B2370 - Machine Design

Learning outcomes

The students acquire in-depth knowledge of the methods and instruments necessary for the optimal structural design of mechanical components, plates, shells and pressure vessels. They deepen their knowledge of engineering materials' nonlinear behaviour and fracture mechanics. They learn the principles of the design for sustainability.

Course contents

1. Fundamentals of Solid Mechanics and Elasticity

• Stress and strain definitions

• Uniaxial and multiaxial stress states

• Linear elastic constitutive laws

• Elastic constants and material behavior

• Superposition principle

• Plane stress and plane strain

• Thermal loading effects

 

2. Stress Transformation

• Stress transformation equations

• Mohr’s circle

• Principal stresses and maximum shear stress

• Principal directions

• Applications to 2D stress states

 

3. Equilibrium and Compatibility Equations

• Differential equilibrium equations

• Body forces and boundary conditions

• Compatibility conditions

• Constitutive–equilibrium relationships

• Material independence in special cases

 

4. Airy Stress Function

• Introduction to Airy stress function

• Biharmonic equation

• Polynomial solutions

• Applications to 2D domains

• Relation to Saint-Venant principle

 

5. Elasticity in Polar Coordinates

• Polar formulation of equilibrium equations

• Axisymmetric stress states

• Lamé solution for thick cylinders

• Stress concentration around holes (Kirsch solution)

• Curved beam bending

 

6. Thin Plates: Bending and Transverse Loads

• Kirchhoff–Love plate theory

• Moment–curvature relations

• One- and two-directional bending

• Rectangular plates under transverse loads

• Navier solutions

• Thermal effects in plates

 

7. Circular Plates

• Axisymmetric formulation

• Closed-form solutions

• Concentrated and distributed loads

• Plates with holes

• Engineering applications

 

8. Thin Shells and Pressure Vessels

• Membrane theory of shells

• Cylindrical and spherical shells

• Pressure vessels with domes

• Local bending effects

• Geometrical and thickness discontinuities

 

9. Flanges and Coupling Elements

• Load transmission through flanges

• Stress state in flanges

• Simplified analytical models

• Pipe–flange connections

 

10. Plasticity of Materials

• Elastoplastic constitutive models

• Perfect plasticity

• Isotropic and kinematic hardening

• Bauschinger effect

• Cyclic material behavior

 

11. Low- and High-Cycle Fatigue

• Wöhler and Manson–Coffin curves

• Mean stress effects

• Goodman, Smith and Morrow criteria

• Cyclic plasticity

• Fatigue life estimation

 

12. Fatigue under Variable Amplitude Loading

• Real loading spectra

• Cycle counting methods (Rainflow)

• Miner’s rule and limitations

• Accelerated testing spectra

• Engineering applications

 

13. Linear Elastic Fracture Mechanics (LEFM)

• Design motivation and criteria

• Energy approach (Griffith, Irwin)

• Stress Intensity Factor (SIF)

• Crack-tip plastic zone

• Fracture toughness

 

14. Fatigue Crack Propagation

• Crack growth mechanisms

• Paris law and advanced models

• Load ratio effects

• Crack stability

• Design philosophies: safe-life, fail-safe, damage tolerance

 

15. Finite Element Method (FEM)

• FEM fundamentals and role in design

• Variational formulation

• Rayleigh–Ritz and Galerkin methods

• One-dimensional elements

• Local and global coordinate systems

• Two-dimensional elements

• Numerical integration (Gauss)

• Post-processing of results

• Convergence, accuracy and locking phenomena

Readings/Bibliography

Metal Fatigue in Engineering, 2nd Edition

Ralph I. Stephens , Ali Fatemi , Henry O. Fuchs

Wiley

ISBN: 978-0-471-51059-8

Theory Of Elasticity

Stephen P. Timoshenko J.N. Goodier

Editore: Mcgraw-hill Education - Europe

ISBN: 0070858055

Teaching methods

Multimedia assisted Frontal lessons

Solution of practical problems by means of the PC or at the blackboard

Assessment methods

Written exam on the part relating to plates and shells, computer based knowledge test and ora presentation. The first test tests the ability to set up problems relating to that type of structures, the computer based test  is used to evaluate the knowledge, while the oral test aims to investigate presentation capabilities

Office hours

See the website of Giangiacomo Minak