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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.
eulerBernoulliBeamScript) using cubicHermite (C¹) finite elements, so both deflection
wand slopetheta = dw/dxarerepresented as nodal DOFs. The fourth-order analogue of the existing scalar 1D solvers
(
heatConductionScript,generalFormPDEScript).hermiteCubicsupport tobasisFunctions.js(shape functions + 2nd ksi-derivative)and a matching 6-point Gauss rule to
numericalIntegration.js. This is general C¹interpolation infrastructure, not beam-specific,
eulerBernoulliBeam.jsis just itsfirst consumer, and it should be directly reusable for future 4th-order models (e.g.
Kirchhoff plate bending).
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.