Shells I

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Related lectures (30)

Covariant Derivatives and Christoffel Symbols

Covers accelerated and inertial coordinate systems, Jacobian, volume elements, covariant derivatives, Christoffel symbols, Lorentz case, and metric tensor properties.

Hyperbolic Geometry

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Gaussian Curvature and Geodesics

Explores the derivative of curve lengths, fixed-end deformations, geodesics, surface point typologies, and sphere parametrization.

Curves with Poritsky Property and Liouville Nets

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Curves in the Oriented Plane

Explores curves in the oriented plane, discussing orientation, vector spaces, equivalence relations, and curvature of regular curves.

Developable Surfaces and Parametrization

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Tensors and Lorentz Transformations

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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.

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

Covers thin pressure vessels, differential geometry of surfaces, and plate buckling theories.

Differential Geometry of Surfaces Log in to Mediaspace to watch this video

Covers linear pressure vessels and the basics of differential geometry of surfaces, including covariant and contravariant base vectors.

Differential Geometry of Surfaces Log in to Mediaspace to watch this video

Covers the fundamentals of differential geometry of surfaces, including the equilibrium of shells, pressure vessels, and the curvature of surfaces.

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.

Linear Shell Theory: Equilibrium Equations Log in to Mediaspace to watch this video

Covers the dimensional reduction of strain energy from 3D to 2D and linear shell theory equilibrium equations.

Gaussian Curvature in Plates Log in to Mediaspace to watch this video

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

Surfaces with Variable Curvature Log in to Mediaspace to watch this video

Explores surfaces with variable curvature, discussing their construction and properties.

Geometric Surfaces: Paraboloids and Hyperboloids in Architecture Log in to Mediaspace to watch this video

Explores the geometric properties of paraboloids and hyperboloids in architecture, emphasizing their design implications and practical applications.

Plates II: Föppl-von Kármán Equations Log in to Mediaspace to watch this video

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

Differential Geometry: Surfaces Log in to Mediaspace to watch this video

Explores the differential geometry of parametric surfaces, covering tangent space, normal curvature, principal curvatures, and asymptotic curves.

Linear Shell Theory: Equilibrium and Energy Log in to Mediaspace to watch this video

Covers the expression of the Kirchhoff-Saint Venant energy in a covariant setting and explores equilibrium equations for spherical shells and linear shell theory.

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