Bibliographic resources
Bibliography mandatory
Bibliography not mandatory
Summary Teaching Assignment
Academic Year 2019/2020
School School of Industrial and Information Engineering
Cfu 5.00 Type of Course Mono-Disciplinary Course
Innovative teaching The course includes  1.0  credits in Innovative Teaching as follows:
  • Blended Learning & Flipped Classroom
Lecturers: Titolare (Co-titolari) Gastaldi Dario

Programme Track From (included) To (excluded) Course


The course introduces to the numerical techniques currently adopted to compute the mechanical response of solids and the fluid dynamics in complex systems. Within the course, the student will practice with two standard commercial codes aimed at structural and fluid-dynamics analysis, respectively. In the last part of the course, students will work in small groups and apply the acquired knowledge and competences by developing new projects in the context of biomedical applications.

Expected learning outcomes

Knowledge (DD1): students are expected to acquire notions on continuum mechanics, on numerical techniques to solve partial differential equations, on the use of two software packages that well represent the standard commercial solvers in the field of structural mechanics and fluid dynamics, respectively. They are also expected to understand the impact of modeling hypotheses and to use their knowledge on real problems.

Competences: by the end of the course, students are expected to be able to i) formulate and solve complex problems in the field of biomedical engineering (DD2), ii) apply engineering methods to the field of biology and biotechnology (DD2), iii) communicate the results of their activity in clear and concise manner (DD4).


The course is organized in two parts, focused on the analysis of structural mechanics through finite element modeling and on computational fluid dynamics through finite volume modeling, respectively. In both parts, students will be introduced to the computational methods implemented in a commercial code with a mix of lectures and tutorials. At the end of each part, students will develop a project working in small teams.

 Part one: finite element modeling and structural mechanics

Solid mechanics and introduction to the finite element method: the governing equations of solid mechanics will be overviewed. Their weak form and the corresponding discretization and solution will be introduced. In details, standard displacement-based approach will be introduced together with discretization strategies of governing equations, numerical integration issues and algorithms for solution of linear and nonlinear problems.

Principles of solid mechanics simulations: the commercial package Abaqus will be introduced, the main steps for the problem solution including the boundary conditions, meshing algorithms and solution strategies will be reviewed for linear and nonlinear simulations. 

Tutorials: by using Abaqus, students will train in teams on tutorials following a step-by-step guide.

Project: working again in team and using Abaqus, students will have to set and run an analysis to tackle a real-world problem. The problem to be simulated will be exhaustively described in terms of design specifications, but students will have to independently choose how to set their model. At the end of the project, each team will have to produce a report.


Part two: finite volume modeling and fluid dynamics

Introduction to fluid dynamics: the equations governing the conservation of mass, of linear momentum and of energy will be derived and discussed. Their weak form, its discretization and solution will be introduced based on the general scheme of convection-diffusion equations. 

Principles of fluid mechanics simulation: lectures will describe:

- how to obtain the linear algebraic form of the field equations

- the iterative methods for algebraic system solution, the upwinding schemes, the pressure-velocity coupling algorithms

- how to check convergence and result accuracy.

Tutorials: the commercial package Ansys-Fluent will be introduced. The team of students will work on tutorials, devoted to introducing progressively more complex features of the software package, including the use of user-defined functions.

Project: working again in team and using Ansys-Fluent, students will have to set and run an analysis to tackle a real world problem. The problem to be simulated will be exhaustively described in terms of design specifications, but students will have to independently choose how to set their model. At the end of the project, each team will have to produce a report.

Important Note

This is a limited number access course. The mandatory procedure for access request is here http://www.ccsbio.polimi.it/?page_id=27  )”


There is no mandatory prerequisite. However, a sound background in continuum mechanics and calculus is highly desirable.


Students will be evaluated at the end of the course on the basis of the two reports produced within the end of the course and of a written examination on the theoretical parts of the course. The final mark will be the average of the marks of each report and of the written examination, which will have to be all sufficient.

Risorsa bibliografica facoltativaH.K. Verstag and W. Malalasekera, An introduction to computational fluid dynamics - The finite volume method, Editore: Prentice Hall College Div (second edition), Anno edizione: 2007, ISBN: 0131274988
Risorsa bibliografica facoltativaE. Onate, Structural Analysis With The Finite Element Method. Linear Statics: Volume 1: Basis And Solids , Editore: Springer, Anno edizione: 2012, ISBN: 9048179718
Risorsa bibliografica facoltativaO.C. Zienkiewicz, R.L.Taylor, J.Z. Zhu, The Finite Element Method: Its Basis And Fundamentals, Editore: Butterworth-Heinemann, Anno edizione: 2005, ISBN: 0750663200

Software used
No software required

Learning format(s)
Type of didactic form Ore di attività svolte in aula
Ore di studio autonome
Computer Laboratory
Experimental Laboratory
Project Laboratory
Total 50:00 75:00

Information in English to support internationalization
Course offered in English
Study material/slides available in English
Textbook/Bibliography available in English
It is possible to take the examination in English
Support available in English
schedaincarico v. 1.10.0 / 1.10.0
Area Servizi ICT