Derivation of the Euler-Bernoulli Beam Equation EI·y″ = M(x)
From plane sections to the moment–curvature relation EI·y″ = M(x), step by step.
Structural-Mechanics
Derivation of the Euler Critical Buckling Load Pcr = π²EI/L²
From equilibrium on the deflected geometry to the Euler critical load Pcr = π²EI/L², step by step.
Derivation of Cantilever Tip Deflection δ = PL³/(3EI)
From the moment–curvature relation to the cantilever tip deflection δ = PL³/(3EI), step by step.
Thick-Walled Cylinder Stress Analysis — Analytical Pipeline (Croccolo 2009)
From internal pressure and geometry to radial/hoop stress distribution — Lamé equations, pipeline, notebook, and numerical verification.