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Stable numerical technique to calculate the bending of flexures with extreme aspect ratios.

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Title: Stable numerical technique to calculate the bending of flexures with extreme aspect ratios.
Authors: Schreyer, Benjamin1 (AUTHOR), Keck, Lorenz2 (AUTHOR), Pratt, Jon R1 (AUTHOR), Schlamminger, Stephan1 (AUTHOR) stephan.schlamminger@nist.gov
Source: Measurement Science & Technology. 2026, Vol. 37 Issue 11, p1-11. 11p.
Subjects: Flexure, Euler-Bernoulli beam theory, Numerical analysis, Deflection (Mechanics), Runge-Kutta formulas, Python programming language
Abstract: Flexures in torsion balances and precision mechanisms often exhibit extreme aspect ratios, causing exponential scaling in Euler–Bernoulli bending models. Standard double-precision arithmetic cannot resolve the small initial conditions required for accurate solutions. This paper presents a semi-analytic method combining an efficient 1D bending model with adaptive Runge–Kutta–Fehlberg integration in arbitrary precision that overcomes this limitation. A quantitative criterion is established when extended precision becomes necessary. Furthermore, an open-source Python implementation is provided, which remains stable even for flexures with extreme aspect ratios. [ABSTRACT FROM AUTHOR]
Copyright of Measurement Science & Technology is the property of IOP Publishing and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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Header DbId: egs
DbLabel: Engineering Source
An: 192440978
AccessLevel: 6
PubType: Academic Journal
PubTypeId: academicJournal
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  Data: Stable numerical technique to calculate the bending of flexures with extreme aspect ratios.
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  Data: <searchLink fieldCode="JN" term="%22Measurement+Science+%26+Technology%22">Measurement Science & Technology</searchLink>. 2026, Vol. 37 Issue 11, p1-11. 11p.
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  Data: <searchLink fieldCode="DE" term="%22Flexure%22">Flexure</searchLink><br /><searchLink fieldCode="DE" term="%22Euler-Bernoulli+beam+theory%22">Euler-Bernoulli beam theory</searchLink><br /><searchLink fieldCode="DE" term="%22Numerical+analysis%22">Numerical analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Deflection+%28Mechanics%29%22">Deflection (Mechanics)</searchLink><br /><searchLink fieldCode="DE" term="%22Runge-Kutta+formulas%22">Runge-Kutta formulas</searchLink><br /><searchLink fieldCode="DE" term="%22Python+programming+language%22">Python programming language</searchLink>
– Name: Abstract
  Label: Abstract
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  Data: Flexures in torsion balances and precision mechanisms often exhibit extreme aspect ratios, causing exponential scaling in Euler–Bernoulli bending models. Standard double-precision arithmetic cannot resolve the small initial conditions required for accurate solutions. This paper presents a semi-analytic method combining an efficient 1D bending model with adaptive Runge–Kutta–Fehlberg integration in arbitrary precision that overcomes this limitation. A quantitative criterion is established when extended precision becomes necessary. Furthermore, an open-source Python implementation is provided, which remains stable even for flexures with extreme aspect ratios. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Measurement Science & Technology is the property of IOP Publishing and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1088/1361-6501/ae507d
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      – Code: eng
        Text: English
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        PageCount: 11
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      – SubjectFull: Flexure
        Type: general
      – SubjectFull: Euler-Bernoulli beam theory
        Type: general
      – SubjectFull: Numerical analysis
        Type: general
      – SubjectFull: Deflection (Mechanics)
        Type: general
      – SubjectFull: Runge-Kutta formulas
        Type: general
      – SubjectFull: Python programming language
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              M: 03
              Text: 2026
              Type: published
              Y: 2026
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