75454 - Advanced Structural Mechanics M

Learning outcomes

At the end of the class, student has extended his/her basic knowledge on Mechanics of Solids and Structures and he/she has advanced understanding of structural behaviour. He/she knows elastic analysis (linear), structural matrix analysis (computer-based simulations), plastic analysis, limit analysis and fundamentals of structural dynamics. In particular, at the end of the course he/she is able to apply classical structural analysis methods to civil engineering systems, with emphasis on historical buildings.

Course contents

1. Introduction and Mathematical Preliminaries

• Introduction
• Vectors
• Tensors
  
• Exercises

2. Review of Equations of Solids Mechanics

• Introduction
• Balance of linear and angular momenta
• Kinematics of deformation
• Constitutive equations
• Theories of straight beams
• Exercises

3. Work, energy, and variational calculus

• Concepts of work and energy
• Strain energy and complementary strain energy
• Total potential energy and total complementary energy
• Virtual work
• Calculus of variations
• Exercises
  

4. Virtual work and energy principles of mechanics

• Introduction
• The principle of virtual displacements
• The principle of minimum total potential energy
• The principle of virtual forces
• principle of minimum total complementary potential
• Clapeyron's, Betti's and Maxwell's theorems
• Exercises

5. Dynamical systems: Hamilton's principle

• Introduction
• Hamilton's principle for discrete systems
• Hamilton's principle for a continuum
• Hamilton's principle for constrained systems
• Rayleigh's method
• Exercises

6. Direct variational methods

• Introduction
• The Ritz method
• Weighted-Residual methods
• Excercises

7. Theory and analysis of plates

• Introduction
• The classical plate theory
• The first-order shear deformation plate theory
• Relationships between bending solutions of classical and shear deformation theories
• Exercises

Readings/Bibliography

• Instructors' notes, solved examples and extra material (available on the web site http://iol.unibo.it).
• J.N. Reddy, Energy Principles and Variational Methods in Applied Mechanics, 3rd edition, Wiley, 2017. ISBN: 978-1-119-08737-3
• A.J.M. Ferreira, MATLAB Codes for Finite Element Analysis, Springer, 2009. ISBN: 978-94-007-8955-5
  

Teaching methods

The course content will be entirely covered by lectures. The course includes laboratory sessions, which will cover some practical aspects of the lectures. The instructors will supervise students during the laboratory activities. Weekly assignments will be given to students for improving and testing their abilities on the course.

Assessment methods

A final written examination is planned, based on questions intended to assess the knowledge and understanding of the topics covered by the course. Furthermore, the student should present and discuss the solutions of some homework assignments.

The assessment of the "expected learning outcomes" is composed of:

• Discussion on homework assignments (up to 10 points).
• Oral composed of 3 questions (8 points each, up to 24 points).

To obtain a passing grade (minimum is 18 points**) students are required to demonstrate a knowledge of the key concepts of the subject, some ability for critical application, and a comprehensible use of technical language. Higher grades (maximum is 30 points, cum laude) will be awarded to students who demonstrate an organic understanding of the subject, a high ability for critical application, and a clear and concise presentation of the contents.

An extra optional oral examination can be planned for improving the final mark obtained.

** in case of failure students can take any next final term, generally there are 6 final terms per academic year.

Teaching tools

The teaching tools are overhead projector, projector and PC. Whiteboard as well as iPad will be used to provide extra material of each class to students based on the lessons given. The course includes some laboratory sessions in which examples and problems are solved and analyzed.

Links to further information

http://iol.unibo.it

Office hours

See the website of Nicholas Fantuzzi