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Academic year
Didactic period
Secondo Semestre

Training objectives

The course aims at providing a first introduction to automated structural analysis. The main course objective is to introduce the student to a critical use of structural analysis codes and provide the foundations of structural analysis required by the engineering profession. The main acquired notions are:
- formulation and solution of structural models made by beam and bar elements.
- solution strategies for the elastic problem by means of finite element strategies.
- formulation of 1D finite elements for Euler and Timoshenko planar beams, planar bars, and curved beams for small displacements.
- formulation of 1D finite elements for Euler and Timoshenko planar beams for large displacements.
- finite element analysis of eigenvalue problems for 1D planar beams (buckling analysis, natural frequency analysis).
- principal workflow in a finite element software.
- convergence and limitations of the finite element analysis.
- use of a commercial finite element code and implementation of finite element algorithms in MATLAB.
The main acquired skills are:
- ability of generalize the finite element formulations presented in the lectures and carry out their implementation in MATLAB.
- ability to critically evaluate the outcomes of finite element analysis from commercial FE codes.
- critical assessment of the problems to be modeled and ability to correctly choose an adequate finite element model.


Manual resolution of simple beam systems by means of equilibrium or compatibility considerations (from Structural Mechanics courses). Basic knowledge of MATLAB language (from Calculus courses).

Course programme

Structural 1D models and finite element formulations: bars, Euler and Timoshenko planar beams, curved planar beams. Buckling and natural frequency analysis of planar beams, geometric and mass stiffness matrices. The structure of FEM codes: pre-processing, analysis, post-processing. Convergence of the FEM: sufficient conditions, inf-sup condition, locking problems. Laboratory activities: use of commercial FEM codes and implementation of FEM algorithms in MATLAB environment.

Didactic methods

Frontal teaching.

Learning assessment procedures

Oral examination. The exam will focus on the theoretical topics presented in the lectures and the homeworks by the students.

Reference texts

[1] Ottosen N.S., Petersson H. 1992. Introduction to the Finite Element Method, Prentice Hall.
[2] Fish J., Belytschko T. 2007. A First Course in Finite Elements, John Wiley & Sons.
[3] Cook R.D., Malkus D.S., Plesha M.E., Witt R.J. 2002. Concepts and applications of finite element analysis, 4th edition, John Wiley & Sons.
[4] Corradi Dell'acqua L. 1992. Meccanica delle strutture (vol.2) “le teorie strutturali e il metodo degli elementi finiti”, McGraw-Hill, Milano.
[5] Zienkiewicz O.C., Taylor R.L. 2000. The finite element method, 5ft edition, Butterworth Heinemann, Oxford.