Beams: Forces, Stresses, and Deformations

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Nonlinear Beam Theory: Mechanics of Slender Structure

Covers strain-displacement relations, simplifications, constitutive relations, equilibrium equations, and circular rings.

Plates II: Mechanics of Slender Structures

Explores the mechanics of slender structures, discussing plate evaluation, bending energy, and curvature tensors.

Plates II: Föppl-von Kármán Equations

Explores the theory of plates, including bending and stretching energies, and the Föppl-von Kármán Equations.

Differential Geometry: Parametric Curves & Surfaces

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

Minimal Surfaces and Discrete Differential Geometry

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

Gothic Surfaces: Curvature, Development, and Stereotomy

Delves into the geometric principles of Gothic architecture, focusing on surface curvature and stereotomy techniques.

Beam Bending: Theory and Applications

Covers the theory of beam bending, historical figures, moment-curvature relation, and implications of distributed loads.

Beam Bending II

Explores the relationship between moment, curvature, and deflection in beam bending scenarios, emphasizing the consideration of shear forces and deformations.

Helical Curves: Theory and Applications

Explores the theory and applications of helical curves, focusing on circular helices with various parameters.

Hyperboloid Surfaces: Sections and Developability

Delves into the properties of hyperboloid surfaces and their sections, emphasizing developability and curvature.