Lecture

Shells I: Mechanics of Slender Structure

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Covers linear pressure vessels, thin shells, and critical buckling pressure, emphasizing the dimensional reduction from 3D to 2D.

Shells I: Mechanics of Slender Structures

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

Differential Geometry of Surfaces

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

Differential Geometry of Surfaces

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

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

Linear Shell Theory: Equilibrium Equations

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

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

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

Conformity and Compliancy in Geometry

Explores conformity and compliancy in geometry, emphasizing angle preservation and function conditions.

Gaussian Curvature and Geodesics

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

Linear Shell Theory: Equilibrium and Energy

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

Closed Surfaces and Integrals

Explains closed surfaces like spheres, cubes, and cones without covers, and their traversal and removal of edges.

Shells II: Mechanics of Slender Structure

Covers the expression of energy, dimensional reduction, equilibrium equations, and the relationship between covariant and contravariant components in shell mechanics.

Tensors and Lorentz Transformations

Covers tensors, Lorentz transformations, and electrodynamics in relativistic notation.

Gaussian Curvature in Plates

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

Mechanics of Slender Structure

Covers the expression of the Kirchhoff-St. Venant energy in a covariant setting and the equilibrium equations for spherical shells, among other topics.

Surfaces in Space

Explores surfaces in space, including paraboloids, spheres, and hyperboloids, and their equations and intersections.

Mechanics of Kirchhoff Rods I

Covers the mechanics of slender structures, focusing on exact kinematics and equilibrium equations of rods.

Geometric Surfaces: Paraboloids and Hyperboloids in Architecture

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

Surface Integrals: Regular Parametrization

Covers surface integrals with a focus on regular parametrization and the importance of understanding the normal vector.