33945 - Plates and Shells M

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

The course provides advanced knowledge of the mechanics of solids and structures, with the aim of giving students the theoretical foundation needed to consciously design two-dimensional structural elements such as plates and shells, which are typical of lightweight structures and structures made of composite materials. The syllabus is organized into the following topics:

 

• 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. 

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.

At the end of the course, students have a solid grasp of structural theories and their rational derivation from elasticity theory. They develop both an intuitive and rigorous understanding of the mechanical behavior of plates and shells. Finally, they are able to carry out numerical simulations, selecting the most appropriate models, consciously choosing boundary conditions, and interpreting the results.

Readings/Bibliography

The course is fully covered by slides, which are made available to students before the lectures, and by extended notes. However, students are advised to study using the course textbooks listed below.

Main 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.

The course is organised following a modular structure and students are allowed to compose them according to their need and interests.

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: virtual blackboard, slides, computer.

Links to further information

https://www.youtube.com/watch?v=Xl9fCpN3DNU

Office hours

See the website of Luca Patruno