Teacher(s)
Language
English
> French-friendly
> French-friendly
Prerequisites
Good knowledge of Strength of Materials, Structural Analysis, and basis of the Finite Element Method, as
taught in the courses LGCIV1022 and LGCIV1023.
taught in the courses LGCIV1022 and LGCIV1023.
Main themes
- Review of the Finite Element Method
- Finite Element Method for Linear Elastic Shells and Solids
- Consistent derivation of 3D beam theory from Continuum Mechanics
- Solution methods in nonlinear problems
- Geometric nonlinearities
- Material nonlinearities
Learning outcomes
At the end of this learning unit, the student is able to : | |
Contribution of the course to the program objectives (N°)
At the end of this learning unit, the student is able to:
|
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Content
- Review of the Finite Element Method: Weak form, Galerkin method, Shape functions, Quadrature,
Stiffness matrix, Local-global numbering, Boundary conditions, System of equations. Mesh
refinement. Application to linear elastic beams. - Finite Element Method for Linear Elastic Shells and Solids: Equations of classical continuum
mechanics, Variational form, Elements, Interpolation, Possible issues (rigid body motion, shear
locking, volumetric locking, hourglass), Reduced integration, Thin-section solids (plates and shells). - Consistent derivation of 3D beam theory from Continuum Mechanics: Timoshenko, Extended
Timoshenko with distortion and warping, Euler-Bernoulli. - Solution methods in nonlinear problems: Nonlinear response, Incremental load application,
Newton-Raphson methods, Convergence criteria, Alternative iterative methods, Incremental-iterative
procedures with variable loading parameter (load-control, displacement-control, work-control, arclength),
Automatic load incrementation. - Geometric nonlinearities: Total Lagrangian, Updated Lagragian, Co-rotational formulations (total
compatibility, incremental compatibility, total equilibrium, incremental constitutive relations). - Material nonlinearities: Elasticity vs plasticity, Elastoplasticity, Plasticity, Yield Criterion, Plastic flow
(associated and non-associated flow rule), Strain hardening, Return mapping.
Teaching methods
Lectures based on course slides; exercise sessions; practical applications.
Evaluation methods
Continuous assessment (40% of the final grade) and final written and oral exam (60% of the final grade).
The continuous assessment is based on one written mini-test during the semester (7.5%) and a project (32.5%).
The assignment is done in groups of 2/3 students and cannot be repeated in a second session; the continuous assessment mark acquired in the first session is retained in the event of a second session.
Failure to comply with the methodological guidelines, particularly with regard to the use of online resources or collaboration between students for the assignment/project, will result in an overall mark of 0 for the continuous evaluation.
The mark submitted for the examination board’s consideration is the most recent mark achieved by the student during the academic year.
The continuous assessment is based on one written mini-test during the semester (7.5%) and a project (32.5%).
The assignment is done in groups of 2/3 students and cannot be repeated in a second session; the continuous assessment mark acquired in the first session is retained in the event of a second session.
Failure to comply with the methodological guidelines, particularly with regard to the use of online resources or collaboration between students for the assignment/project, will result in an overall mark of 0 for the continuous evaluation.
The mark submitted for the examination board’s consideration is the most recent mark achieved by the student during the academic year.
Other information
The course involves:
- The use / development of Python scripts;
- The use of a commercial/research finite element software (Abaqus).
- The use / development of Python scripts;
- The use of a commercial/research finite element software (Abaqus).
Online resources
Available in Moodle.
Bibliography
Notes et supports de cours.
Faculty or entity
Programmes / formations proposant cette unité d'enseignement (UE)
Title of the programme
Sigle
Credits
Prerequisites
Learning outcomes
Master [120] in Civil Engineering
Master [120] in Mechanical Engineering
Master [120] in Electro-mechanical Engineering
Master [120] in Mathematical Engineering
Master [120] in Energy Engineering