Beams: Forces, Stresses, and Deformations

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Gaussian Curvature in Plates

Explores Gaussian curvature, principal curvatures, and nonlinear strain in thin elastic plates.

Beam Bending II: Internal Forces, Curvature, and Stiffness

Covers advanced topics in beam bending, stress tensors, elasticity, and Atomic Force Microscopy.

Introduction to Structural Mechanics

Explores beam bending, stiffness, and curvature in mechanical systems using OCR-extracted slides from EPFL's Spring 2021 session.

Structural Mechanics: Beam Bending and Boundary Conditions

Explores the moment-curvature relation for beams, emphasizing stress distribution and typical boundary conditions.

Curvature and Inflection Points

Explores curvature, inflection points, and angular functions in plane curves, highlighting the importance of inflection points.

Plates II: Föppl-von Kármán Equations

Covers the framework for plates, bending and stretching energies, and Föppl-von Kármán Equations, exploring mean and Gaussian curvatures.

Plates I: Deformation and Energy

Covers the deformation of plates in pure bending, total strain energy, and wrinkling phenomena, exploring applications and implications of substrate stiffness on wrinkling.

Curvature and Osculating Circle

Covers curvature, osculating circles, and the evolute of plane curves, with examples and equations.

Stresses due to Flexure

Covers the calculation of curvature in beams and the design of beams for stress considerations.

Hyperbolic Geometry

Introduces hyperbolic geometry, covering complete metric spaces, isometries, and Gaussian curvature in dimension 2.