66787 - Advanced Structural Mechanics

Course Unit Page


This teaching activity contributes to the achievement of the Sustainable Development Goals of the UN 2030 Agenda.

Quality education

Academic Year 2021/2022

Learning outcomes

The course is an extension and intensification of Mechanics of Solids and Structures. The goal of the course is to advance the understanding of structural behavior and enhance the ability to apply classical structural analysis methods to civil engineering systems. The advanced methods for the analysis of structures will be applied to some structural examples which will be developed by the students.

Course contents

1. Introduction and Mathematical Preliminaries

  • Introduction
  • Vectors
  • Tensors
  • Problems

2. Review of Equations of Solids Mechanics

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

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
  • Problems

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
  • Problems

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
  • Problems

6. Direct variational methods

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

7. The Finite Element Method

  • Introduction
  • Finite Element Analysis of Straight Bars
  • Finite Element Analysis of Bernoulli-Euler
  • Finite Element Analysis of Timoshenko Beam Theory
  • Problems

8. Analysis of Functionally Graded Beams

  • Introduction
  • Functionally Graded Beams
  • Navier's solutions
  • Finite Element Models
  • Problems


  • 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, N. Fantuzzi, MATLAB Codes for Finite Element Analysis, 2nd Edition, Springer, 2020. ISBN: 978-3-030-47951-0

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 test is planned, based on questions intended to assess the knowledge and understanding of the topics covered by the course. Furthermore, the student should present the solutions of homework assignments.

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

  • Presentation of homework assignments (compulsory to access the final test).
  • Test composed of 11 questions (3 points each, up to 33 points).
  • Oral discussion.

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, with honors) 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.

** 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.

iPad will be used as whiteboard support tool for extra material details given to students at the end of each class.

All the classes will be recorded via MS Teams and they will be available to students.

The course includes some laboratory sessions in which examples and problems are solved and analyzed.

Office hours

See the website of Nicholas Fantuzzi