ME-411: Mechanics of slender structures

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Lectures in this course (96)

Euler's Elastica: Mechanics of Slender Structures

Covers the total energy functional of bending and gravitational contributions in slender structures.

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Dimensional Analysis and Scalings

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.

Elasto-gravity Bending: Mechanics of Slender Structure

Explores the deformations of an inextensible sheet bent under self-weight and its equilibrium shapes under gravity.

Nonlinear Curved Beams

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

Nonlinear Beam Theory: Mechanics of Slender Structure

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

Calculus of Variations and Euler's Elastica

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

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

Mechanics of Slender Structure: Loaded Beam Approximations

Covers matched approximations of a loaded beam, focusing on strain approximation and constitutive models.

Mechanics of Slender Structure: Matched Approximations

Covers the analysis of slender structures under different approximations, including inextensible, extensible, and hybrid cases.

Kirchhoff Rods: Equilibrium Equations and Kinematics

Covers the kinematics and equilibrium equations of Kirchhoff rods, discussing geometric coupling between bending and twist.

Calculus of Variations and Euler's Elastica

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

Mechanics of Kirchhoff Rods I

Covers the mechanics of slender structures, focusing on exact kinematics and equilibrium equations of rods.

Nonlinear Beam Theory: Curved Beams Mechanics

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

Naturally Curved Hair in 2D

Explores the shape of naturally curved hair in 2D under gravity.

Naturally Curved Hair Mechanics

Delves into the mechanics of naturally curved hair, exploring its shape under gravity and the effects of weak and strong gravity.

Kirchhoff Rods: Kinematics and Twisted Solutions

Explores the kinematics of 3D structures and twisted solutions in rod mechanics, including the mechanics of knots.

Mechanics of Kirchhoff Rods II

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

Matched Approximations of a Clamped Filament

Covers the derivation of equations for the equilibrium of an inextensible string and the development of a hybrid model.

Mechanics of Helix under Gravity: Slender Structure

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

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