OVERVIEW

The course aim is to introduce the mechanics of solids by the formulation of the field equations for the linear elastic boundary value problem. A collection of solutions is presented in detail referring to plane problems and bidimensional theories for plates and shells. Moreover, the course provides the basic knowledge of the finite elements method useful to determine numerical approximate solutions. Some problems of practical interest are also formulated and solved.

LEARNING OUTCOMES

The course provides the theoretical development of the mechanics of solids and structures with sufficient rigor to give students a good foundation for the determination of solutions to a broad class of problems of engineering interest. The primary goal is to formulate models, develope solutions and understand the results. 

Teaching methods

The course consists of theoretical lectures and discussion of case studies.

Detailed lecture notes are available on aulaweb.

SYLLABUS/CONTENT

Linear Elasticity Theory. Field equations. Solution strategies for the elastic problem: analytical and numerical approaches. Collections of elastic solutions to introduce structural theories. Plane strain and stress problems.  Stress formulation with Airy funtion. Polynomial solution. Polar formulation. Lamé problem. Plate with hole. Radial plane solutions. Bidimensional structural theories.  Kirchhoff Love for plates: membrane and bending theory. Field equations and boundary conditions. Navier and Levy solution methods. Plate effect. Mindlin-Reissner theory. Circular plates. Comparisons between the two models. Von Karman theory and applications. Membrane shell theory. Bending effects in shells. Spherical and cylindrical shells. Examples. 
Introduction to the finite elements method for numerical analyses. Variational formulation. Theorem of the minimum of potential energy. Finite element method. Phases and procedure. in linear context. Finite element examples (1D,2D,3D). Shape functions, stiffness matrix, assemblage,... Examples of elastic analysis with a finite element code.

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).
• Zienkiewicz, O.C., The finite element method in Engineering Science, McGraw-Hill, London (1971).
• Madenci E., Guven I., The finite element method and Applications in Engineering using Ansys (2015).

Lecture notes on aulaweb

Exam Board

GIUSEPPE PICCARDO (President)

FEDERICA TUBINO

ROBERTA SBURLATI (President Substitute)

Teaching methods

The course consists of theoretical lectures and discussion of case studies.

Detailed lecture notes are available on aulaweb.

LESSONS START

19 September 2016

Assessment methods

Oral examination

Exam schedule