Symmetries and Conservation Laws

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Related lectures (44)

Plates III: Buckling Theory and Applications Log in to Mediaspace to watch this video

Explores Föppl-von Kármán plate theory, including buckling equations and an example of plate compression.

Shells I: Mechanics of Slender Structures Log in to Mediaspace to watch this video

Covers linear and membrane theories of pressure vessels, differential geometry of surfaces, and the reduction of dimensionality from 3D to 2D.

Tucker Decomposition: Multilinear rank and applications in data compression Log in to Mediaspace to watch this video

Covers the Tucker decomposition and its applications in data compression, explaining the notion of multilinear rank and the HOSVD method.

Buckling of Plates: Post-Buckling Deformation Behavior Investigation Log in to Mediaspace to watch this video

Investigates post-buckling deformation behavior, bending energy derivation, and in-plane stretching energy considerations in square plates.

Curvature and Osculating Circle Log in to Mediaspace to watch this video

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

Beam Bending II: Internal Forces, Curvature, and Stiffness Log in to Mediaspace to watch this video

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

Buckling of Plates: Post-Buckling Deformation Analysis Log in to Mediaspace to watch this video

Investigates post-buckling deformation of plates, deriving bending and stretching energies.

Differential Geometry: Parametric Curves & Surfaces Log in to Mediaspace to watch this video

Introduces the basics of differential geometry for parametric curves and surfaces, covering curvature, tangent vectors, and surface optimization.

Plates III: Mechanics of Slender Structure Log in to Mediaspace to watch this video

Covers Föppl-von Kármán equations, Airy potential, plate theory simplifications, and buckling of plates.

Nonlinear Beam Theory: Mechanics of Slender Structure Log in to Mediaspace to watch this video

Covers strain-displacement relations, simplifications, constitutive relations, equilibrium equations, and circular rings.

Linear Momentum Conservation and Stress in Continuum Log in to Mediaspace to watch this video

Explores the conservation of linear momentum and stress in a continuum, focusing on governing equations and constitutive laws.

Cylinders: Pressure and Geometry Log in to Mediaspace to watch this video

Explores cylindrical pressure vessels, surfaces parametrization, and geometrical properties computation.

Cylinders: Pressure and Geometry Log in to Mediaspace to watch this video

Explores equilibrium of cylindrical shells, parametrization of surfaces, and geometrical properties.

Minimal Surfaces and Discrete Differential Geometry Log in to Mediaspace to watch this video

Explores minimal surfaces, curvature, Laplace-Beltrami operator, numerical solutions, Laplacian smoothing, diffusion flow, and time integration.

Introduction to Arrows and Differential Relations Log in to Mediaspace to watch this video

Introduces arrows in beams and how to calculate deflection using differential relations.

Sintering Fundamentals: Basics of Solid State Grain Growth Log in to Mediaspace to watch this video

Explores the basics of sintering, including diffusion mechanisms, control parameters, and vapor pressure effects on curved surfaces.

Nonlinear Curved Beams Log in to Mediaspace to watch this video

Covers the mechanics of slender structures, focusing on nonlinear curved beams.

Curvature and Oriented Curvature Log in to Mediaspace to watch this video

Explores the concepts of curvature, oriented curvature, and inflection points in regular curves.

Beam Bending II Log in to Mediaspace to watch this video

Explores the relationship between moment, curvature, and deflection in beam bending scenarios, emphasizing the consideration of shear forces and deformations.

Surface Tension and Wetting: Solid/Liquid/Gas Interfaces Log in to Mediaspace to watch this video

Explores surface tension, wetting, and the law of Laplace at interfaces.

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