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Civil Engineering
Advanced Solid Mechanics (Web)
Syllabus
Co-ordinated by :
IIT Madras
Available from :
2013-03-20
Lec :
1
Modules / Lectures
1. Introduction
1.1 Basic Concepts in Mechanics
1.2 Basic Equations in Mechanics
1.3 Classification of the Response of Materials
1.4 Solution to Boundary Value Problems
1.5 Summary
2. Mathematical Preliminaries
2.1 Overview
2.2 Algebra of vectors
2.3 Algebra of second order tensors
2.4 Algebra of fourth order tensors
2.5 Eigenvalues, eigenvectors of tensors
2.6 Transformation laws
2.7 Scalar, vector, tensor functions
2.8 Gradients and related operators
2.9 Integral theorems
2.10 Summary
2.11 Self-Evaluation
3. Kinematics
3.1 Overview
3.2 Body
3.3 Deformation Gradient
3.4 Lagrangian and Eulerian description
3.5 Displacement, velocity and acceleration
3.6 Transformation of curves, surfaces and volume
3.7 Properties of the deformation tensors
3.8 Strain Tensors
3.9 Normal and shear strain
3.10 Homogeneous Motions
3.11 Compatibility condition
3.12 Summary
3.13 Self-Evaluation
4. Traction and Stress
4.1 Overview
4.2 Traction vectors and stress tensors
4.3 Normal and shear stresses
4.4 Principal stresses and directions
4.5 Stresses on a Octahedral plane
4.6 Examples of state of stress
4.7 Other stress measures
4.8 Summary
4.9 Self-Evaluation
5. Balance Laws
5.1 Overview
5.2 System
5.3 Conservation of Mass
5.4 Conservation of momentum
5.5 Summary
5.6 Self-Evaluation
6. Constitutive Relations
6.1 Overview
6.2 Definition of elastic process
6.3 Restrictions on constitutive relation
6.4 Isotropic Hooke’s law
6.5 Material parameters
6.6 Restriction on material parameters
6.7 Internally constraint materials
6.8 Orthotropic Hooke’s law
6.9 Summary
6.10 Self-Evaluation
7. Boundary Value Problem: Formulation
7.1 Overview
7.2 Formulation of boundary value problem
7.3 Techniques to solve boundary value problems
7.4 Illustrative example
7.5 General results
7.6 Summary
7.7 Self-Evaluation
8. Bending of Prismatic Straight Beams
8.1 Overview
8.2 Symmetrical bending
8.3 Asymmetrical bending
8.4 Shear center
8.5 Summary
8.6 Self-Evaluation
9. End Torsion of Prismatic Bars
9.1 Overview
9.2 Twisting of thick walled closed section
9.3 Twisting of solid open section
9.4 Twisting of hollow section
9.5 Summary
9.6 Self-Evaluation
10. Bending of Curved Beams
10.1 Overview
10.2 Winkler-Bach formula for curved beams
10.3 2D Elasticity solution for curved beams
10.4 Summary
10.5 Self-Evaluation
11. Beam on Elastic Foundation
11.1 Overview
11.2 General formulation
11.3 Example 1: Point load
11.4 Example 2: Concentrated moment
11.5 Example 3: Uniformly distributed load
11.6 Summary
11.7 Self-Evaluation
Bibliography
Bibliography
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