Add 1D Euler-Bernoulli beam solver #87
Description
- Add a 1D Euler-Bernoulli beam bending solver (
eulerBernoulliBeamScript) using cubic
Hermite (C¹) finite elements, so both deflectionwand slopetheta = dw/dxare
represented as nodal DOFs. The fourth-order analogue of the existing scalar 1D solvers
(heatConductionScript,generalFormPDEScript). - Add
hermiteCubicsupport tobasisFunctions.js(shape functions + 2nd ksi-derivative)
and a matching 6-point Gauss rule tonumericalIntegration.js. This is general C¹
interpolation infrastructure, not beam-specific,eulerBernoulliBeam.jsis 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
nikoscham commentedon Aug 17, 2026
This task has been implemented by @ferrari212.
See also here.
[-]Add 1D Euler-Bernoulli beam bending solver[/-][+]Add 1D Euler-Bernoulli beam solver[/+]