First cycle
degree courses
Second cycle
degree courses
Single cycle
degree courses
School of Engineering
MATHEMATICAL ENGINEERING
Course unit
ADVANCED SOLID MECHANICS
INP5070425, A.A. 2018/19

Information concerning the students who enrolled in A.Y. 2017/18

Information on the course unit
Degree course Second cycle degree in
MATHEMATICAL ENGINEERING
IN2191, Degree course structure A.Y. 2017/18, A.Y. 2018/19
N0
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Degree course track MATHEMATICAL MODELLING FOR ENGINEERING AND SCIENCE [001PD]
Number of ECTS credits allocated 9.0
Type of assessment Mark
Course unit English denomination ADVANCED SOLID MECHANICS
Department of reference Department of Civil, Environmental and Architectural Engineering
E-Learning website https://elearning.unipd.it/dicea/course/view.php?idnumber=2018-IN2191-001PD-2017-INP5070425-N0
Mandatory attendance No
Language of instruction English
Branch PADOVA
Single Course unit The Course unit can be attended under the option Single Course unit attendance
Optional Course unit The Course unit can be chosen as Optional Course unit

Lecturers
Teacher in charge GIANLUCA MAZZUCCO ICAR/08

ECTS: details
Type Scientific-Disciplinary Sector Credits allocated
Core courses ICAR/08 Construction Science 9.0

Course unit organization
Period First semester
Year 2nd Year
Teaching method frontal

Type of hours Credits Teaching
hours
Hours of
Individual study
Shifts
Lecture 9.0 72 153.0 No turn

Calendar
Start of activities 01/10/2018
End of activities 18/01/2019

Examination board
Board From To Members of the board
3 2018 01/10/2018 30/11/2019 MAZZUCCO GIANLUCA (Presidente)
SALOMONI VALENTINA (Membro Effettivo)
MAIORANA CARMELO (Supplente)
POMARO BEATRICE (Supplente)
2 2017 01/10/2017 30/11/2018 SALOMONI VALENTINA (Presidente)
MAZZUCCO GIANLUCA (Membro Effettivo)
MAIORANA CARMELO (Supplente)

Syllabus
Prerequisites: Continuum Mechanics
Target skills and knowledge: The course is based on the analysis and modelling of non-linear solids and structures for material (and geometry). Emphasis is given to modelling aspects and on the development of the theory in a form adequate for the modelling itself. The idea is to present theory and correspondent numerical methods as a gradual development, from simple systems as trusses and beams to threedimensional bodies, characterized by non-linear kinematics and material behaviour.
Examination methods: Practical application. Each student will develop autonomously a mechanical detail using the numerical tecniques learnt during the course.
Assessment criteria: The evaluation is based on:
- exercises (some exercises can be developed by the candidate)
- practical test and oral discussion on theoretical subjects
Course unit contents: General formulation of the finite element method and application to solid mechanics in statics field (weighted residual method, variational method, Bubnov-Galerkin method, principle of virtual work, discretization in space, isoparametric finite elements).

Finite element method for non-linear problems (linearization, Newton's method, quasi-Newton and modified Newton).

Linear and Non-linear trusses and beams: deformation - equilibrium - tangent stiffness matrix - use of shape functions - assembling - total or lagrangian formulation.
Euler-Bernoulli beam.

Elasto-plastic solids: elastic solids - general theory of plasticity - return mapping algorithm - models for granular materials (finite elasto-plasticity).

Deformation and equilibrium of solids: deformation - non-linear deformation - strain decomposition - virtual work and stresses (Piola-Kirchhoff, Cauchy, stress rates) - total and updated lagrangian formulation.

Computational Contact Mechanics: - General formulation - Penalty method - Lagrange multiplier method.

Techniques of three dimensional modeling.
Planned learning activities and teaching methods: Frontal lectures
Textbooks (and optional supplementary readings)
  • Marsden, J., Hughes, T.J.R., Mathematical Foundations of Elasticity. --: Prentice Hall, 1983. Cerca nel catalogo
  • Krenk, S., Non-linear Modeling and Analysis of Solids and Structures. --: Cambridge University Press, 2009. Cerca nel catalogo
  • Zienkiewicz, O.C., Taylor, R., The Finite Element Method - Voll. 1 & 2. --: McGraw-Hill, 1994. Cerca nel catalogo
  • Simo, J.C, Hughes, T.J.R., Computational Inelasticity. --: Springer, 1998. Cerca nel catalogo
  • Onate, E., Structural Analysis with the Finite Element Method: Linear Statics - Vol. 2. --: Springer, 2013. Cerca nel catalogo

Innovative teaching methods: Software or applications used
  • Matlab
  • Abaqus, Straus7, Inventor