dynamic Relaxation . Comput Methods for Transient Anal , ( 1983 ). Pages: 265 bbook

    1983

  62. [71]

    , Lewis , J.G

    barticle Grimes , R.G. , Lewis , J.G. , Simon , H.D. : A Shifted Block Lanczos Algorithm for Solving Sparse Symmetric Generalized Eigenproblems . SIAM Journal on Matrix Analysis and Applications 15 ( 1 ), 228 -- 272 ( 1994 ) 10.1137/S0895479888151111 barticle

    1994 doi

  63. [72]

    , Ramm , E

    barticle Brendel , B. , Ramm , E. : Nichtlineare Stabilit\"atsuntersuchungen mit der Methode der Finiten Elemente . Ingenieur-Archiv 51 ( 5 ), 337 -- 362 ( 1982 ) 10.1007/BF00536659 barticle

    1982 doi

  64. [73]

    : A Fast Incremental / Iterative Solution Procedure That Handles `` Snap-Through ''

    bchapter Crisfield , M.A.M. : A Fast Incremental / Iterative Solution Procedure That Handles `` Snap-Through '' . In: Computational Methods in Nonlinear Structural and Solid Mechanics , pp. 55 -- 62 . Pergamon , ??? ( 1981 ). 10.1016/B978-0-08-027299-3.50009-1 bchapter

    1981 doi

  65. [74]

    , Wagner , W

    barticle Wriggers , P. , Wagner , W. , Miehe , C. : A quadratically convergent procedure for the calculation of stability points in finite element analysis . Computer Methods in Applied Mechanics and Engineering 70 ( 3 ), 329 -- 347 ( 1988 ) 10.1016/0045-7825(88)90024-2 barticle

    1988 doi

  66. [75]

    , Mantzaflaris , A

    barticle Marsala , M. , Mantzaflaris , A. , Mourrain , B. : G1 Smooth biquintic approximation of Catmull-Clark subdivision surfaces . Computer Aided Geometric Design 99 , 102158 ( 2022 ) 10.1016/j.cagd.2022.102158 barticle

    2022

  67. [76]

    : A Refineable Space of Smooth Spline Surfaces of Arbitrary Topological Genus

    barticle Reif , U. : A Refineable Space of Smooth Spline Surfaces of Arbitrary Topological Genus . Journal of Approximation Theory 90 ( 2 ), 174 -- 199 ( 1997 ) 10.1006/jath.1996.3079 barticle

    1997

  68. [77]

    , Speleers , H

    barticle Toshniwal , D. , Speleers , H. , Hughes , T.J.R. : Smooth cubic spline spaces on unstructured quadrilateral meshes with particular emphasis on extraordinary points: Geometric design and isogeometric analysis considerations . Computer Methods in Applied Mechanics and E...

    2017 doi

  69. [78]

    , Toshniwal , D

    barticle Takacs , T. , Toshniwal , D. : Almost- C1 splines: Biquadratic splines on unstructured quadrilateral meshes and their application to fourth order problems . Computer Methods in Applied Mechanics and Engineering 403 , 115640 ( 2023 ) 10.1016/j.cma.2022.115640 barticle

    2023

  70. [79]

    , Sangalli , G

    barticle Collin , A. , Sangalli , G. , Takacs , T. : Analysis-suitable G1 multi-patch parametrizations for C1 isogeometric spaces . Computer Aided Geometric Design 47 , 93 -- 113 ( 2016 ) 10.1016/j.cagd.2016.05.009 barticle

    2016 doi

  71. [80]

    , Speleers , H

    barticle Toshniwal , D. , Speleers , H. , Hiemstra , R.R. , Hughes , T.J.R. : Multi-degree smooth polar splines: A framework for geometric modeling and isogeometric analysis . Computer Methods in Applied Mechanics and Engineering 316 , 1005 -- 1061 ( 2017 ) 10.1016/j.cma.2016....

    2017 doi

  72. [81]

    : Isogeometric analysis for subdivision surfaces

    botherref Barendrecht , P.J. : Isogeometric analysis for subdivision surfaces. PhD thesis, Eindhoven University of Technology (2013) botherref

    2013

  73. [82]

    , Johnson , E.L

    barticle Herrema , A.J. , Johnson , E.L. , Proserpio , D. , Wu , M.C.H. , Kiendl , J. , Hsu , M.-C. : Penalty coupling of non-matching isogeometric Kirchhoff Love shell patches with application to composite wind turbine blades . Computer Methods in Applied Mechanics and Engine...

    2019 doi

  74. [83]

    : Nonlinear solid mechanics: A continuum approach for engineering , ( 2000 ) bbook

    bbook Holzapfel , G. : Nonlinear solid mechanics: A continuum approach for engineering , ( 2000 ) bbook

    2000

  75. [84]

    , Natori , M.C

    botherref Nakashino , K. , Natori , M.C. : Efficient Modification Scheme of Stress-Strain Tensor for Wrinkled Membranes . AIAA JOURNAL 43(1) (2005) 10.2514/1.7143 botherref

    2005 doi

  76. [85]

    , Nordmark , A

    barticle Nakashino , K. , Nordmark , A. , Eriksson , A. : Geometrically nonlinear isogeometric analysis of a partly wrinkled membrane structure . Computers and Structures 239 , 106302 ( 2020 ) 10.1016/j.compstruc.2020.106302 barticle

    2020

  77. [86]

    , Xin , M

    barticle Panaitescu , A. , Xin , M. , Davidovitch , B. , Chopin , J. , Kudrolli , A. : Birth and decay of tensional wrinkles in hyperelastic sheets . Physical Review E ( 2019 ) 10.1103/PhysRevE.100.053003 https://arxiv.org/abs/1906.10054 arxiv:1906.10054 barticle

    2019 arXiv

  78. [87]

    , Akbarzadeh , A

    barticle Rafsanjani , A. , Akbarzadeh , A. , Pasini , D. : Snapping Mechanical Metamaterials under Tension . Adv. Mater. 27 ( 39 ), 5931 -- 5935 ( 2015 ) 10.1002/adma.201502809 barticle

    2015 doi

  79. [88]

    , Giannelli , C

    barticle Bracco , C. , Giannelli , C. , V \' a zquez , R. : Refinement Algorithms for Adaptive Isogeometric Methods with Hierarchical Splines . Axioms 7 ( 3 ), 43 ( 2018 ) 10.3390/axioms7030043 barticle

    2018 doi

  80. [89]

    : OptimLib (2025) botherref

    botherref O'Hara , K. : OptimLib (2025) botherref

    2025

  81. [90]

    : An incremental approach to the solution of snapping and buckling problems

    barticle Riks , E. : An incremental approach to the solution of snapping and buckling problems . International Journal of Solids and Structures 15 ( 7 ), 529 -- 551 ( 1979 ) 10.1016/0020-7683(79)90081-7 barticle

    1979 doi

  82. [91]

    , J \" u ttler , B

    barticle Buchegger , F. , J \" u ttler , B. , Mantzaflaris , A. : Adaptively refined multi-patch B-splines with enhanced smoothness . Appl. Math. Comput. 272 , 159 -- 172 ( 2016 ) 10.1016/j.amc.2015.06.055 barticle

    2016 doi

  83. [92]

    write newline

    " write newline "" before.all 'output.state := FUNCTION string.to.integer 't := t text.length 'k := #1 'char.num := t char.num #1 substring 's := s is.num s "." = or char.num k = not and char.num #1 + 'char.num := while char.num #1 - 'char.num := t #1 char.num substring FUNCTI...

Pith tools

Reviewed August 5, 2026 · model on record in the stance chip above.