OVERVIEW

The course Structural Mechanics presents mechanical models for different structural types, which allow to determine reliable and efficient solutions for structural design and verification. First, the elastic problem for the Cauchy continuum is introduced. Then, mono- and two-dimensional structural models are illustrated. Finally, some basics of the Finite Element Method are provided.

AIMS AND CONTENT

LEARNING OUTCOMES

The unit is focused on the analysis of the elastic system equilibrium and strain; particularly, the course aims to study the redundant structure equilibrium, strength and stability conditions.

AIMS AND LEARNING OUTCOMES

The aim of the Course is to provide the fundamentals of Solid and Structural Mechanics, with particular attention to 1-D and 2-D structural theories, useful in structural applications.

The main learning outcomes of the Course are:

• Acquisition of the theoretical bases concerning the analysis of strain and stress in the Cauchy continuum

• Acquisition of the theoretical bases on the constitutive modeling of materials

• Acquisition of the theoretical bases on plane stress and strain problems

• Acquisition of the theoretical basis of the 1-D (Euler Bernoulli and Timoshenko) and 2-D (Kirchhoff and Mindlin-Reissner) structural theories

• Ability to recognize physical problems of structural engineering which can be solved through 3-D, 2-D and 1-D structural theories

• Ability to determine the principal stresses and strains in a point of the solid and the relative directions

• Ability to determine the stress state in 1-D and 2-D structures subjected to different loading conditions

TEACHING METHODS

The course is divided into lectures aimed to introduce the theoretical concepts underlying solid mechanics and structural theories and exercises for the resolution of practical problems (analysis of the stress and strain states).

SYLLABUS/CONTENT

The course is articulated in four parts.

1) Solid Mechanics. Equilibrium and stress concept according to Cauchy - The Cauchy theorem - The equilibrium equations - Principal stresses and principal stress directions - Mohr's circle - Analysis of deformation – Compatibility Equations – Principal strains and principal directions of strain - The constitutive equations – Elasticity – Formulation of the boundary value problem.

2) Plane problems. Two-dimensional problem in elasticity in Cartesian and polar coordinate systems - Plane strain and plane stress - Explicit solutions for specific loading and geometry conditions (e.g. rectangular domains, thick-walled cylinder in pressure, stress intensity factor around a hole in a plate).

3) 1-D and 2-D Structural Theories. Euler Bernoulli beam theory – Timoshenko beam theory – Euler’s critical buckling load for beams - Kirchhoff’s plate theory - Mindlin-Reissner plate theory - Von Karman theory and critical buckling load for plates.

4) Introduction to the Finite Element Method (FEM). Discrete formulation of the elastic problem. Bar element: stiffness matrix, equilibrium equations, assembly, boundary conditions, displacement, strain and stress - Beam element: stiffness matrix, equilibrium equations, assembly, boundary conditions, displacement, strain and stress- Ritz method – Finite Element Method.

RECOMMENDED READING/BIBLIOGRAPHY

Corradi Dell’Acqua, L., Meccanica delle strutture 2, McGraw-Hill, London (2010).

Nunziante, L., Gambarotta, L., Tralli, A., Scienza delle Costruzioni, McGraw-Hill (2008).

Mase, G.T. Mase, G.E., Continuum Mechanics for Engineering, CRC Press, New York (1999).

Sadd, M.H., Elasticity: Theory, Applications, and Numerics, Elsevier (2014).

TEACHERS AND EXAM BOARD

Exam Board

FEDERICA TUBINO (President)

CESARE MARIO RIZZO

ROBERTA GIOVANNA SBURLATI (President Substitute)

LESSONS

LESSONS START

https://corsi.unige.it/9268/p/studenti-orario

Class schedule

The timetable for this course is available here: Portale EasyAcademy

EXAMS

EXAM DESCRIPTION

The exam is oral with two/three questions concerning the different parts of the program.

ASSESSMENT METHODS

The exam is aimed at ascertaining the understanding of the theoretical knowledge of Solid and Structural Mechanics acquired by the student (stress and strain analysis in solids, constitutive equations for the continuum, 1-D and 2-D structural theories, basics of Finite Element Methods). The exam focuses on the formulation of the problems and the related demonstrations. The assessment will take into account the level of knowledge achieved, the degree of preparation, the ability of critical analysis and the acquisition of a correct terminology.

Exam schedule