Curved bodies in point contact has an elliptical shape

Hertz Contact Stress in Deep Groove Ball Bearings — Analytical Pipeline

Given a bearing and a radial load → maximum subsurface shear stress → engineering verdict. Pipeline, notebook, and verification case for bearing 6206.

Interference fit analysis — hub on hollow shaft, axonometric and cross-section view

Hybrid Joint Optimization — Analytical Pipeline (Croccolo 2012)

From torque requirement and materials to optimal hub ratio, coupling geometry, and design merit — six-step closed-form pipeline with three canonical scenarios.

N*: The Spectrum of Geometric Efficiency

Concrete Penetration Depth — Analytical Pipeline (Li & Chen 2003)

From projectile geometry and impact velocity to penetration depth — dimensionless formulation, regime selection (shallow/deep), and numerical verification against 82 test points.

Fatigue Life of Notched Plates — Analytical Pipeline (Hazizi 2023)

10-node analytical pipeline for fatigue life of plates with semicircular notches, with corrections to Hazizi et al. (2023).

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.