# 33945 - Plates and Shells M

### Course Unit Page

• Teacher Luca Patruno

• Credits 6

• SSD ICAR/08

• Language Italian

• Teaching Material

• Course Timetable from Sep 18, 2018 to Dec 17, 2018

## Learning outcomes

Provide skills for the analysis and design of structures in surface development. In particular, the different theories used to model plates and shells are applied to the resolution of problems of industrial engineering. It emphasizes the importance of the approximations and their influence on the results.

## Course contents

• Elements of three-dimensional elasticity;
• Elements of beam theory;
• Thin plates;
• Elements of variational principles;
• Buckling (plates);
• Surfaces geometry;
• Shells;
• Membrane theory of shells;
• Bending theory of shells.

If time is enough within the 60 h of the course:

• Free vibrations (plates);
• Elements of Finite Element Method.

In the following some images of the results that students will be able to obtain at the end of the course.

Fig. 1 - Normal force distribution for a spherical dome subjected to self weight: (N1) along the meridian and (N2) along the parallel.

Fig. 2 - Radial displacement of a circular cylinder loaded with a bending moment at the free edge.

Principal reference:

Ventsel, E., Krauthammer, V., Thin Plates and Shells Theory, Analysis, and Applications, TM Marcel Dekker Inc, 2001.

Secondary references:

Corradi Dell'Acqua, L., Meccanica delle strutture (1 e 2), McGraw-Hill Education, 2010.

Lanczos, C., The Variational Principles of Mechanics, Dover Books on Physics, 1986.

## Teaching methods

The program of the course is entirely presented during classtime. Theoretical lectures are complemented by excercises which involve the use of computers in order to facilitate the comprehension of the concepts introduced during lectures.

## Assessment methods

An oral exam will be used in order to evaluate the competences achieved during the course and the overall knowledge of the subject. Particular attention is devoted to the student's awareness and the interiorisation of the principal topics covered by the course. Attention should be paid in order to fully understand hypotheses and limitations of the developed models and, in general, to gain a good understanding of structural mechanics.

## Teaching tools

The tools to support teaching are: blackboard, slides, computer.

## Office hours

See the website of Luca Patruno