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Lecture
Cylinders: Pressure and Geometry
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Related lectures (46)
Geometric Principles in Architecture: Hyperboloids and Paraboloids
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Discusses geometric principles in architecture, focusing on hyperboloids and paraboloids and their applications in design and structural engineering.
Surfaces with Constant Curvature
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Explores surfaces with constant curvature, emphasizing the significance of minimal oriented radius and the properties of pseudo-spheres.
Hyperboloid Surfaces: Sections and Developability
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Delves into the properties of hyperboloid surfaces and their sections, emphasizing developability and curvature.
Normal Curvature
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Explores normal curvature on a surface, discussing oriented curvature, existence proofs, and elimination methods for finding curvature.
Differential Geometry: Surfaces
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Explores the differential geometry of parametric surfaces, covering tangent space, normal curvature, principal curvatures, and asymptotic curves.
Nonlinear Beam Theory: Mechanics of Slender Structure
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Covers strain-displacement relations, simplifications, constitutive relations, equilibrium equations, and circular rings.
Minimal Surfaces and Discrete Differential Geometry
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Explores minimal surfaces, curvature, Laplace-Beltrami operator, numerical solutions, Laplacian smoothing, diffusion flow, and time integration.
Curvature and Oriented Curvature
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Explores the concepts of curvature, oriented curvature, and inflection points in regular curves.
Introduction to Arrows and Differential Relations
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Introduces arrows in beams and how to calculate deflection using differential relations.
Sintering Fundamentals: Basics of Solid State Grain Growth
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Explores the basics of sintering, including diffusion mechanisms, control parameters, and vapor pressure effects on curved surfaces.
Nonlinear Curved Beams
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Covers the mechanics of slender structures, focusing on nonlinear curved beams.
Shells I: Mechanics of Slender Structures
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Covers linear and membrane theories of pressure vessels, differential geometry of surfaces, and the reduction of dimensionality from 3D to 2D.
Linear Shell Theory: Equilibrium Equations
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Covers the dimensional reduction of strain energy from 3D to 2D and linear shell theory equilibrium equations.
Beam Bending II
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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
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Explores surface tension, wetting, and the law of Laplace at interfaces.
Plates III: Buckling Theory and Applications
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Explores Föppl-von Kármán plate theory, including buckling equations and an example of plate compression.
Plastic Hinge Analysis: Seismic Engineering
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Discusses plastic hinge analysis in seismic engineering and key seismic design concepts.
Helix Trajectory and Coordinate Systems
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Covers the trajectory and speed of a ball on a helix using cylindrical coordinates.
Plates III: Mechanics of Slender Structure
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Covers Föppl-von Kármán equations, Airy potential, plate theory simplifications, and buckling of plates.
Coordinate Systems: Polar and Spherical
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Covers polar and spherical coordinate systems, position vectors, equations of motion, and Frenet frame concepts.
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