
Course unit
NON LINEAR SOLID AND STRUCTURAL MECHANICS
INO2043807, A.A. 2017/18
Information concerning the students who enrolled in A.Y. 2016/17
ECTS: details
Type 
ScientificDisciplinary Sector 
Credits allocated 
Core courses 
ICAR/08 
Construction Science 
9.0 
Mode of delivery (when and how)
Period 
Second semester 
Year 
2nd Year 
Teaching method 
frontal 
Organisation of didactics
Type of hours 
Credits 
Hours of teaching 
Hours of Individual study 
Shifts 
Lecture 
9.0 
72 
153.0 
No turn 
Start of activities 
26/02/2018 
End of activities 
01/06/2018 
Prerequisites:

Structural Dynamics 
Target skills and knowledge:

The course deals with the analysis and modeling of nonlinear solids and structures. The main emphasis is on the modeling aspect, i.e. the justification and properties of the theory, and the development of the theory in a form suitable for computational analysis. The idea is to present the theory and the corresponding numerical methods as a gradual development, from simple bar and truss systems via finite rotations, up to beams and shells with nonlinear kinematics and material behavior. 
Examination methods:

Practical applications 
Assessment criteria:

The evaluation will be based on:
 exercises (a collection of exercises must be presented by each candidate)
 oral discussion on the theoretical arguments 
Course unit contents:

Theory: Mathematical preliminaries: vector and tensor algebra, linearization and directional derivative, tensor analysis. Finite rotations: the vector and tensor representation of rotations in 3D space, quaternion representation. Formulation of a beam undergoing finite deformation: kinematic, balance laws and constitutive relationships. Formulation of shell undergoing finite displacements, rotations and deformations: kinematic and balance laws. Numerical methods for solving nonlinear equations: NewtonRaphson, Orthogonal Residual and ArcLength. Introduction to non linear dynamic analysis: Newmark algorithm and energyconserving methods. Classes of problems and solutions: problems of solid and structures undergoing with finite displacements and rotations, problems involving beams in finite deformations, problems dealing with shells in finite deformations.
Exercises: Introduction to MatLab Scilab Ansys code; analyses using nonlinear truss elements; analyses with nonlinear beam elements; analyses with nonlinear brick element; implementation of elastoplastic constitutive laws; implementation of different solution techniques; non linear dynamic analyses. 
Planned learning activities and teaching methods:

The course is composed by theoretical lectures and exercises carried out in computer lab. 
Additional notes about suggested reading:

Simo, J.C. and co., Series of papers on nonlinear beams and shells (1990 – 1996). 
Textbooks (and optional supplementary readings) 

Marsden, Jerrold E.; Hughes, Thomas J. R., Mathematical foundations of elasticityJerrold E. Marsden, Thomas J. R. Hughes. New York: Dover, 1994.

Krenk, Steen, Nonlinear modeling and analysis of solids and structuresSteen Krenk. Cambridge: Cambridge University press, 2009.

Zienkiewicz, Olgierd Cecil; Taylor, R.L; Taylor, Robert Leroy; Zhu, J. Z.; Zienkiewicz, Olek C, <<The>> Finite Element Method: Its Basis and Fundamentals, 7th ed. Elsevier: Inc., 2013.

Simo, Juan C.; Hughes, Thomas J. R., Computational inelasticityJ.C. Simo, T.J.R. Hughes. New York \etc.!: Springer, .


