Gaussian Curvature in Plates

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Minimal Surfaces and Discrete Differential Geometry

Explores minimal surfaces, curvature, Laplace-Beltrami operator, numerical solutions, Laplacian smoothing, diffusion flow, and time integration.

Nonlinear beam theory

Covers strain-displacement relations, equilibrium equations, and energy functional in nonlinear beam theory with small strain and moderate rotation.

Beams under Flexure

Discusses stresses in beams under flexure, including shear forces and bending moments.

Nonlinear Curved Beams

Covers the mechanics of slender structures, focusing on nonlinear curved beams.

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.

Plates I: Deformation, Strain, Stress, and Wrinkling

Covers deformation, strain, stress, and wrinkling in plates under pure bending, exploring applications and bending stiffness.

Hyperbolic Geometry

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

Beams: Forces, Stresses, and Deformations

Analyzes beams, forces, stresses, deformations, curvature, deflection, and rigidity.

Riemann Tensor and Ricci Scalar

Covers the properties of the Riemann tensor and Ricci scalar in normal coordinates.

Curvature and Osculating Circle

Covers curvature, osculating circles, and the evolute of plane curves, with examples and equations.