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ME-411: Mechanics of slender structures

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Lectures in this course (96)

Dimensional Analysis and Scalings Log in to Mediaspace to watch this video

Covers fundamental concepts of dimensional analysis, physical similarity, and scalings, exploring the importance of expressing physical laws independently of units and the process of parameterizing problems.

Calculus of Variations and Euler's Elastica Log in to Mediaspace to watch this video

Explores the calculus of variations and Euler's Elastica in the context of beam equilibrium and inextensible elastic curves under large rotations.

Elasto-gravitary Bending: Mechanics of Slender Structure Log in to Mediaspace to watch this video

Explores large deformations of inextensible sheets bent under self-weight and their equilibrium shapes under gravity.

Calculus of Variations and Euler's Elastica Log in to Mediaspace to watch this video

Explores variational methods, Euler's Elastica, numerical and analytical methods, and the buckling of slender structures.

Nonlinear Beam Theory: Curved Beams Mechanics Log in to Mediaspace to watch this video

Covers the theory of nonlinear curved beams, discussing inextensible strains, finite rotations, and the exact inextensionable theory.

Truss Structures and Beams Log in to Mediaspace to watch this video

Covers the analysis of internal loads in truss structures and beams, including a two-dimensional model of a crane structure and modes of failure.

3D Linear Elasticity & Beams Log in to Mediaspace to watch this video

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

Mechanics of Kirchhoff Rods II Log in to Mediaspace to watch this video

Explores the mechanics of Kirchhoff rods, focusing on determining rod shapes in 3D and twisted solutions.

Mechanics of Helix under Gravity: Slender Structure Log in to Mediaspace to watch this video

Explores the equilibrium shapes of helical thin rods under weak gravity.

Plates I: Deformation, Strain, Stress, Wrinkling Log in to Mediaspace to watch this video

Covers the deformation, strain, and stress in plates under pure bending, as well as the total strain energy related to in-plane stretching and out-of-plane bending energy.

Untitled Log in to Mediaspace to watch this video

Circular Plate: Displacement Behavior and Simplification of Equations Log in to Mediaspace to watch this video

Studies the displacement behavior of a circular plate under distributed load.

Gaussian Curvature in Plates Log in to Mediaspace to watch this video

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

Plates III: Mechanics of Slender Structure Log in to Mediaspace to watch this video

Covers Föppl-von Kármán equations, Airy potential, plate theory simplifications, and buckling of plates.

Buckling of Plates in Mechanics of Slender Structures Log in to Mediaspace to watch this video

Covers critical force, post-buckling behavior, bending energy, strain tensor, stretching energy, and shear buckling.

Cylinders: Pressure and Geometry Log in to Mediaspace to watch this video

Explores cylindrical pressure vessels, surfaces parametrization, and geometrical properties computation.

Differential Geometry of Surfaces Log in to Mediaspace to watch this video

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

Dimensional Analysis & Scaling Laws Log in to Mediaspace to watch this video

Covers dimensional analysis, physical similarity, and structural mechanics, emphasizing the importance of scaling laws in solving complex problems.

Shells II: Mechanics of Slender Structure Log in to Mediaspace to watch this video

Covers the expression of energy, dimensional reduction, equilibrium equations, and the relationship between covariant and contravariant components in shell mechanics.

Membrane Theory of Shells Log in to Mediaspace to watch this video

Explores membrane forces in thin shell structures under various loadings, focusing on cylindrical and spherical shell roofs.

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