This course introduces students to theoretical and practical aspects of finite element method, regarding the static structural analysis in dynamic and non linear field. .

This course introduces students to theoretical and practical aspects of Finite Element Method, regarding the static structural analysis in linear in dynamic and non linear field. Main finite element codes structures is introduced. Focusing on Modelling techniques and post processing of results.

The student must have frequented the courses of 'Machine Design' 'Linear Finite Element Method for structural static engineering problems'

- Dynamics Finite Element Method for structural engineering problems
Main concepts of structural dynamics. Free and force vibrations. Single d.o.f systems equations. Response functions : receptance , mobility and inertance. Equation of motion in matrix form. Mass matrix : lumped and consistent formulation with principle of virtual work. Modal analysis. Guyan reduction.. Subspace iteration. Transient dynamic solutions. Modal superposition. Modal participation factor. Direct integration methods: explicit (central difference method) and implicit methods: . Houbolt method; Newmark and Wilson-theta method. Stability and precision analysis of the direct integration methods. Stability criteria and critical time step determination. Harmonic response.
- Non-linear Finite Element Method for structural engineering problems
Introduction to the Finite Element Method for non linear engineering problems; classification. Large displacement, large strain. Example of determination of a stiffness matrix of a beam element in the stress stiffening behaviour.
material non linearity classification and introduction to the non linear algorithm selection in a finite element code. Newton-Rapson method for the determination of the tangential stiffness. Finite element simulation and modelling for contact problem. Element classification.

The practical lab will be done on the basic problems studied in the theoretical part of the course. Student groups have to prepare two reports. Practical lab consists in beam-like static analysis with ANSYS for the first report and the second report regarding the simulation of 2d and 3d structure modelling with plane or shell / solid elements.

' Gugliotta Elementi Finiti ' Otto Editore
' Aurelio Somà - Esercitazioni di laboratorio
' R.D. Cook, Concepts and applications of finite element analysis, Wiley.
' K.J. Bathe, E.L. Wilson, Numerical methods in finite element analysis, Prentice Hall.

Exams consist is oral. Examination starts from the discussion of the exercises regarding the practical lab and on the theoretical aspects presented in the classes.