Block A “Thermo Mechanics”

block A

—> Dedicated to BS: Electronic Engineering – Biomedical Engineering with a background in Electronics

SPECIFIC SUBJECTS – Block A
Year sem CFU SSD class hours
FUNDAMENTALS OF MECHANICS OF SYSTEMS 1 1 6 ING-IND/13 60
MECHANICS OF MATERIALS AND STRUCTURES 1 2 6 ICAR/08 60
THERMODYNAMICS AND HEAT TRANSFER 1 2 6 ING-IND/10 60
MACHINE DESIGN 2 2 6 ING-IND/14 60
TOTAL ECTS
    24    

1st Year – I semII sem


2nd Year (2023-24) – I semII sem

 

COMPUTER VISION (2024-25)

COMPUTER VISION (2024-25)
2 YEAR II semester  6 CFU
Arianna Mencattini A.Y. 2023-24 (ex MEASUREMENT SYSTEMS FOR MECHATRONICS)
A.Y. 24-25
Code: 8039787
SSD: ING/INF/07

LEARNING OUTCOMES:
Learning of basic concepts in digital image processing and analysis as a novel measurement system in biomedical fields. The main algorithms will be illustrated, particularly devoted to the mechatronics fields.

KNOWLEDGE AND UNDERSTANDING:
The student acquires the knowledge related to the possibility to use an image analysis platform to monitor the dynamics of a given phenomenon and to extract quantitative information from digital images such as object localization and tracking in digital videos.

APPLYING KNOWLEDGE AND UNDERSTANDING:
The student acquires the capability to implement the algorithms in Matlab through dedicated lessons during the course to the aim of being able to autonomously develop new codes for the solution of specific problems in different application fields.

MAKING JUDGEMENTS:
The student must be able to integrate the basic knowledge provided with those deriving from the other courses such as probability, signal theory, and pattern recognition. some fundamentals of measurement systems as well as of basic metrological definitions will be provided in support of background knwoledge.

COMMUNICATION SKILLS:
The student solves a written test and develops a project in Matlab that illustrates during the oral exam. The project can be done in group to demonstrate working group capabilities.

LEARNING SKILLS:
Students will be able to read and understand scientific papers and books in English also to deepen some topics. In some cases, students will develop also experimental tests with time-lapse microscopy acquisition in department laboratory.

SYLLABUS

Fundamentals of metrology. Basic definitions: resolution, accuracy, precision, reproducibility and their impact over an image based measurement system . Image processing introduction. Image representation. Spatial and pixel resolution. Image restoration. Deconvolution. Deblurring. Image quality assessment. Image enhancement. Image filtering for smoothing and sharpening. Image segmentation: pixel based (otsu method), edge based, region based (region growing), model based (active contour, Hough transform), semantic segmentation. Morphological operators. Object recognition and image classification. Case study: defects detection, object tracking in biology, computer assisted diagnosis, facial expression in human computer interface.
Matlab exercises.

TEXTS

Digital image processing, Gonzalez and Woods, Prentice Hall, New York, 2002.

BiPM, I. E. C., IFCC, I., IUPAC, I., & ISO, O. (2012). The international vocabulary of metrology— basic and general concepts and associated terms (VIM). JCGM, 200, 2012.

ATTENDANCE

Although attendance is optional, it is strongly recommended to follow the lessons. The professor recommends the students to subscribe the course on the Delphi website. The teams platform will be used as a consequence to communicate with the Professor, ask for doubts, and download the materials used for the lessons.

MEASUREMENT SYSTEMS FOR MECHATRONICS (2023-24) –> COMPUTER VISION (2024-25)

MEASUREMENT SYSTEMS FOR MECHATRONICS (2023-24) –> COMPUTER VISION (2024-25)
2 YEAR II semester  6 CFU
Arianna Mencattini A.Y. 2021-22

A.Y. 2022-23

A.Y. 2023-24

Computer Vision A.Y. 24-25

Code: 8039787
SSD: ING/INF/07

LEARNING OUTCOMES: Learning basic concepts in digital image processing and analysis as a novel measurement system in biomedical fields. The main algorithms will be illustrated particularly devoted to the image medical fields.

KNOWLEDGE AND UNDERSTANDING: The student acquires knowledge related to the possibility to use an image analysis platform to monitor the dynamics of a given phenomenon and to extract quantitative information from digital images such as object localization and tracking in digital videos.

APPLYING KNOWLEDGE AND UNDERSTANDING: The student acquires the capability to implement the algorithms in Matlab through dedicated lessons during the course with the aim of being able to autonomously develop new codes for the solution of specific problems in different application fields.

MAKING JUDGEMENTS: :
The student must be able to integrate the basic knowledge provided with those deriving from the other courses such as probability, signal theory, and pattern recognition. some fundamentals of measurement systems as well as basic metrological definitions will be provided in support of background knowledge.

COMMUNICATION SKILLS:
The student solves a written test and develops a project in Matlab that illustrates during the oral exam. The project can be done in a group to demonstrate working group capabilities.

LEARNING SKILLS:
Students will be able to read and understand scientific papers and books in English and also to deepen some topics. In some cases, students will develop also experimental tests with time-lapse microscopy acquisition in the department laboratory.

 

SYLLABUS:

Fundamentals of metrology. Basic definitions: resolution, accuracy, precision, reproducibility, and their impact over an image based measurement system. Image processing introduction. Image representation. Spatial and pixel resolution. Image restoration. Deconvolution. Deblurring. Image quality assessment. Image enhancement. Image filtering for smoothing and sharpening. Image segmentation: pixel based (otsu method), edge based, region based (region growing), model based (active contour, Hough transform), semantic segmentation. Morphological operators. Object recognition and image classification. Case study: defects detection, object tracking in biology, computer assisted diagnosis, facial expression in human computer interface.
Matlab exercises.

ELECTRONICS OF IOT AND EMBEDDED SYSTEMS

ELECTRONICS OF IOT AND EMBEDDED SYSTEMS

 

2 YEAR 1 semester 12 CFU
Patrick LONGHI (3cfu)
Giancarlo ORENGO (3cfu)
Gian Carlo CARDARILLI (4cfu)
Luca DI NUNZIO (2cfu)
since A.Y. 2019-20
M-5519 – ELECTRONICS OF IOT (6cfu)
M-5520 – DESIGN OF EMBEDDED SYSTEMS FOR MECHATRONICS (6cfu)
Code: 8039795
SSD: ING-INF/01

EDUCATIONAL OBJECTIVES:
The objectives of the course are:
1) to provide the tools to carry out a radio link assessment in a real application context.
2) learn the fundamental parameters of the antennas used in IoT applications
3) provide the tools to interpret the electrical diagram of the RF front end of a typical trans receiver.

KNOWLEDGE AND UNDERSTANDING:
Provide the fundamental tools to understand the most advanced and updated content from publications, magazines, forums, blogs, etc., to always be updated on the state of the art.

ABILITY TO APPLY KNOWLEDGE AND UNDERSTANDING:
Practical radio link budget, electronic noise evaluation on receiver behavior, installation effects of the antennas, understanding of key parameters of commonly used antennas in the targeted scenario, analysis of an RF transceiver block diagram

AUTONOMY OF JUDGMENT:
With the enormous amount of information that is available today to developers of IoT applications, the course seeks to develop the ability of the student to select the highest quality and most validated content.

COMMUNICATION SKILLS:
The final test is based on an oral exam in which the student illustrates a part of the module

LEARNING ABILITY:
The course aims to develop in the student the ability to independently learn new and constantly updated content because the knowledge acquired today soon becomes obsolete.

SYLLABUS:

(Longhi):

Introduction to radiating elements and their key parameters.
Ideal and practical link budget.
The effect of noise in electronic receivers, figures of merit and mathematical modelling. Receiver G/T.
Practical aspects of IoT RF systems
RFID
Radiating elements key parameters, gain, directivity, HPBW, nulls, radiation pattern, polarization, and input impedance. Some practical cases: the mono/di-pole family, microstrip antennas, parabolic reflector, wearables
Introduction to RF transceiver systems and key-components (switches, HPA, LNA, mixers, frequency generators).

(G.Orengo):

Summary of Digital Electronics: digital encoding of information, binary (fixed and floating point), hexadecimal and ASCII; operators and main logic circuits, registers and memories, programmable devices. Prototyping boards for IoT (Arduino, Rasberry), Systems on Chip (SoC), architecture of a microcontroller, description of the Arduino Uno board. Programming languages ​​(assembly, compiled, interpreted), structure of an Arduino sketch (libraries, setups, loops, functions, interrupts), programming elements in C (variables, math and logical operations, cycles, conditional statements). Use of digital and analog I/O ports (A/D conversion, PWM output). Synchronous and asynchronous serial communication modes, wired (USB) and wireless with Bluetooth, RF and WiFi modules. Remote control of electronic modules (sensors, dc stepper and servo motors, LED/LCD displays etc.) from portable devices (Windows, IoS), through applications developed in Processing and Python, and mobile (Android), through Apps developed with the MIT App Inventor platform. Internet protocols for device local/remote control through WiFi modules connected as access points/clients to web platforms or public/private cloud servers controlled by laptops and/or mobile devices.

(G.Cardarilli):

– Introduction to the Internet of Things (IoT) and embedded systems
– Wireless and mobile communications
– The Sensors
– Low power processing
– IoT and machine learning applications
– Future developments in the field of IoT and embedded systems

 

CONTROL OF MECHANICAL SYSTEMS

CONTROL OF MECHANICAL SYSTEMS
2 YEAR
1 semester 9 CFU
Riccardo MARINO Since 2019-20
Code: 8039823
SSD: ING-INF/04

LEARNING OUTCOMES:

Ability to understand scientific papers on the control of mechanical systems

KNOWLEDGE AND UNDERSTANDING:

Knowledge of dynamic modeling of mechanical systems. Knowledge of basic feedback control techniques for single input single output systems and of decoupling techniques for multi input multi output nonlinear systems

APPLYING KNOWLEDGE AND UNDERSTANDING:

Ability to simulate using Matlab Simulink complex controlled mechanical systems

MAKING JUDGEMENTS:

Ability to evaluate stability, robustness, and performance of a control system

COMMUNICATION SKILLS: Ability to present and discuss an autonomous design project

LEARNING SKILLS: Ability to fully understand a scientific paper on the control of mechanical systems

SYLLABUS:

BASIC CONTROL TOOLS
Bounded- input bounded- output linear systems. Pole placement theorem for controllable and observable linear systems. Luenberger observers for observable systems. Design of dynamic compensators for linear systems. Integral feedback control to reject constant disturbances. PID control. System inverses for minimum phase linear systems. The combination of feedback and feedforward control actions.
ADVANCED CONTROL TOOLS
Linear approximations of nonlinear control systems about operating conditions. The definition of region of attraction for an operating condition. Output feedback compensators with integral actions to control nonlinear systems about a given operating condition. Liapunov matrix equations to determine quadratic Liapunov functions and assess the region of attraction. The definition of the sensitivity transfer function and its properties. The gang of four: sensitivity, complementary sensitivity, load sensitivity and noise sensitivity functions. How to determine the robustness of a control loop using the gang of four functions. Bode’s integral formula and the limitations imposed by unstable open loop poles. Youla parametrization to design stable compensation. Kalman filters, Riccati equations and robust control design.

CONTROL DESIGN FOR MULTIVARIABLE NONLINEAR SYSTEMS
Relative degree for a single input single output nonlinear system. State feedback control design for input-output linearization. State feedback linearization when the relative degree is equal to the state space dimension. The definition of nonlinear inverse systems. Relative degrees or decoupling indices for multivariable (multi-input, multi-output) nonlinear systems. The definition of the decoupling matrix. State feedback control design for input-output linearization when the decoupling matrix is full rank using the Penrose pseudoinverse. State feedback linearization when the sum of relative degrees is equal to the state space dimension and the decoupling matrix is full rank.

CASE STUDIES OF NONLINEAR MECHANICAL CONTROL SYSTEMS
Control of bycicles, robots, vehicles and aircrafts

Fundamentals of Mechanisms of Systems (block A) (since 2022-23)

Fundamentals of Mechanisms of Systems (block A) (since 2022-23)
1 YEAR
1 semester 6 CFU
Marco Ceccarelli A.Y. 2021-22

A.Y. 2022-23

Code: 803000062
SSD: ING-IND-13
(by Engineering Sciences)

OBJECTIVES

LEARNING OUTCOMES: The course aims to teach students the knowledge and tools that are needed to address the issues that are related to the identification, modeling, analysis, and design of multi-body planar systems in English language and terminology

KNOWLEDGE AND UNDERSTANDING: modeling and procedures to recognize the structure and characteristics of mechanisms and machines

APPLYING KNOWLEDGE AND UNDERSTANDING: acquisition of analysis procedures for the understanding of kinematic and dynamic characteristics of mechanisms and machines

MAKING JUDGEMENTS: possibility of judging the functionality of mechanisms and machines with their own qualitative and quantitative assessments

COMMUNICATION SKILLS: learning technical terminology and procedures for presenting the performance of mechanisms

LEARNING SKILLS: learning technical terminology and procedures for the presentation of the performance of mechanisms


PREREQUISITES: knowledge of basic mechanics of rigid bodies and computation skills

SYLLABUS

Structure and classification of planar mechanical systems, kinematic modeling, mobility analysis, graphical approaches of kinematics analysis, kinematic analysis with computer-oriented algorithms; dynamics and statics modeling, graphical approaches of dynamics analysis, dynamic analysis with computer-oriented algorithms, performance evaluation; elements of mechanical transmissions.

BOOKS:

Lopez-Cajùn C., Ceccarelli M., Mecanismos, Trillas, Città del Messico
Shigley J.E., Pennock G.R., Uicker J.J., “Theory of Machines and Mechanisms”, McGraw-Hill, New York
Handnotes and papers by the teachers

Machine Design (block A)

Machine Design (block A)
2 YEAR II semester  6 CFU
Luciano CANTONE A.Y. 2023-24
(by Engineering Sciences)
Code: 80300065
SSD:

LEARNING OUTCOMES: Designing mechanical components considering the need to save weight, material and energy while respecting safety, to promote the usefulness and social impact of the designed product.
KNOWLEDGE AND UNDERSTANDING: The design of mechanical systems, in particular, basic knowledge of the design methodologies of important machine components.
APPLYING KNOWLEDGE AND UNDERSTANDING: Know how to recognise, distinguish, and use the main techniques and tools to design mechanical components.
MAKING JUDGEMENTS: Students must assume the missing data of a problem and be able to independently formulate basic hypotheses (such as that on safety coefficients) based on the operational and functional context of the system/component they have to design.
COMMUNICATION SKILLS: Transfer information, ideas and solutions to specialist and non-specialist interlocutors through intensive use of English terminology.
LEARNING SKILLS: Students, by learning the basics of design, acquire the tools to learn the necessary design techniques of systems/components not directly addressed during the course.

VERIFICATION CRITERIA

Solution of the assignments given during the teaching. The written exam consists of 4 exercises, similar to those solved during the lessons. After passing the written test, there is an oral examination with two questions. The student’s evaluation is related to the understanding and mastery of the principles and methods of design for both written and oral exams.
The oral exam questions aim to ascertain the student’s knowledge and reasoning skills in connecting the different topics covered within the course.
The final vote of the exam is expressed out of thirty and follows the next graduation system:
Not pass, essential deficiencies in the knowledge and understanding of the topics; limited capacity for analysis and synthesis, frequent generalizations and limited critical and judgmental capacity, the topics are set out inconsistently and with inappropriate language
18-21, the student has acquired the basic concepts of the discipline and has an analytical capacity that emerges only with the teacher’s help. The way of speaking and the language used are, on the whole, correct.
22-25, the student has acquired the basic concepts of the discipline discreetly, knows how to orient himself or herself among the various topics covered and has an autonomous analysis capacity that knows how to express with the correct language.
26-29, the student has a well-structured knowledge base. He/She can independently rework the knowledge acquired in the context of the choice of conventional and unconventional materials according to the application; the way of speaking and the technical language are correct.
30 and 30 cum laude, the student has a complete and in-depth knowledge base. The cultural references are rich and up-to-date, expressed with brilliance and properties of technical language.

The midterm tests are optional and allow you to avoid the oral examination with an overall mark of at least 18/30.

Syllabus

Consolidation of basic knowledge to put the student in the right conditions to face a generic machine design problem: Mechanical Engineering design in Broad, Perspective, Load Analysis, Materials, Static Body Stresses, Elastic strain, Deflection, Stability (Eulerian buckling), Vibrations (beam Eigen-modes), Failure Theories,Safety Factors, Reliability, High cycles Fatigue, Low cycles Fatigue, Surface Damage, Contact and impact problems. During the course, several design activities will be demonstrated by exercises and by real life applications.

TEXTS

Machine Component Design, 7th Edition International Student Version Robert C. Juvinall – (University of Michigan), Kurt M. Marshek (University of Texas at Austin)
Teacher’s slides

POWERTRAIN TECHNOLOGIES FOR FUTURE MOBILITY (ex Internal Combustion Engines)

POWERTRAIN TECHNOLOGIES FOR FUTURE MOBILITY (ex Internal Combustion Engines)
1 YEAR (Block C)

2 YEAR (Blocks A|B|D|E)

II semester  9 CFU
Stefano CORDINER (6/9 cfu)
Lorenzo BARTOLUCCI (3/9 cfu)
A.Y. 2021-22

Internal Combustion Engines

Since A.Y. 2022-23

POWERTRAIN TECHNOLOGIES FOR FUTURE MOBILITY

Code: 80300079
SSD: ING/IND/08
(by Mechanical Engineering)

PREREQUISITES: Technical Physics, Fluid Machinery

FORMATIVE OBJECTIVES

LEARNING OUTCOMES:

The course aims to provide students with in-depth scientific training to correctly address the problems of designing, choosing and managing new propulsion systems for sustainable mobility starting from current solutions with internal combustion engines as well as creating the conditions for the development of innovative and low environmental impact solutions. To this end, students will develop in-depth knowledge of the operating principles of propulsion systems for transport and will learn simulation procedures for their verification and sizing. Finally, particular attention is dedicated to the most recent technological development of internal combustion engine technology aimed at overcoming current limits in terms of emissions and efficiency and defining innovative scenarios for sustainable mobility.

KNOWLEDGE AND UNDERSTANDING:
Course aim is to provide the students with tools for the analysis of the performances and the evaluation of proper design solution for internal combustion engines and their core components. At the end of the course, the student will be able to independently understand the functional link between design variables and the performance of internal combustion engines also in case of innovative design,

APPLYING KNOWLEDGE AND UNDERSTANDING:
The course, through the analysis of specific problems and quantitative data, is aimed at providing the tools for analysis and evaluation of the effects of different design choices. The theme of energy efficiency and pollution reduction are at the heart of the teaching organization. The student will be able to interpret and propose design solutions, even innovative ones, adapted to the specificity of the problems that are presented to him.

MAKING JUDGEMENTS:
By studying theoretical and practical aspects of engine design and critically assessing the influence of different design variables, the student will be able to improve his judgment and proposal in relation to design. and the management of internal combustion engines.

COMMUNICATION SKILLS:
The presentation of the theoretical and application profiles underlying the operation of internal combustion engines will be carried out to allow the knowledge of the technical language of the appropriate specialist terminology; The development of communication skills, both oral and written will also be stimulated through classroom discussion, participation in seminary activities and through final tests.

LEARNING SKILLS:
The learning capacity, even individual, will be stimulated through numerical exercises, the drafting of papers on specialized topics, the discussion in the classroom, also aimed at verifying the actual understanding of the topics treated. The learning capacity will also be stimulated by integrative educational aids (journal articles and economic newspapers) in order to develop autonomous application capabilities.

SYLLABUS:

Legislation evolution on Internal Combustin Engines. Definition of the performance of the propulsion systems and their operating characteristics in relation to the mission, driving cycles. Generalities on reciprocating internal combustion engines: Characteristics and classification, thermodynamic and performance analysis of reciprocating internal combustion engines.
Air supply for 4-stroke engines: volumetric efficiency and its evaluation; Design elements of intake systems: quasi-stationary effects; valve sizing; influence of other engine parameters; Variable Valve Actuation systems. 2-stroke engines: construction schemes; Non-stationary phenomena in intake and exhaust ducts: inertia and wave propagation; variable geometry systems; calculation models; Supercharging.
In cylinder charge Motion: Turbulence; swirl, squish, tumble; stratified charge engines.
Traditional and alternative fuels; Properties of motor fuels. Generalities: combustibles; stoichiometric air; calorific value Gaseous fuels: natural gas, hydrogen and mixtures. bio-ethanol, bio-diesel and DME. Characteristics and their use in engines: technical solutions, performance and emissions.
Fuel supply Premixed combustion engines; Non-pre-mixed combustion engines.
Combustion : Analytical elements of combustion; thermodynamics of combustion processes; calculation of the chemical composition and of the adiabatic equilibrium temperature ; transport phenomena ; chemical kinetics.
Pollutant emissions and abatement systems; Emissions: formation mechanisms, effects on health and the environment, measurement of emissions; influence of engine parameters; Innovative combustion solutions, Advanced Thermodynamic Cycles. Sustainable mobility. Operating principles of hybrid vehicles: series and parallel solution; motors a.c. and electrical employees; regenerative braking; lithium batteries, performance and prospects. Plug-in hybrid vehicles, i.c. engines “range extender”. Innovative control logics for optimal powersplitting between the different energy sources. Electric vehicles, characteristics and prospects. Numerical simulation tools will be presented for all course topics

ATTENDANCE

Course attendance is strongly recommended. During the course, students are invited to interact with the Professor during the class or office hours for any clarification or insight in specific topics related to the program.

Mechanics of Materials and Structures (block A-E)

Mechanics of Materials and Structures (block A-E)
1 YEAR II semester  6 CFU
Andrea Micheletti

Edoardo Artioli

A.Y. 2021-22 (9 cfu)
Andrea Micheletti A.Y. 2022-23
A.Y. 2024-25 (6 cfu)
Code: 80300064
SSD: ICAR/08
(by Engineering Sciences)

FORMATIVE OBJECTIVES

LEARNING OUTCOMES: The goal of this course, composed of two Modules, is to provide the student with basic knowledge of the mechanics of linearly elastic structures and of the strength of materials. By completing this class successfully, the student will be able to compute simple structural elements and reasonably complex structures.

KNOWLEDGE AND UNDERSTANDING: At the end of this course, the student will be able to:
– compute constraint reactions and internal actions in rigid-body systems and beams subjected to point/distributed forces and couples
– compute centroid position and central principal second-order moments of area distributions
– understand the formal structure of the theory of linear elasticity for beams and 3D bodies
– analyze strain and stress states in 3D bodies
– compute the stress state in beams subjected to uniaxial bending, biaxial bending, eccentric axial force
– understand the behaviour of beams subjected to shear with bending and torsion
– understand how to compute displacements/rotations in isostatic beam systems, how to solve statically underdetermined systems, how to apply yield criteria, and how to design beams against buckling

APPLYING KNOWLEDGE AND UNDERSTANDING: The student will apply the knowledge and understanding skills developed during the course to the analysis of practical problems. This includes the analysis of linearly elastic structures and structural members in terms of strength and stiffness.

MAKING JUDGEMENTS: The student will have to demonstrate his awareness of the modeling assumptions useful to describe and calculate structural elements, as well as his critical judgement on the static response of elastic structures under loads, in terms of stresses, strains, and displacements.

COMMUNICATION SKILLS: The student will demonstrate, mostly during the oral test, his capacity of analyzing and computing the static response of linearly elastic structures, as well as his knowledge of the underlying theoretical models.

LEARNING SKILLS: The student will get familiar with the modeling of structures and structural elements in practical problems, mostly during the development of his skills for the written test. This mainly concerns beams and three-dimensional bodies.

PREREQUISITES: The student should have already attended the basic courses of calculus, geometry, and physics.
It is required that the student has good skills with regard to differential and integral calculus, linear algebra and matrix calculations.

SYLLABUS:

Together with the other Module of this course, the following topics are covered.

Review of basic notions of vector and tensor algebra and calculus.
Kinematics and statics of rigid-body systems.
Geometry of area distributions.
Strain and stress in 3D continuous bodies and beam-like bodies.
Virtual power and virtual work equation for beams and 3D bodies.
One-dimensional beam models: Bernoulli-Navier model, Timoshenko model, constitutive equations, governing differential equations.
Constitutive equation for linearly elastic and isotropic bodies, material moduli.
Hypothesis in linear elasticity, equilibrium problem for linearly elastic beams and 3D bodies.
Three-dimensional beam model: the Saint-Venant problem, uniaxial and biaxial bending, eccentric axial force, shear and bending, torsion.
Elastic energy of beams and 3D bodies, work-energy theorem, Betti’s reciprocal theorem, Castigliano’s theorem.
Yield criteria (maximum normal stress, maximum tangential stress, maximum elastic energy, maximum distortion energy).
Buckling instability, bifurcation diagrams, load and geometry imperfections, Euler buckling load, design against buckling.
Basic notions on the finite element method and structural analysis software.