Lectures related to Buckling of Plates in Mechanics of Slender Structures

Structural Mechanics: Beam Bending and Boundary Conditions

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

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

Explores the theory of plates, including bending and stretching energies, and the Föppl-von Kármán Equations.

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

Buckling of Plates: Post-Buckling Deformation Analysis

Investigates post-buckling deformation of plates, deriving bending and stretching energies.

Trigonometric Equations: Sinus and Cosinus

Covers the resolution of simple trigonometric equations involving sinus and cosinus functions.

Trigonometric Formulas: Addition Theorem

Explores trigonometric addition theorem, double angles, and tangent properties.

Deformation and Strain Tensors

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

Buckling of Plates: Post-Buckling Deformation Behavior Investigation

Investigates post-buckling deformation behavior, bending energy derivation, and in-plane stretching energy considerations in square plates.

Trigonometric Functions: Sin and Cos

Covers the definition of sine and cosine functions, their graphs, and notable points.

Cosine Theorem

Explores the cosine theorem in triangles, analyzing side and angle relationships.

Triangle Resolution: Trigonometric Functions

Covers the resolution of triangles using trigonometric functions and the importance of cosine and sine theorems.

Symmetries of Trigonometric Functions

Explores the symmetries of trigonometric functions, periodicity, and properties of even and odd functions.

Wave Equations: Vibrating String

Explores the wave equation for a vibrating string and its numerical solution using finite difference formulas and the Newmark scheme in MATLAB/GNU Octave.

Nonlinear Beam Theory: Mechanics of Slender Structure

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

Trigonometric Functions: Arcsin and Arccos

Covers the definitions and properties of arcsin and arccos functions.

Continuity of Trigonometric Functions

Explores the continuity of trigonometric functions and demonstrates specific limits and propositions related to them.

Mechanics of Kirchhoff Rods: Finite Strain and Rotation Theory

Explores the theory of finite strain and rotation in Kirchhoff rods, covering inextensible strains, finite rotations, and equilibrium.

Gaussian Curvature and Geodesics

Explores the derivative of curve lengths, fixed-end deformations, geodesics, surface point typologies, and sphere parametrization.

Finite & Infinite Deformation: Key Distinction

Explains the geometric interpretation of eigen vectors and values in material deformation.