LEARNING OUTCOMES

To provide criteria and methods for design and verification of mechanical components and simple structural parts under static and fatigue loads. To present basic lumped mass models used in rotor dynamics. To teach fundamental knowledge on finite element method applied to structural analysis of 3-D frames and simple 2-D models of continuous elastic solids.

AIMS AND LEARNING OUTCOMES

The course aims to:

1) present and apply the criteria for the mechanical design of components and machine parts subjected to static, dynamic and fatigue loads ;

2) describe the classical analytical models used  for the structural analysis, and aplly  them for simple design calculations;

3) introduce the fundamentals of numerical finite element technique for 2D and 3D structures composed of  discrete elements (trusses and beams).

TEACHING METHODS

Contextual lectures and worked examples held by the titular teacher

SYLLABUS/CONTENT

Part 1 - Fundamentals of mechanic structural design under static loads. Recalls on :
a) Solid Mechanics and Structural Mechanics.

b) Elementary one-dimensional structures (beams and rods).

c) Special problems of solid mechanics : plane stress / strain  problems  and axisymmetric problems.

d) Rotating disks and cylindrical shells.

e) Causes of stress. Concentrated and distributed forces (surface and volume forces). Initial deformation (thermal and interference). Causes of collapse. Failure due to overcoming of static strength, fatigue, and crash. Failure due to elastic instability and  high-temperature creep. Coefficients of safety against structural failure.
- Physical nonlinearities : plasticity. Examples of elastic-plastic calculations : plastic hinge.

- Geometric nonlinearitie: large displacement. Contact nonlinearities: unilateral constraints.

Part 2 - Fundamentals of the finite element method. Matrix methods for the analysis of discrete element structures . Stiffness matrix. Vectors of  forces and nodal displacements. Assembly,  constraint  specification and solution of equations. Post-processing of results. Shape functions and stiffness matrix for a generic finite element. Convergence of the solution. Tension matrix and deformation matrix. Criteria for the discretization of a solid into 2D / 3D finite elements. Plane triangular element with three nodes . Axisymmetric triangular element with three nodes .

Part 3 - Linear approach to the mechanical dynamic structural design . The simple oscillator (recalls). Examples of dynamic systems with 1 or 2 degrees of freedom. Overview of distributed parameter dynamic systems . Axial , bending and torsional vibrations. Torsional bi-pendulum. Torsional tri-pendulum.

Part 4 - Rotor Dynamics : the Jeffcott rotor. Critical speeds. Causes of damping in a turbine rotor. Examples of modeling and examples of dynamic calculations of rotating systems. Inertia redution in a  torque crank rod.  Inertia and elasticity reduction of a system rotating on two axes to a torsional bi/tri-pendulum

Part 5 - Notes on the structural design of gas and steam turbines. Static calculation (with the ANSYS code) of a turbine rotor ..Modal analysis of a low-pressure blade for a steam turbine. Materials for gas turbines subject to creep. Seminars Ansaldo Energia of mechanical design of steam turbines.

Part 6 - Theory of thin plates. Uniformly deflected circular plate.  Axisymmetric  plates

RECOMMENDED READING/BIBLIOGRAPHY

Lecture notes.  Any text in Machine design  (e.g.  J.E. Shigley, C.R. Mischke, R.G. Budynas : “Progetto e costruzione di macchine” , McGraw Hill)