Lectures related to Continuum Mechanics: Governing Equations

Linear Momentum Conservation and Stress in Continuum

Explores the conservation of linear momentum and stress in a continuum, focusing on governing equations and constitutive laws.

Continuum Mechanics: Conservation Laws, Tensor Objects, and Fluid Dynamics

Covers conservation laws, tensor objects, and fluid dynamics in Continuum Mechanics.

Continuum Mechanics: Forces and Deformation

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

Angular Momentum Balance in Continua

Explores stress tensor symmetry through angular momentum balance in continua, covering topics like energy conservation and constitutive laws.

Continuum Mechanics: Conservation Laws and Kinematics

Introduces continuum mechanics, focusing on conservation laws and kinematics for continuous media.

Continuum Mechanics: Newton's Laws and Stress Tensor Symmetry

Discusses Newton's third law, stress tensor symmetry, and the governing equations in continuum mechanics.

Linear Elasticity in 3D: Beam Bending

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

Stress Tensor and Transformation Laws in Continuum Mechanics

Covers stress tensors, their components, and transformation laws in continuum mechanics.

Stress Components & Transformation of Tensors

Covers stress components, tensor transformation, and invariants in continuum mechanics.

Continuum Mechanics: Stress and Tensor Analysis

Provides an overview of continuum mechanics, focusing on stress tensor analysis and transformation laws in material behavior under stress.

Continuum Mechanics: Tensor Analysis and Kinematics

Covers tensor analysis, kinematics, and fluid mechanics in continuum mechanics.

Linear Momentum Balance in Continuum Mechanics

Covers the evaluation of linear momentum balance in continua, focusing on stress vectors and tensors, and deriving the governing equations for momentum conservation.

Continuum Mechanics: Forces and Motion

Covers the governing equations for forces and motion in continua, including stress, energy conservation, solid deformation, and fluid motion.

Continuum Mechanics: Theory and Applications

Explores continuum mechanics, covering laws of thermodynamics, stress analysis, energy conservation, constitutive laws, and material response.

Structural Mechanics: Beam Bending and Boundary Conditions

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

Fluid Dynamics: Navier-Stokes Equations

Explores fluid dynamics, covering Navier-Stokes equations, momentum conservation, stresses, and dimensional analysis.

Deformation and Strain Tensors

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

3D Linear Elasticity & Beams

Introduces 3D linear elasticity, beams, dimensional analysis, and mechanics of slender structures.

Theory of Elasticity

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

Mechanics of Slender Structures: Final Review and Overview

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