Lectures related to Shells III: Nonlinear Theory and Pressure Buckling

Shells III: Nonlinear Theory and Zoelly's Solution

Explores the nonlinear theory of spherical shells and Zoelly's solution for pressure buckling.

Explores Reissner's solution for shells, the DMV theory, and Zoelly's solution for pressure buckling.

Mechanics of Slender Structure: Shells III

Explores the nonlinear theory of spherical shells, including Reissner's solution and Zoelly's solution for pressure buckling.

Linear Shell Theory: Equilibrium Equations

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

Linear Shell Theory: Equilibrium and Energy

Covers the expression of the Kirchhoff-Saint Venant energy in a covariant setting and explores equilibrium equations for spherical shells and linear shell theory.

Differential Geometry of Surfaces

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

Physical Meaning of Terms in Acoustic Waves

Explores the physical interpretation of terms in acoustic wave equations and the balance between wave steepening and linear dispersion.

Shells I: Mechanics of Slender Structures

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

Differential Forms on Manifolds

Introduces differential forms on manifolds, covering tangent bundles and intersection pairings.

Plasma Instabilities: Microinstabilities in Magnetized Plasmas

Explores microinstabilities in magnetized plasmas, emphasizing drift waves and resonant wave-particle interactions.

Resonators: Coupling and Nonlinearity

Explores resonator coupling, eigenvalues, and nonlinearity origins, including built-in tension effects.

Christoffel Symbols and Gravity Before Einstein

Introduces Christoffel symbols and gravity concepts before Einstein, discussing mathematical tensors and the Nobel Prize in Physics.

Shells I

Covers linear pressure vessels, thin shells, and critical buckling pressure, emphasizing the dimensional reduction from 3D to 2D.

Solving unbounded PDE's using Fourier Transforms and Convolution: Obtaining the d'Alembert solution of the wave equation

Explores elementary properties of Fourier Transforms, convolution, Parseval's Theorem, and the d'Alembert solution of the wave equation using Fourier Transforms and convolution.

Structural Mechanics: Beam Bending and Boundary Conditions

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

Ball Rolling on Hemisphere

Analyzes the motion of a ball on a hemisphere surface with forces and equations of motion.