Undergraduate Course: Real Structural Behaviour and its Analysis 5 (CIVE11002)
Course Outline
School  School of Engineering 
College  College of Science and Engineering 
Credit level (Normal year taken)  SCQF Level 11 (Year 5 Undergraduate) 
Availability  Available to all students 
SCQF Credits  10 
ECTS Credits  5 
Summary  This course develops the student's comprehension of the nonlinear behaviour of structures. The concepts of geometrical and material nonlinearity are introduced and followed by numerical methods employed for modelling nonlinearities through the medium of finite element analysis. These advanced topics give the student the ability to analyse realistic systems with confidence. The student will develop and understand of many aspects of structural behaviour and its modelling. The course prepares the student well for a career in computational modelling in civil or structural engineering. 
Course description 
L1 Introduction
Structure and aims of the course. Subject in the context of theoretical and applied mechanics and structural engineering practice. The limitations of linear analysis and associated assumptions of small displacement and unchanged geometry. The need for going beyond linear analysis. The concept of equilibrium path and critical points along the path with appropriate examples.
L2 Sources of nonlinearity and types of problems
How do nonlinearities arise and what types of problems in structural
engineering they produce. How can these problems be dealt with
mathematically.
L3 Analysis of nonlinear problems I
Nonlinear analysis using the stiffness method and the finite element
method. Formulation of a nonlinear truss element with a geometric
stiffness. Applicaton to examples of linear bifurcation analysis (LBA) to
solve elastic critical load problems.
L4 Analysis of nonlinear problems II
Geometrically nonlinear analysis (GNA) of simple problems using the
truss element with load increments and Newton iterations.
L5 Analysis of nonlinear problems III
Beamcolumn elements with combined bending and axial force,
geometric stiffness matrix. Solution of simple LBA and GNA type
problems.
L69 Fundamentals of continuum mechanics
Eulerian and Lagrangian frames of reference, Green and Almansi strain measures and corresponding (PiolaKirchoff) stress measures,
deformation gradient, total Lagrangian, updated Lagrangian and corotational approaches to GNA.
L10 Introduction to material nonlinearity; linear elasticity; nonlinear elasticity; viscoelasticity; elastoplasticity; elastoviscoplasticity.
L11 1D elastoplasticity 1
Concepts of hardening, softening and perfect plasticity; load and
displacement control; uniaxial behaviour of different materials _$ú steel, aluminium, concrete, Gray cast iron, rubber.
L12 1D elastoplasticity 2
Solution nonlinear problems; issues associated with satisfying equilibrium and constitutive law; example problems; nonlinear solution in the context of FE analysis.
L13 Numerical solution approaches
Concept of tangent stiffness; incremental methods; incrementaliterative methods; Newton Raphson method; modified Newton Raphson method; convergence criterial.
L14 Multiaxial stress
Nonlinear models for multiaxial states; principal sresses and stress
invariants; convenient form of invariants for plasticity; recap of linear rlstic stressstarin relations.
L15 Yield criteria
Concept of yielding in a multiaxial stress state; Rankine, von Mises,
Tresca, Mohr Coulomb and Drucker Prager yield criteria; representation in principal stress space; hydrostatic axis and deviatoric plane; deviatoric
plane and plane stress representations; expressing criteria in principal
stress and stress invariant forms.
L16 Multiaxial plasticity 1
Hardening, softening and perfect plasticity; Bauschinger effect;
decomposition of strain; incremental stressstrain relations; flow rule;
consistency condition; tangential modulus matrix.
L17 Multiaxial plasticity 2
Elastic predictor _$ú plastic corrector concept; numerical evaluation of
the flow vector; evaluation of flow vector terms for Rankine, von Mises,Tresca, Mohr Coulomb and Drucker Prager yield criteria; issues
associated with singular regions; evaluation of hardening parameters.
L18 Revision

Information for Visiting Students
Prerequisites  None 
High Demand Course? 
Yes 
Course Delivery Information
Not being delivered 
Learning Outcomes
On completion of this course, the student will be able to:
 describe material and geometric nonlinearities through terms such as equilibrium path, limit load, collapse, bifurcation, and snapthrough buckling etc.
 show an understanding of large displacement behaviour including the need for more precise measures of stress and strain and associated analysis methods
 use nonlinear finite element analysis to manually solve simple problems with geometrically nonlinear behaviour including stability and bifurcation
 distinguish between the roles of eigenvalue and nonlinear analysis of geometrically nonlinear structural systems
 solve simple 1D plasticity problems through hand calculations

Reading List
McGuire, Gallagher, Ziemian (2000) "Matrix Structural Analysis, 2nd Edition". Wiley, London, UK.

Additional Information
Graduate Attributes and Skills 
Not entered 
Keywords  Nonlinear structural analysis,geometric nonlinearity,material nonlinearity,large displacement ana 
Contacts
Course organiser  Dr David Rush
Tel: (0131 6)50 6023
Email: D.Rush@ed.ac.uk 
Course secretary  Mr Craig Hovell
Tel: (0131 6)51 7080
Email: c.hovell@ed.ac.uk 

