Postgraduate Course: Real Structural Behaviour (European Masters) (PGEE11071)
Course Outline
| School | School of Engineering |
College | College of Science and Engineering |
| Credit level (Normal year taken) | SCQF Level 11 (Postgraduate) |
Availability | Not available to visiting students |
| SCQF Credits | 12 |
ECTS Credits | 6 |
| 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 |
Segment 1 Geometrically nonlinear behaviour and stability
This segment is given as an explanation of phenomena, structural behaviour, analysis formulation and key ideas in geometrically nonlinear behaviour and stability.
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 non-linear 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
Beam-column elements with combined bending and axial force, geometric stiffness matrix. Solution of simple LBA and GNA type problems.
L6-9 Fundamentals of continuum mechanics
Eulerian and Lagrangian frames of reference, Green and Almansi strain measures and corresponding (Piola-Kirchoff) stress measures, deformation gradient, total Lagrangian, updated Lagrangian and co-rotational approaches to GNA.
Segment 2 Materially nonlinear behaviour and analysis
L1 Introduction
Structure and aims of the course; types of nonlinearilties; linear elasticity; nonlinear elasticity; viscoelasticity; elastoplasticity; elasto-viscoplasticity.
L2 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.
L3 1D elastoplasticity 2
Solution nonlinear problems; issues associated with satisfying equilibrium and constitutive law; example problems; nonlinear solution in the context of FE analysis.
L4 Numerical solution approaches
Concept of tangent stiffness; incremental methods; incremental-iterative methods; Newton Raphson method; modified Newton Raphson method; convergence criterial.
L5 Multiaxial stress
Nonlinear models for multiaxial states; principal sresses and stress invariants; convenient form of invariants for plasticity; recap of linear rlstic stress-starin relations.
L6 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.
L7 Multiaxial plasticity 1
Hardening, softening and perfect plasticity; Bauschinger effect; decomposition of strain; incremental stress-strain relations; flow rule; consistency condition; tangential modulus matrix.
L8 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.
L9 Revision
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Entry Requirements (not applicable to Visiting Students)
| Pre-requisites |
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Co-requisites | |
| Prohibited Combinations | |
Other requirements | None |
| Additional Costs | 0 |
Course Delivery Information
| Not being delivered |
Learning Outcomes
By the end of the course, the student should be able to:
¿ describe the meanings of the terms such as, equlibrium path, limit load, collapse, bifurcation, and snap-through buckling etc.;
¿ show an understanding of large displacement behaviour including the need for more precise measures of stress and strain and associated analysis methods;
¿ distinguish between the roles of eigenvalue and non-linear analysis of geometrically nonlinear structural systems;
¿ use nonlinear finite element analysis to manually solve simple problems with geometrically nonlinear behaviour including stability and bifurcation.
¿ describe different kinds of material nonlinearities;
¿ solve simple 1D plasticity problems through hand calculations;
¿ show an understanding of the theory of plasticity;
¿ describe theories of non-linear material behaviour used for different materials;
¿ describe how plasticity is implemented in numerical analysis.
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Additional Information
| Graduate Attributes and Skills |
Not entered |
| Keywords | Structural Engineering |
Contacts
| Course organiser | Dr Asif Usmani
Tel: (0131 6)50 5789
Email: Asif.Usmani@ed.ac.uk |
Course secretary | Mr Craig Hovell
Tel: (0131 6)51 7080
Email: c.hovell@ed.ac.uk |
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