Teacher

prof. Mircea Gheorghe MUNTEANU

Credits

12 CFU

Language

Italian

Objectives

With regard to the aided design of mechanical structures, this course aims to provide advanced tools for the design and verification of the organs of the machines, with particular attention to numerical methods appropriate for computer using. Therefore some analytical methods, matriceal analysis of structures, finite element method are presented. Regarding principles and methodologies of mechanical design, this course addresses the case of some mechanical parts such as rotating disks subject to centrifugal field and temperature gradient, thin wall recipients subjected to internal pressure etc.  Some aspects of using the finite element method in the modeling of the mechanical parts, especially with regard to the strategies of the practical use of the method in the modeling of structural issues of mechanical interest are presented.

Acquired skills

- Ability of performing finite element analysis of mechanical structures.
- Knowing of the structure and organization of a finite element computer code.
- Ability to use a commercial finite element computer code (ANSYS).

Lectures and exercises (topics and specific content)

Matriceal analysis of structures: linear algebra in Matlab (4 hours).
Numerical method in engineering: short description of finite difference method, finite element method, finite boundary method (4 hours).
Theory of elasticity: equations of theory of elasticity in Cartesian coordinates and in cylindrical coordinates, axi-symmetrical bodies, temperature effect (thermoelsticity), virtual work, energetic theorems (6 hours).
Finite element method: element characterizing: Truss element, flexibility and stiffness, local and global reference frame, reference frame changing, equivalent nodal forces (6 hours).
Structure characterization: assembling process of the finite elements, forming of the global stiffness matrix, boundary conditions, linear solution solving (6 hours).
Finite element method: finite element characterization, triangular finite element, shape function, conform finite elements, the most important finite element types, finite element convergence (6 hours).
Finite elements: numerical method: isoparametric formulation, numerical integration, selective integration; stress computing; Didactic MATLAB programs, description and using of these programs; comparing with results obtained in Ansys (12 hours).
Finite elements: domain meshing: FE model building: symmetry and anti-symmetry, meshing rules, boundary condition problems; result interpretation, model improving (6 hours).
Other types of finite elements: beam element, Euler-Bernoulli beam theory and Timoshenko beam theory; rectangular finite element, quadrilateral finite element. Isoparametric finite elements, natural coordinates, Jacobian, Gauss integration method (10 hours).
Finite element method: practical aspects: automatic mesh generation, adaptive techniques.; boundary condition problems; ill-conditioned problems; FE model improving; elastic supports (6 hours).
Rotating disks &thin walled recipients with internal pressure: general expression of the solution; constant thickness disks, centrifugal forces, non-uniform axi-symmetrical temperature field; stress concentration; axi-symmetrical shells; conical recipient; localized bending stress; computing of the stress concentration for a cylindrical recipient with spherical ends (16 hours).
Introduction to the dynamics of mechanical structures: mass matrix, damping matrix; vibration of Multi-DOF System, differential equation, numerical method for differential equation with initial conditions (finite difference method, Newmark method), numerical examples (4 hours).
Exercises: finite element analysis of simple widely spread structures using a commercial code (ANSYS), confronting numerical solution with the analytical ones (32 hours).
Tutorials / Seminars (4 hours).

References

- Course notes
- A.Strozzi, Appunti del Corso di Costruzione di Macchine, Pitagora, 1998
- K.J. Bathe, Numerical methods in finite element analysis, Prentice-Hall, 1976
- C. Felippa, http://www.colorado.edu/engineering/CAS/Felippa.d/FelippaHome.d/Home.html

Type of exam

Written and oral

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