# 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

8. The finite element method

• Introduction
• Finite element analysis of straight bars
• Finite element analysis of the Bernoulli-Euler beam theory
• Finite element analysis of the Timoshenko beam theory
• Finite element analysis of the Classical plate theory
• Finite element analysis of the first-order shear deformation plate theory
• Exercises

• Instructors' notes (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.

## Assessment methods

A final oral exam is used to assess the knowledge and understanding of the topics covered in the course. In addition, homework and projects will be assigned and assessed during the course and will be used to calculate the final grade.

## Teaching tools

The teaching tools are overhead projector, projector and PC. The course includes some laboratory sessions in which structural analysis software is used.