The aim of the course is to provide the basis for the comprehension of the methods and procedures the finite element method and the multi body analysis are based on. The basic knowledge acquired during the course will give the student the possibility to explore the possible applications of the methods to solve engineering problems with particular attention to the structural field.

Students attending the course will learn about the wide capabilities of the numerical methods in the virtual simulation of the behaviour of structures and automotive systems. On successfully completing this course unit, students will be able to solve structural (static and dynamic) problems of simple complexity by using commercial codes widely present in industries. For example, they will be able to: - prepare the numerical models of simple structures and multi body systems - set up the boundary conditions for static and quasi-static analyses - critically analyse the results of a virtual simulation and verify their reliability

Students attending the course must have the basic knowledge of geometry and numerical calculation. Moreover, they should be able to: - evaluate the static equilibrium of frames with prescribed boundary conditions - evaluate the stress and strain state of loaded beams within frameworks - analyse kinematics and dynamics of a single rigid body

1 - Multi-body systems Reference systems of rigid bodies. Position and orientation of reference systems. Change of coordinates, translation, rotation: matrix operators. Examples. 2 - Open chains multi-body: Denavit-Hartenberg’s convention, recursive numerical methods for the solution of the kinematic and dynamic problem. 3 - Closed chains multi-body: kinematic and dynamic problems. 4 Exercises in classroom.

The course is organized in frontal lectures, classroom practices and laboratory practices. The frontal lectures concern the theory part of the course syllabus. The classroom practices concern the execution of exercises on the matrix calculus. These exercises are preparatory for a part of the exam. The laboratory practices concern the dynamic solution of multi-body systems by using both Matlab and a commercial software devoted to the MBD simulation. All the parts in which the course is structured can be followed without significant differences in presence or remotely.

-Ahmed A. Shabana. Dynamics of multibody systems. Cambridge, 3th edition. -Mike Blundell, Damian Harty. The multibody systems approach to vehicle design. Elsevier. -F. Colombo, A. Trivella. Exercises of multi-body kinematics and dynamic. Clut editrice. Torino.

Modalità di esame: Prova scritta (in aula); Prova orale facoltativa; Elaborato progettuale individuale;

Exam: Written test; Optional oral exam; Individual project;

... To verify the expected learning outcomes, the exam of the Numerical Modelling and Simulation course is made up of: - A written exam - 2 laboratory reports (A and B) - An optional oral exam (only on student’s request) Written exam: The written exam is divided in two separate parts (part A and part B). - The two parts of the written exam are carried out separately - The duration of each part of the written exam is 1.5 hours For what concerns the part B of the course, the written exam is aimed to verify the capability to solve problems of positioning, kinematic and dynamic of simple multi body systems by numerical methods. The written exam is also aimed to verify the knowledges about the theory of multi body dynamics To this aim, the written exam of the part B can be made up of: - one or two exercises with matrix calculus to solve positioning, kinematic and dynamic problems - one or two questions about the theory of the multi body dynamics. The evaluation of the exercises and questions is based on the correctness of the results and on the clarity of the resolution procedure and answers . The maximum score of the written exam for part B is 14/30. The maximum score of the report for part B is 2/30. General aspects for the written exam (A+B): The maximum score of the written exam (A+B) is 27/30 - It is forbidden the use of books or any type of notes. If necessary, a formulary will be provided by the teaching staff in the text of the exam - It is strictly forbidden to use any web connection, therefore no electronic devices (computers or calculators with connection devices of any kind, mobile phones, smartphones, smartwatches, etc.) of any kind are allowed for any data retrieval or for any communication purpose during the exam. - It is possible to use a pocket calculator that cannot be connected to internet. The use of any other type of electronic device is strictly forbidden worth the cancellation of the exam - The student must use, also for the draft, only the sheets with the stamp of the Politecnico di Torino that will be provided by the teaching staff. - It is strictly forbidden to communicate with other people inside or outside the classroom in any way and for any reason. - The student can verify his/her written exam and any errors in a public meeting fixed for the registration of the exam. The meeting will be scheduled by the teaching staff after the written exam and the schedule will be communicated when the scores of the exam will be available. Laboratory reports: The two reports concern, separately, the two parts of the course. In the laboratory reports the student has to describe the procedures followed to perform the numerical analysis and the obtained results. The results have to be critically commented and discussed by the student. The evaluation of the reports is based on: - the amount of work carried out - the correctness and the reliability of the results - the ability of the student to summarize the descriptions of the procedures - the ability of the student to critically analyse the results For the part B, the requested report consists in a short technical presentation (2/30). - The laboratory reports must be submitted within a defined deadline - The laboratory reports must be submitted with upload operation on the course webpage (“Portale della Didattica”) - The deadline for the upload of the laboratory reports is mandatory: laboratory reports uploaded after the deadline will not be taken into consideration for any reason - The deadline for the laboratory reports will be communicated through the webpage of the course (“Portale della Didattica”). - If even just one of the two laboratory reports will be missing, the maximum score of the written exam (A+B) will be automatically reduced to 24/30 if higher. - The laboratory reports can be done by teams of students: the teams must have a maximum number of students equal to 3. Optional oral exam: From the assessment point of view, the optional oral exam has the same targets of the written exam. It consists in 2÷4 questions on the contents of the complete course (theory, classroom practice, laboratory practice of both part A and part B) - The optional oral exam must be attended at the same date of the exam registration of the written exam. - The optional oral exam can be carried out only by student having a minimum score on the written exam (score of the part A + score of the part B) + the score of the laboratory reports A and B of 18/30 - The optional oral exam is evaluated with a maximum score of 30/30 General rules: - The final score of the exam is given by the sum between the score of the written exam (the score of the part A plus the score of the part B) plus the score for the laboratory reports. - If the student decides to attend the optional oral exam, the final score of the exam is given by the mean score between: - the written exam (score of the part A + score of the part B) + the score for the laboratory reports - the optional oral exam. - The minimum score to pass the exam is 18/30 - A score larger than 30/30 will be registered as 30/30 with laude - Only the total score of the written exam (score of the part A + score of the part B) can be rejected whereas the score of the written exam of a single part cannot be rejected. The score of the written exam can be rejected at every exam session. -If the student decides to attend the optional oral exam, the final score of the exam cannot be rejected. - The student must verify that they are properly enrolled in the exam. Only student regularly enrolled can carried out the exam. 

Gli studenti e le studentesse con disabilità o con Disturbi Specifici di Apprendimento (DSA), oltre alla segnalazione tramite procedura informatizzata, sono invitati a comunicare anche direttamente al/la docente titolare dell'insegnamento, con un preavviso non inferiore ad una settimana dall'avvio della sessione d'esame, gli strumenti compensativi concordati con l'Unità Special Needs, al fine di permettere al/la docente la declinazione più idonea in riferimento alla specifica tipologia di esame.