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Add 1D Euler-Bernoulli beam solver #87

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@nikoscham
  • Add a 1D Euler-Bernoulli beam bending solver (eulerBernoulliBeamScript) using cubic
    Hermite (C¹) finite elements, so both deflection w and slope theta = dw/dx are
    represented as nodal DOFs. The fourth-order analogue of the existing scalar 1D solvers
    (heatConductionScript, generalFormPDEScript).
  • Add hermiteCubic support to basisFunctions.js (shape functions + 2nd ksi-derivative)
    and a matching 6-point Gauss rule to numericalIntegration.js. This is general C¹
    interpolation infrastructure, not beam-specific, eulerBernoulliBeam.js is just its
    first consumer, and it should be directly reusable for future 4th-order models (e.g.
    Kirchhoff plate bending).
  • Add a worked example reproducing the "Bending of a Beam" problem from J.N. Reddy,
    An Introduction to the Finite Element Method, 3rd ed. (FEM1D reference program,
    Chapter 7): a beam clamped at one end, supported by a roller at midspan and a linear
    spring at the free end, carrying a distributed load, a point moment, and a point load.

Activity

added this to the 0.3.0 milestone on Aug 17, 2026
added theissue type on Aug 17, 2026

nikoscham commented on Aug 17, 2026

@nikoscham
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This task has been implemented by @ferrari212.
See also here.

changed the title [-]Add 1D Euler-Bernoulli beam bending solver[/-] [+]Add 1D Euler-Bernoulli beam solver[/+] on Aug 17, 2026
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