Euler-Bernoulli beam EI w''''(x) = q(x); 4th-order ODE; Bernstein basis FEM

Layer 1 — Physicsin the engineering-physics subtree

Euler-Bernoulli beam-bending framework (Bernoulli D 1742; Euler 1750 Methodus inveniendi lineas curvas). Setup: small-deflection bending of a slender prismatic beam under transverse load q(x) is governed by the 4th-order ODE EI w''''(x) =…

Related concepts

Bernstein polynomials B_{k,n}(x): partition of unity + Weierstrass proof
Theorem: w(L) - q L^4/(8 EI) = 0 (cantilever end-deflection identity)

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