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.

Modalitŕ di esame: Prova orale facoltativa; Prova scritta tramite PC con l'utilizzo della piattaforma di ateneo;

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 - 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). 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 rigid bodies by matrix calculus - the knowledges about the kinematics and dynamic of a multi body system - the knowledges about the computing procedures in 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 two parts of the written exam will be carried out separately - The duration of each part of the written exam is 1.5 hours - The maximum score of each part is 14/30. The total score of the written exam is made up of the sum of the score of the two parts. Therefore, the maximum score of the written exam is 28/30 - The written exam will be carried out via PC by using the Polito exam platform integrated with proctoring tools (Respondus) - The general procedure for this type of exam is provided by the Politecnico di Torino For what concerns the part B of the written exam: - During the exam, the student cannot leave the desk and the workstation, moreover he has to be always clearly visible by the webcam. - The webcam has to capture the desk where the student will take the exam and the student himself. - In the written exam 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 questions. - You can use a pocket calculator that cannot be connected to internet. - Your smartphone has to switched on (it will be necessary at the end of the test), muted, and its screen has to be oriented toward the surface of the table. - For each question it is required to do one picture of the written answer by the webcam. It is possible to add more pictures for each question. Each picture can be repeated more time before to select it. During the exam are no allowed attached files. - For an acceptable quality of the picture the sheet must be approached to the camera. Sheets of size A5 are preferable for this operation (A5 is half sheet A4). - Just after the conclusion of the exam it is required to upload ONE (only one) pdf file for the whole solution (your written sheets) on "Elaborati" section of Portale della Didattica. Number each written sheet before to take the photo of the written sheets with your smartphone. - The additional file will be useful in case of no good resolution of the pictures during the test with Respondus platform. Only the solution visible in the picture will be considered for the verification of the solution on the additional pdf file. Format different than pdf type or multiple files will be not considered. Laboratory reports: The aim of the laboratory reports is to verify the knowledges about the use of the commercial codes used for the laboratory practices. The two reports concern, separately, the two parts of the course. In the laboratory reports the students have to show the procedures followed to perform the numerical analysis and the obtained results. The results have to be critically commented and discussed by the students. - For the part B, the report can be made in .docx format (or similar) and it must submitted in .pdf format - The maximum score of each report is 2/30 - The laboratory reports must be submitted within a defined deadline - The laboratory report 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 will be automatically reduced to 24/30 - The laboratory reports can be done by teams of students: the teams must have a maximum number of students equal to 3 - A single upload has to be made for each student’s team. On the technical report the members of the student’s team have to be clearly indicated Optional oral exam: 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 students having a minimum score on the written exam (score of the part A + score of the part B) + the score of the laboratory report of 18/30 - The optional oral exam is evaluated with a maximum score of 30/30 - The optional oral exam will be carried out using a video communication system. The general procedure for oral examination is provided by the Politecnico di Torino. More details will be provided during the course by the teaching staff General rules: - The maximum score of each part is 14/30. The total score of the written exam is made up of the sum of the score of the two parts. Therefore, the maximum score of the written exam is 28/30 - 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 (if applicable) - 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. If the student decides to attend the optional oral exam, the final score of the exam cannot be rejected. - Students must verify that they are properly enrolled in the exam. Only student regularly enrolled can carried out the exam - Students must check, well in advance, that they are equipped with the adequate means to take the exam according to the exam procedure proposed by the teaching staff (personal computer equipped with webcam or tablet, browser, network connection suitable for videoconferencing). To this aim, some tests will be organized during the course - The starting time of the exam is published on the teaching portal (Portale della Didattica) or communicated by professors (Italian time zone - CEST). Students are required to respect the start time of the test by checking the functionality of the necessary devices in time. - Participation in the exam implies acceptance of the examination procedures defined by Politecnico, including video recording to ensure the regularity of the written test. - All students are required to comply with the University's Code of Ethical Conduct of the Politecnico di Torino

Modalitŕ di esame: Prova scritta (in aula); Prova orale facoltativa; Prova scritta tramite PC con l'utilizzo della piattaforma di ateneo;

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 - 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). 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 rigid bodies by matrix calculus - the knowledges about the kinematics and dynamic of a multi body system with open chain - the knowledges about the computing procedure in 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 two parts of the written exam will be carried out separately - The duration of each part of the written exam is 1.5 hours - The maximum score of each part is 14/30. The total score of the written exam is made up of the sum of the score of the two parts. Therefore, the maximum score of the written exam is 28/30 - The written exam will be carried out: - via PC by using the Polito exam platform integrated with proctoring tools (Respondus) for students which will attend the exam online - in classroom with traditional paper sheets, for students which will attend the exam onsite Online exam: - The general procedure for the online exam is provided by the Politecnico di Torino For what concerns the part B of the written exam: - During the exam, the student cannot leave the desk and the workstation, moreover he has to be always clearly visible by the webcam. - The webcam has to capture the desk where the student will take the exam and the student himself. - In the written exam 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 questions. - You can use a pocket calculator that cannot be connected to internet. - Your smartphone has to switched on (it will be necessary at the end of the test), muted, and its screen has to be oriented toward the surface of the table. - For each question it is required to do one picture of the written answer by the webcam. It is possible to add more pictures for each question. Each picture can be repeated more time before to select it. During the exam are no allowed attached files. - For an acceptable quality of the picture the sheet must be approached to the camera. Sheets of size A5 are preferable for this operation (A5 is half sheet A4). - Just after the conclusion of the exam it is required to upload ONE (only one) pdf file for the whole solution (your written sheets) on "Elaborati" section of Portale della Didattica. Number each written sheet before to take the photo of the written sheets with your smartphone. - The additional file will be useful in case of no good resolution of the pictures during the test with Respondus platform. Only the solution visible in the picture will be considered for the verification of the solution on the additional pdf file. Format different than pdf type or multiple files will be not considered. Onsite exam For both the part A and B of the written exam: - It is forbidden the use of books or any type of notes. If necessary, a formulary will be provided by the teaching staff - During 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 allowed the use of a 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 students 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 speak with other people inside or outside the classroom in any way and for any reason Laboratory reports: The aim of the laboratory reports is to verify the knowledges about the use of the commercial codes used for the laboratory practices. The two reports concern, separately, the two parts of the course. In the laboratory reports the students have to show the procedures followed to perform the numerical analysis and the obtained results. The results have to be critically commented and discussed by the students. - For the part B, the requested report can be made in .docx format (or similar) and it must submitted in .pdf format. - The maximum score of each report is 2/30 - The laboratory reports must be submitted within a defined deadline - The laboratory report 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 will be automatically reduced to 24/30 - The laboratory reports can be done by teams of students: the teams must have a maximum number of students equal to 3 - A single upload has to be made for each student’s team. On the technical report the members of the student’s team have to be clearly indicated. Optional oral exam: 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 students having a minimum score on the written exam (score of the part A + score of the part B) + the score of the laboratory report of 18/30 - The optional oral exam is evaluated with a maximum score of 30/30 - The optional oral exam will be carried out - via PC using a video communication system. The general procedure for oral examination is provided by the Politecnico di Torino. More details will be provided during the course by the teaching staff for students which will attend the exam online - in classroom with traditional execution, for students which will attend the exam onsite General rules: - The maximum score of each part is 14/30. The total score of the written exam is made up of the sum of the score of the two parts. Therefore, the maximum score of the written exam is 28/30 - 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 (if applicable) - 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. If the student decides to attend the optional oral exam, the final score of the exam cannot be rejected. - Students must verify that they are properly enrolled in the exam. Only student regularly enrolled can carried out the exam - The students which will held the exam online must check, well in advance, that they are equipped with the adequate means to take the exam according to the exam procedure proposed by the teaching staff (personal computer equipped with webcam or tablet, browser, network connection suitable for videoconferencing). To this aim, some tests will be organized during the course -The starting time of the exam is published on the teaching portal (Portale della Didattica) or communicated by professors (Italian time zone - CEST). Students are required to respect the start time of the test by checking the functionality of the necessary devices in time. - Participation in the online exam implies acceptance of the examination procedures defined by Politecnico, including video recording to ensure the regularity of the written test. - All students are required to comply with the University's Code of Ethical Conduct of the Politecnico di Torino