Linear Shell Theory: Equilibrium and Energy

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

Deformation and Strain Tensors

Explores deformation and strain tensors, Lagrange representation, elasticity theory, and the divergence theorem.

Continuum Mechanics: Mass Conservation

Explores mass conservation in continuum mechanics, covering stress, dynamics, constitutive laws, and solid deformation.

Shells I: Mechanics of Slender Structure

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

3D Linear Elasticity & Beams

Covers 3D linear elasticity, stress, strain, beams' behavior under loads, and torsion.

Stress Components & Transformation of Tensors

Covers stress components, tensor transformation, and invariants in continuum mechanics.

Tensors and Lorentz Transformations

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

Differential Geometry of Surfaces

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

Plates II: Föppl-von Kármán Equations

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

Gaussian Curvature in Plates

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