Bibliographic Details
| 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] |
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| Database: |
Engineering Source |
