cod. 1002362

Academic year 2021/22
1° year of course - First semester
Enrica RIVA
Academic discipline
Progettazione meccanica e costruzione di macchine (ING-IND/14)
A scelta dello studente
Type of training activity
Student's choice
48 hours
of face-to-face activities
6 credits
course unit

Learning objectives

Knowledge and understanding: by means of lectures, the student acquires the basis of the Finite Element method and knowledge required to describe, understand and develop a structural analysis
Applying knowledge and understanding: Through Lab activity connected to some important topics, students learn how to apply the acquired knowledge in a real context of mechanical design.
Making judgements: The student must be able to understand and critically evaluate the real work conditions of the component and using acquired knowledge, they will have to define a numerical model to simulate his mechanical behaviour
Communication skills: Through the Lecture and the assistance of the teacher, the student acquires the specific vocabulary inherent to the Finite Element methos.
At the end of the course, the student is expected to be able to communicate the main contents of the course, both written and orally, such as ideas, engineering issues and related solutions. The student must communicate his knowledge through appropriate tools, so numerical problems are solved using common Finite Element softwares
Learning skills: The student who has attended the course will be able to deepen his knowledge of the Finite Element Method through the autonomous reading of specialized books, web sites, even outside the topics explained during lectures.


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Course unit content

The course introduces the basic concepts of an computational method of analysis increasingly used in mechanical design.
The course deals with the theoretical aspects of the Finite Element Method, in detail, with the main Finite Elements, Rod elements, Beam Elements, Plane Elements, axisymmetric 2D elements, 3D elements
Moreover the course describes the criteria to definite the numerical model, how to realize the mesh, how to define boundary conditions, numerical integration methods and how to analyse the results in the post-processing step.
At the same in the Lab activity students will apply the method to practical cases and appreciate its potential and limitations.

Full programme

Matrix notation and matrix operations, review of continuum mechanics,
Principle of virtual work; plane structs: stiffness matrix of the rod
element and assembly of the stiffness matrix of the structure; beam
element: exact and approximate solutions, transformation matrix,
frames; plane stress, plane strain and axisymmetric 2D elements,
rectangular and triangular elements, isoparametric elements, numerical
integration; linear elasticity, meshing criteria, boundary conditions,
assembly and solution, analysis of results


Lectures notes, exercises, and all the supporting material provided during the course are available to students and shared in the web site Elly.
To access to the material students during the first lecture the teacher will give an access password.
For students that are not in class, to receive the Web Password to access to Elly web site they have to send an e. mail to the professor writing "Material FEM Elly" in the Object field.
In addition to the shared material, the student can personally study some of the topics discussed during the course in the following books:
• Cesari “ Introduzione al metodo degli elementi finiti”, Pitagora Editrice Bologna, 1989
• R. D. Cook “Finite Element Modelling for Stress Analysis”, John Wiley & Sons, Inc.
• O. C. Zienkiewicz, R. L. Taylor, J. Z. Zhu, “The Finite Element Method: Its Basis and Fundamentals”, 6th Ed., Butterworth-Heinemann
O. C. Zienkiewicz, R. L. Taylor, “The Finite Element Method for Solid and Structural Mechanics”, 6th Ed., Butterworth-Heinemann

Teaching methods

The course counts 6 CFUs which corresponds to 24 hours of lectures and 32 hours of Lab. The didactic activities are composed of frontal lessons alternating with exercises. During the frontal lessons, the course topics are proposed from the theoretical and design point of view.
During Lab activity students are allowed to bring their own computers and tablets, and they will apply theoretical knowledge to an exercise, a real case study.
The slides and notes used to support the lessons will be uploaded to the Elly Platform. To download the slides from Elly is required to enroll in the online course, while to be added to the share folder you need to send an email to the teacher as the object "Shared folder IM Drive".
Notes, slides and all shared material are part of the didactic material. For non-attending students, it is important to stay up-to-date on the course through the Elly platform, the only communication tool used for direct teacher / student contact.

Assessment methods and criteria

Verification of the knowledge takes place through a oral test, where the student will apply the method to a practical cases.

Final mark will be defined on the basis of the
corrects and complets answers and of the use of specific vocabulary about the structural analysis developed, i.e. definied numerical model, seplified hypotesis, use of symmetry, mesh, boundary conditions and also on the basis of the questions about the teoretical aspects of the method.

The exam is passed if it reaches a score of at least 18 points. “30 cum laude” is given to students who achieve the highest score on each item and use specific technical vocabulary.

Other information

There are no mandatory propedeuticities.