Mechanics of slender structures
ME-411
Video archive of Lectures and Pre-Studios (MediaSpate)
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ME-411 Mechanics of Slender Structures (Fall 2024)
ME-411 (Fall 2023) Lecture 13: Final Overview and Review of the Course
12.12.2024, 12:19
ME-411 (Fall 2024) Lecture 12: Shells III (extra material)
28.11.2024, 15:28
* Point indentation of shells (Reissner's solution)
* A nonlinear theory of (spherical) shells: Donnel-Mushtari-Vlasov (DMV)
* Pressure buckling of a spherical shell (Zoelly's solution)
ME-411 (Fall 2024) Lecture 11: Shells II
28.11.2024, 15:20
* Expression of the Kirchhoff-Stain Venant energy in a covariant setting;
* Dimensional reduction for shells (3D-to-2D);
* Equilibrium equations for spherical shells: Linear shell theory;
ME-411 (Fall 2024) Lecture 10: Shells I
21.11.2024, 12:50
* Linear pressure vessels
* Differential geometry of surfaces: a brief primer
- covariant and contravariant base vectors
- first and second fundamental forms
- 3D metric tensor
ME-411 (Fall 2024) Lecture 09: Plates III
14.11.2024, 16:48
ME-411 (Fall 2024) Lecture 08: Plates II
07.11.2024, 15:29
* Framework for the theory of plates:
- Curvature tensor;
- Nonlinear component of strain;
- Bending and Stretching energies.
* Variation of bending and stretching energies.
* Föppl-von Kármán Equations (Equations of equilibrium)
Pre-studio 08a: Circular plate under distributed load (ME-411 Fall 2024)
06.11.2024, 15:17
ME-411 (Fall 2024) Lecture 07: Plates I
31.10.2024, 14:27
* Plates in pure bending: deformation, strain, stress;
* Total strain energy: in-plane stretching energy and out-of-plane bending energy;
* Wrinkling, an application.
ME-411 (Fall 2024) Lecture 06: Mechanics of Kirchhoff Rods II
17.10.2024, 13:56
How to use the Kirchhoff equations of rods. Examples (in 3D):
* Example of kinematics in 3D: Determine the shape of a rod, given the Darboux vector.
* Example of twisted solutions in the Kirchhoff equations: Determine the shape of a rod, given the boundary conditions.
ME-411 (Fall 2024) Lecture 05: Mechanics of Kirchhoff Rods I
10.10.2024, 17:50
* Differential geometry of curves
* Frénet-Serret frame
* Cosserat frame
* Darboux Vector
* Kirchhoff's equilibrium equations of rods
ME-411 (Fall 2024) Lecture 04: Nonlinear beam theory
03.10.2024, 14:09
* Strain-displacement relations for a nonlinear beam;
* Simplifications of the general theory;
* First-order constitutive relation for linear elastic behavior;
* Equations of equilibrium from variational methods;
* Small strain, moderate rotation for circular rings.
ME-411 (Fall 2024) Lecture 03: Calculus of Variations and Euler's Elastica
26.09.2024, 17:38
* Variational methods
* Calculus of variations with constraints
* Example: Equilibrium shape of a bent inextensible beam clamped at its ends
* Euler's Elastica
* Numerical methods and examples (the shooting method)
* Analytical methods for Euler's Elastica (elliptic integrals)
ME-411 (Fall 2024) Lecture 02: Dimensional Analysis & Scaling Laws
19.09.2024, 12:56
- Base dimensions and units
- Buckingham-Pi Theorem
- Summary of the recipe to solve a problem using dimensional analysis
- Physical similarity
- Scalings
ME-411 (Fall 2024) Lecture 01: Review - 3D Linear Elasticity & Beams
12.09.2024, 14:02
* Introduction to ME-411 and Logistics
* 3D Linear Elasticity (Review)
* Beams:
- internal loads
- bending
- torsion
Pre-Studio 11: Membrane theory of shells (ME-411 Fall 2024)
10.09.2024, 14:31
Pre-Studio 10: Cylinders: pressure and geometry (ME-411 Fall 2024)
10.09.2024, 14:31
Pre-studio 09: Buckling of plates (ME-411 Fall 2024)
10.09.2024, 14:31
Pre-Studio 08 - Extra: Notes on the derivation of boundary conditions (ME-411 Fall 2024)
10.09.2024, 14:31
Pre-Studio 07: Tearing of an adhesive thin film (ME-411 Fall 2024)
10.09.2024, 14:31
Pre-Studio 06: Mechanics of a helix under gravity (ME-411 Fall 2024)
10.09.2024, 14:31
Pre-Studio 05: Naturally curved hair in 2D (ME-411 Fall 2024)
10.09.2024, 14:31
Pre-Studio 04: Nonlinear beams: matched approximations (ME-411 Fall 2024)
10.09.2024, 14:30
Pre-Studio 03: Elasto-gravity bending (ME-411 Fall 2024)
10.09.2024, 14:30
Pre-Studio 02: Dimensional analysis and Scaling Laws (ME-411 Fall 2024)
10.09.2024, 14:30
Pre-Studio 01: Truss Structures and Beams (ME-411 Fall 2024)
06.09.2024, 17:13
ME-411 Mechanics of Slender Structures (Fall 2024)
ME-411 (Fall 2023) Lecture 13: Final Overview and Review of the Course
12.12.2024, 12:19
ME-411 (Fall 2024) Lecture 12: Shells III (extra material)
28.11.2024, 15:28
* Point indentation of shells (Reissner's solution)
* A nonlinear theory of (spherical) shells: Donnel-Mushtari-Vlasov (DMV)
* Pressure buckling of a spherical shell (Zoelly's solution)
ME-411 (Fall 2024) Lecture 11: Shells II
28.11.2024, 15:20
* Expression of the Kirchhoff-Stain Venant energy in a covariant setting;
* Dimensional reduction for shells (3D-to-2D);
* Equilibrium equations for spherical shells: Linear shell theory;
ME-411 (Fall 2024) Lecture 10: Shells I
21.11.2024, 12:50
* Linear pressure vessels
* Differential geometry of surfaces: a brief primer
- covariant and contravariant base vectors
- first and second fundamental forms
- 3D metric tensor
ME-411 (Fall 2024) Lecture 09: Plates III
14.11.2024, 16:48
ME-411 (Fall 2024) Lecture 08: Plates II
07.11.2024, 15:29
* Framework for the theory of plates:
- Curvature tensor;
- Nonlinear component of strain;
- Bending and Stretching energies.
* Variation of bending and stretching energies.
* Föppl-von Kármán Equations (Equations of equilibrium)
Pre-studio 08a: Circular plate under distributed load (ME-411 Fall 2024)
06.11.2024, 15:17
ME-411 (Fall 2024) Lecture 07: Plates I
31.10.2024, 14:27
* Plates in pure bending: deformation, strain, stress;
* Total strain energy: in-plane stretching energy and out-of-plane bending energy;
* Wrinkling, an application.
ME-411 (Fall 2024) Lecture 06: Mechanics of Kirchhoff Rods II
17.10.2024, 13:56
How to use the Kirchhoff equations of rods. Examples (in 3D):
* Example of kinematics in 3D: Determine the shape of a rod, given the Darboux vector.
* Example of twisted solutions in the Kirchhoff equations: Determine the shape of a rod, given the boundary conditions.
ME-411 (Fall 2024) Lecture 05: Mechanics of Kirchhoff Rods I
10.10.2024, 17:50
* Differential geometry of curves
* Frénet-Serret frame
* Cosserat frame
* Darboux Vector
* Kirchhoff's equilibrium equations of rods
ME-411 (Fall 2024) Lecture 04: Nonlinear beam theory
03.10.2024, 14:09
* Strain-displacement relations for a nonlinear beam;
* Simplifications of the general theory;
* First-order constitutive relation for linear elastic behavior;
* Equations of equilibrium from variational methods;
* Small strain, moderate rotation for circular rings.
ME-411 (Fall 2024) Lecture 03: Calculus of Variations and Euler's Elastica
26.09.2024, 17:38
* Variational methods
* Calculus of variations with constraints
* Example: Equilibrium shape of a bent inextensible beam clamped at its ends
* Euler's Elastica
* Numerical methods and examples (the shooting method)
* Analytical methods for Euler's Elastica (elliptic integrals)
ME-411 (Fall 2024) Lecture 02: Dimensional Analysis & Scaling Laws
19.09.2024, 12:56
- Base dimensions and units
- Buckingham-Pi Theorem
- Summary of the recipe to solve a problem using dimensional analysis
- Physical similarity
- Scalings
ME-411 (Fall 2024) Lecture 01: Review - 3D Linear Elasticity & Beams
12.09.2024, 14:02
* Introduction to ME-411 and Logistics
* 3D Linear Elasticity (Review)
* Beams:
- internal loads
- bending
- torsion
Pre-Studio 11: Membrane theory of shells (ME-411 Fall 2024)
10.09.2024, 14:31
Pre-Studio 10: Cylinders: pressure and geometry (ME-411 Fall 2024)
10.09.2024, 14:31
Pre-studio 09: Buckling of plates (ME-411 Fall 2024)
10.09.2024, 14:31
Pre-Studio 08 - Extra: Notes on the derivation of boundary conditions (ME-411 Fall 2024)
10.09.2024, 14:31
Pre-Studio 07: Tearing of an adhesive thin film (ME-411 Fall 2024)
10.09.2024, 14:31
Pre-Studio 06: Mechanics of a helix under gravity (ME-411 Fall 2024)
10.09.2024, 14:31
Pre-Studio 05: Naturally curved hair in 2D (ME-411 Fall 2024)
10.09.2024, 14:31
Pre-Studio 04: Nonlinear beams: matched approximations (ME-411 Fall 2024)
10.09.2024, 14:30
Pre-Studio 03: Elasto-gravity bending (ME-411 Fall 2024)
10.09.2024, 14:30
Pre-Studio 02: Dimensional analysis and Scaling Laws (ME-411 Fall 2024)
10.09.2024, 14:30
Pre-Studio 01: Truss Structures and Beams (ME-411 Fall 2024)
06.09.2024, 17:13