Numerical analysis of civil engineering structures

lgciv2041  2024-2025  Louvain-la-Neuve

Numerical analysis of civil engineering structures
4.00 credits
20.0 h + 15.0 h
Q2
> Schedule
Teacher(s)
Rattez Hadrien; Saraiva Esteves Pacheco De Alm João;
Language
English
> 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.
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 :

1 Contribution of the course to the program objectives (N°)
AA1.1, AA1.2, AA1.3, AA2.1, AA2.2, AA2.3, AA2.4, AA3.1, AA3.2, AA4.2, AA4.4, AA5.6.
Specific learning outcomes of the course
At the end of this learning unit, the student is able to:
  • Understand the principles and application of the finite element method as relevant to the analysis of civil engineering structures (namely beams, plates, and solid finite elements).
  • Develop and code several finite elements in Python, explore their features and issues, and get acquainted with a general-purpose finite-element software. This includes the treatment of input data and the post-treatment of the results.
  • Understand alternative approaches to modelling geometric and material nonlinear effects, and corresponding finite element implementation.
  • Understand advantages and limitations of different solution methods for nonlinear problems, and corresponding finite element implementation.
 
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 and final oral exam.
The continuous assessment is based on two written exams of 15 minutes each during the semester and an assignment.
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 use of generative artificial intelligence (such as ChatGPT, Consensus, Perplexity, Bard, etc.) is prohibited for this course.
Other information
The course involves:
- 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
> GC


Programmes / formations proposant cette unité d'enseignement (UE)

Title of the programme
Sigle
Credits
Prerequisites
Learning outcomes
Master [120] in Civil Engineering
GCE2M
4
Master [120] in Mechanical Engineering
MECA2M
4
Master [120] in Electro-mechanical Engineering
ELME2M
4
Master [120] in Mathematical Engineering
MAP2M
4
Master [120] in Energy Engineering
NRGY2M
4