Lectures related to Deformation and Rotation

Finite & Infinite Deformation: Key Distinction

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

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

Structural Mechanics: Beam Bending and Boundary Conditions

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

Relative Deformation in 3D: Strain Matrix

Explores relative deformation in 3D through strain matrix and displacement gradient, emphasizing constraints, stress-strain relations, and equilibrium equations.

Generalized Hooke Law: Deformation and Stiffness Matrices

Explores the Generalized Hooke Law, stiffness matrices, and deformation effects in materials.

Continuum Mechanics: Kinematics and Deformation Analysis

Covers kinematics and deformation in continuum mechanics, focusing on displacement vectors and the deformation gradient tensor.

Continuum Mechanics: Forces and Deformation

Covers the basics of continuum mechanics, including forces transmission, energy conservation, and body motion geometry.

Nonlinear Beam Theory: Mechanics of Slender Structure

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

Nonlinear beam theory

Covers strain-displacement relations, equilibrium equations, and energy functional in nonlinear beam theory with small strain and moderate rotation.

Theory of Elasticity

Explores the theory of elasticity, including Hooke's law, strain tensors, stress tensor, and thermodynamics of deformation.

Polar Decomposition Theorem

Explains the Polar Decomposition Theorem, which isolates stretching from rotation to prevent stress induction in the body.

Linear Elasticity in 3D: Beam Bending

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

Deformation Analysis: Small Strain and Kinematics

Explores small strain theory, kinematics, and compatibility conditions in solid mechanics.

Linear Elasticity: 3D

Covers linearity between stress and strain in 3D and isotropic linear elasticity equations.

Geometrically Necessary Dislocations in Materials

Explains geometrically necessary dislocations in materials and their role in reducing work hardening.

Inviscid Flows: Understanding Fluid Dynamics

Explores inviscid flows, Reynolds number importance, linear deformations, and volume change in fluid dynamics.

Elastic Deformation: Material Properties

Explores material properties, stress, strain, and deformation gradient in elastic deformation.

Elasticity: Deformation and Strain

Explores stress, strain, equilibrium, and Hooke's law in elasticity.

Relative Deformations in 3D

Explores normal and shear strains, displacement fields, and the matrix of relative strains in 3D.

Continuum Mechanics: Forces and Deformation

Explores the laws of dynamics, stress, energy conservation, and deformation in continuum mechanics.