[
next
] [
tail
] [
up
]
Contents
1
Mathematical Preliminaries
1.1
A vector and its representation: NPTEL link
1.2
Dot-product, Cross-product and Tensor-product of two vectors: NPTEL link
1.3
Second order tensors and their representation: NPTEL link
1.4
Multiplying a second order tensor with a vector: dot product and tensor product: NPTEL link
1.5
Multiplying two second order tensors: single-contraction, double-contraction and tensor product: NPTEL link
1.6
Calculus of tensors: divergence and gradient
1.7
Rotation tensor: NPTEL link
1.8
Solved examples
1.9
Objective questions to recall concepts
1.10
Questions to practise
2
On Traction Vector, Stress Tensor and Stress Matrix
2.1
Definition of traction vector: NPTEL link
2.2
Relating traction on different planes at a point: NPTEL link
2.3
Stress Tensor: NPTEL link
2.4
Stress matrix as a representation of stress tensor: NPTEL link
2.5
Transformation of Stress matrix: NPTEL link
2.6
Solved examples
2.7
Objective questions to recall concepts
2.8
Questions to practise
3
Stress Equilibrium Equations
3.1
Linear momentum balance: NPTEL link
3.2
Angular momentum balance: NPTEL link
3.3
Derivation of traction boundary condition: NPTEL link
3.4
Solved examples
4
Maximizing Normal and Shear components of Traction
4.1
Finding principal planes: NPTEL link
4.2
Properties of Principal Planes: NPTEL link
4.3
Maximizing shear component of traction: NPTEL link
4.4
Mohr’s circle: NPTEL link
4.4.1
Trigonometric formulas for normal and shear components of traction on arbitrary planes: NPTEL link
4.4.2
A graphical representation of the derived formulas: NPTEL link
4.4.3
Other conclusions that can be drawn using Mohr’s circle: NPTEL link
4.5
Mohr’s stress plane: NPTEL link
4.6
Stress invariants: NPTEL link
4.7
Hydrostatic and deviatoric parts in stress tensor: NPTEL link
4.8
Solved examples
5
On Strain Tensor and the associated Strain Matrix
5.1
Longitudinal strain in a general body: NPTEL link
5.2
Reference and deformed configurations: NPTEL link
5.3
Relating line elements in reference and deformed configurations: NPTEL link
5.4
Formula for longitudinal strain: NPTEL link
5.5
Formula for shear strain: NPTEL link
5.6
Formula for volumetric strain: NPTEL link
5.7
Strain tensor: NPTEL link
5.8
Local rotation tensor: NPTEL link
5.9
Strain compatibility conditions: NPTEL link
5.10
Similarity between stress and strain tensors: NPTEL link
5.11
Solved examples
6
Stress - Strain relation
6.1
Linear stress-strain relation: NPTEL link
6.2
Independent components in stiffness tensor: NPTEL link
6.3
Voigt Notation: NPTEL link
6.4
Isotropic materials: NPTEL link
6.5
On Young’s modulus, shear modulus and Poisson’s ratio: NPTEL link
6.6
Isotropic thermoelasticity: NPTEL link
6.7
Anisotropic materials: NPTEL link
6.8
Inelastic behavior: NPTEL link
6.9
Solved examples
7
Solving Axisymmetric Problems: Extension, Torsion and Inflation
7.1
Cylindrical coordinate system: NPTEL link
7.2
LMB Formulation:NPTEL link
7.2.1
Force on \(+z\) and \(-z\) planes: NPTEL link
7.2.2
Force on \(+r\) and \(-r\) planes: NPTEL link
7.2.3
Force on \(+\theta \) and \(-\theta \) planes: NPTEL link
7.3
Strain matrix in cylindrical coordinate system: NPTEL link
7.3.1
Physical significance of strain components: NPTEL link
7.4
Relating stress and strain in cylindrical coordinate system: NPTEL link
7.5
Extension, torsion and inflation of cylinders: NPTEL link
7.5.1
Simplification using physical considerations: NPTEL link
7.5.2
Simplified equilibrium equations: NPTEL link
7.6
Solving the simplified equations: NPTEL link
7.6.1
Relating axial force and axial strain: NPTEL link
7.6.2
Relating torque and end-to-end rotation: NPTEL link
7.6.3
Thin tube approximation for pressurized tubes with application to pressure vessels
7.7
Solved examples
8
Bending of Beams
8.1
Pure bending of beams: NPTEL link
8.2
Non-uniform bending of beams: NPTEL link
8.2.1
Variation of \(\tau _{yx}\) in the cross-sectional plane: NPTEL link
8.3
Bending of unsymmetrical beams: NPTEL link
8.3.1
Pure bending: NPTEL link
8.3.2
Non-uniform bending of thin and open cross-sections: NPTEL link
8.4
Concept of shear center: NPTEL link
8.5
Solved examples
9
Theory of Beams
9.1
Motivation for beam theory: NPTEL link
9.2
Euler-Bernouli Beam Theory: NPTEL link
9.3
Timoshenko Beam Theory: NPTEL link
9.3.1
When to use EBT/TBT?: NPTEL link
9.4
Buckling of Beams: NPTEL link
9.5
Solved examples
10
Energy Methods
10.1
Linearity and superposition of elasticity equations: NPTEL link
10.2
Energy stored in the body due to a applied force: NPTEL link
10.3
Reciprocal relation: NPTEL link
10.3.1
Maxwell-Betti-Rayleigh reciprocal theorem: NPTEL link
10.4
Generalized forces and generalized displacements: NPTEL link
10.5
Castigliano’s First Theorem: NPTEL link
10.6
Application of Castigliano’s theorem for solving beam problems: NPTEL link
10.7
Solved examples
11
Theory of Failure
11.1
Various theories of failure
11.2
Solved examples
[
next
] [
front
] [
up
]