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Course Co-ordinated by :
IIT Guwahati
Course Available from :
28-November-2016
NPTEL
Mechanical Engineering
Continuum Mechanics (Web)
Modules / Lectures
Tensor Algebra
Introduction to Continuum Mechanics
Vector and Vector Spaces
Index Notation and Conventions
The Second-Order Tensor
The Principal Invariants and the Inverse of Tensor
The Eigenvalues and Eigenvectors
The Skewsymmetric Tensor
Representation of the Orthogonal Tensor
Relation between Skewsymmetric and Orthogonal Tensors
The Symmetric Tensor
Positive Definite Tensor and the Polar Decomposition
The Isotropic Functions
Higher-Order Tensors
Exercise 1
Tensor Calculus
The Directional Derivative and the Fr´ehet Derivative
The Gradient, Divergence and Curl
The Time Derivative and Some Integral Theorems
Exercise 2
Kinematics
The Lagrangian and Eulerian Descriptions
The Strain and Stretch Tensors
Area and Volume Transformation
Material and Spatial Time Derivatives
The Rate of Deformation and Spin
The Reynolds’ Transport Theorem
The Vorticity and Circulation
Exercise 3
Balance Laws
Law of Conservation of Mass
The Laws of Dynamics and the CauchyaAZs Hypothesis
The Linear Momemntum Balance and the Cauchy Stress Tensor
The Angular Momentum Balance and the Properties of Cauchy Stress
The Equations of Motion in Lagrangian Description
The First Law of Thermodynamics
The Second Law of Thermodynamics
The Frame of Reference and the Transformation of Kinematical Quantities
The Principle of Frame-Indifference
Application of the Principle of Frame-Indifference to the First Law of Thermodynamics
Exercise 4
Constitutive Relations
Necessity of Constitutive Equations and the Principle of Material Frame-Indifference
Implications of the Principle of Material Frame-Indifference and the Material Symmetry
Thermomechanics of Elastic Solids
Linear Elasticity
Thermomechanics of Fluids
Linear Viscous Heat-Conducting Fluids
Thermomechanics of Incompressible Fluids
Exercise 5
Reference
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