Plates II: Föppl-von Kármán Equations

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Explores deformation and strain tensors, Lagrange representation, elasticity theory, and the divergence theorem.

Covers the framework for plates, bending and stretching energies, and Föppl-von Kármán Equations, exploring mean and Gaussian curvatures.

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

Explores the moment-curvature relation for beams, emphasizing stress distribution and typical boundary conditions.

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

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

Explores 3D elasticity, beam bending, and buckling phenomena in slender structures.

Covers the main learning objectives of ME-411, focusing on dimensional analysis, scalings, and mechanical elements.

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

Covers advanced topics in beam bending, stress tensors, elasticity, and Atomic Force Microscopy.

Covers the mechanics of plates, focusing on curvature, bending, and stretching energy.

Covers linear elasticity in 3D, focusing on beam bending and stress-strain behavior of materials.

Covers linear and membrane theories of pressure vessels, differential geometry of surfaces, and the reduction of dimensionality from 3D to 2D.

Covers the review of 3D Linear Elasticity and beams, focusing on mechanics of slender structures.

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

Covers the dimensional reduction in slender structures, constitutive laws, and mechanics of plates and shells.

Covers the deformation of plates in pure bending, total strain energy, and applications like wrinkling.

Covers curvature, osculating circles, and the evolute of plane curves, with examples and equations.

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

Explores linear elasticity, stress-strain relationships, and beam bending kinematics with a focus on stress tensors and internal forces.

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