Plates III: Mechanics of Slender Structures

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

Explores the differential geometry of parametric surfaces, covering tangent space, normal curvature, principal curvatures, and asymptotic curves.

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

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

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

Explores Föppl-von Kármán plate theory, including buckling equations and an example of plate compression.

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

Covers global relief indicators, altitude models, slope, orientation, curvature, and morphological indices for terrain description.

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

Explores surfaces with constant curvature, emphasizing the significance of minimal oriented radius and the properties of pseudo-spheres.