Linear Shell Theory: Equilibrium and Energy

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

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.

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.

Linear Momentum Conservation and Stress in Continuum

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

Shells I

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

Structural Mechanics: Beam Bending and Boundary Conditions

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

Mechanics of Slender Structures: Final Review and Overview

Covers the main learning objectives of ME-411, focusing on dimensional analysis, scalings, and mechanical elements.

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.

Special Relativity

Covers the main points of special relativity, including symmetries, transformations, 4-vectors, Maxwell equations, and proper time.