# ELEMENTS OF CALCULUS OF STRUCTURES

Academic year and teacher
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Versione italiana
Academic year
2022/2023
Teacher
ANDREA CHIOZZI
Credits
6
Didactic period
Secondo Semestre
SSD
ICAR/08

#### 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.

#### Prerequisites

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.