Advanced Mechanics of Solids and Structures,

1. Stress
1.1 Definition of stress
1.2 Nomenclature of stresses – stress components of a point
1.3 Stress tensor – symmetry of stresses
1.4 Stresses components on an arbitrary plane ABC
1.5 Normal and shear stress on an arbitrary plane ABC
1.6 Stress vector transformation to a rotated coordinate system
1.7 Stress tensor transformation to a rotated coordinate system
Exercise 1
Exercise 2
1.8 Principal Stresses
1.9 Determination of the orientation l, m, n of the principal planes
1.10 Octahedral stresses
Exercise 3
1.11 Spherical and Deviatoric stress tensor
1.12 Plane stress: stress tensor in rotated coordinate system
Exercise 4
Exercise 5
Exercise 6
1.13 Differential equations of motion in cartesian coordinate system
1.14 Differential equations of motion in polar coordinate system
1.8 References

2. Strain
2.1 Definition of strain
2.1.1 Normal strain
2.1.2 Shear strain
2.2 Strain vector and strain tensor
2.2.1 Transformation of strain vectors
2.2.2 Transformation of strain tensors
2.2.3 Plane strain
2.3 Principal strains
2.4 Compatibility conditions of strains
2.5 Strain-displacement equations
2.6 NDT of strain measurements
2.7 Problems
2.8 References

3. Stress-strain relationships
3.1 Generalized Hooke’s law for isotropic materials
3.2 Strain energy density
3.3 Thermoelasticity
3.4 Problems
3.5 References

4. Mechanical behaviour of materials and material characterization
4.1 Stress-strain curve and basic mechanical properties of materials
4.2 Parameters affecting the stress-strain behaviour
4.2.1 Loading rate effect
4.2.2 Temperature effect
4.2.3 Surface quality effect
4.2.4 Specimen size effect
4.3 Material response in impact loading
4.4 Material response in high temperature – Creep
4.5 Material response in cyclic loading – Fatigue
4.6 Material hardness and hardness measurement
4.7 Corrosion, corrosion measurement, corrosion protection
4.8 Non-destructive evaluation of material properties
4.9 Problems
4.19 References

5. Inelastic material response and yield criteria
5.1 Types of inelastic response under mechanical stresses
5.2 Yield criteria for isotropic materials
5.2.1 Maximum principal stress criterion
5.2.2 Maximum principal strain criterion
5.2.3 Stain energy density criterion
5.2.4 Maximum shear stress criterion (Tresca criterion)
5.2.5 Distortional energy density criterion (von Mises criterion)
5.3 Problems
5.4 References

6. Beam theory – Bending and Torsion
6.1 Kirchhoff’s hypothesis for beam cross sections
6.2 Symmetric and nonsymmetric bending
6.3 Bending stresses of straight beams
6.3.1 Normal stresses
6.3.2 Shear stress
6.3.3 Neutral line
6.4 Deflection of straight beams
6.5 Curved beams
6.5.1 Circumferential stresses
6.5.2 Radial stresses
6.5.3 Bleich’s factors
6.5.4 Deflections
6.5.5 Closed rings
6.6 Torsion of beams with compact cross section
6.7 Torsion of hollow thin-walled beams with closed cross section
6.8 Torsion of hollow thin-walled beams with open cross section
6.9 Shear center
6.10 Torsion of beams with composite cross section
6.11 Bending-Torsion interaction
6.12 Elastoplastic bending – Residual stresses
6.13 Problems
6.14 References

7. Energy methods
7.1 Thermodynamics of material response under mechanical loads
7.2 Principle of minimum potential energy
7.3 Stain energy of members under axial, shear, bending and torsion loading
7.4 Castigliano’s theorem
7.5 Applications on statically indeterminate beams, trusses, and frames
7.6 Problems
7.7 References

8. Beams on elastic foundation and application in thin-walled cylinders
8.1 Infinite beams on elastic foundation under concentrated load
8.2 Infinite beams on elastic foundation under distributed load
8.3 Semi-infinite and finite beams on elastic foundation
8.4 Short beams on elastic foundation
8.5 The method of integral transforms
8.6 Application in thin-walled cylinders
8.7 Problems
8.8 References

9. Flat plates
9.1 Kirchhoff’s assumption for plates
9.2 Equilibrium equations of stresses
9.3 Strain-displacement relations
9.4 Stress-strain relations
9.5 Boundary conditions
9.6 The biharmonic equation of plate bending
9.7 Westergaard approximate solution for rectangular plates
9.8 Circular plates
9.8.1 Symmetric bending of circular plates
9.8.2 Non-symmetric bending of circular plates
9.9 Problems
9.10 References

10. Plates on elastic foundation
10.1 Infinite plates on elastic foundation
10.2 Finite plates on elastic foundation
10.3 The method of integral transforms
10.4 Problems
10.5 References

11. Airy’s stress function – Stress concentration – Thick-walled cylinders
11.1 Equilibrium equations, compatibility conditions, and biharmonic equation
11.2 Stress concentration
11.2.1 Circular hole in infinite flat plate under in-plane loads
11.2.2 Elliptical hole in infinite flat plate under in-plane loads
11.2.3 Hole in finite flat plate under in-plane loads
11.2.4 Crack in infinite flat plate under in-plane loads
11.3 Thick-walled cylinders
11.3.1 Open cylinder
11.3.2 Cylinder with closed ends
11.3.3 Compound cylinder
11.3.4 Temperature effect
11.3.5 Rotating disks
11.4 Problems
11.5 References

12. Contact stresses
12.1 Deformation of contact surface
12.2 Fundamental equations of bodies under contact
12.3 Approximate results
12.4 Bodies in point contact
12.4.1 Contact between two spheres
12.4.2 Contact between a sphere and a flat or a curved surface
12.5 Bodies in line contact
12.5.1 Contact between two cylinders
12.5.2 Contact between a cylinder and a flat or a curved surface
12.6 Elastic half-space under point load
12.7 Elastic half-space under uniform surface pressure
12.8 Problems
12.9 References

13. Elastic stability
13.1 Buckling of columns
13.1.1 Euler column under axial load
13.1.2 Euler column with a rotational restrained junction
13.1.3 Euler column with continuous elastic restrain
13.1.4 Euler column with distributed load
13.2 Buckling of beams
13.2.1 Flexural-Torsional buckling of beams of rectangular cross section
13.2.2 Flexural-Torsional buckling of beams of I cross section
13.3 Buckling of arches and rings
13.4 Buckling of plates
13.4.1 Rectangular plates
13.4.2 Circular plates
13.5 Problems
13.6 References

14. Elements of anisotropic elasticity – Composite materials
14.1 Anisotropic materials
14.2 Coordinate systems – Principal directions
14.3 Stiffness matrix of anisotropic layer
14.4 Transformation of stress and strain components of anisotropic layer
14.5 Transformation of engineering properties of anisotropic layer
14.6 Anisotropic laminates
14.7 Classical lamination theory
14.8 Kirchhoff’s assumption – Laminate strains and stresses
14.9 Laminate stiffness matrix
14.10 Failure criteria
14.11 Problems
14.12 References

Appendixes
I. Elements from mathematics
I1 Vectors
I2 Tensors
I3 Integral transforms
II Geometrical Properties of cross-sections
II1 Centroid
II2 Moments of inertia of cross sections
II3 Transformation of moments of inertia
II4 Principal axes
II5 Tables of properties of usual cross sections
III. Mechanical properties of selected materials