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Computational structural mechanics

Presentation

Linear elasticity problem

-       Mathematical analysis, finite element discretization

 

Elastodynamic problem: spectral analysis and time integration

 

Numerical modeling of beams and plates (introduction)

 

CAD: introduction to isogeometric analysis

-       CAD representation of surfaces: tensor product of B-Splines and NURBS

-       Use of Splines for the computation

 

Mixed formulations and Mortar coupling

 

Organisation:

 

Conventional lectures/tutorials + class work (labwork)

 

Main difficulties for students:

 

To connect their mathematical knowledge and modelling problems in mechanics.

 

To step back on the finite element method for its application to structural mechanics.

Objectives

The fundamentals of Mechanics for deformable solids, from a physical, mathematical and numerical point of view.

 

The student will be able to:

 

-       Write the elasticity problem and extend the finite element methodology to this problem.

-       Formulate and solve the elastodynamic problem.

-       Know beam and plate modelling.

-       Know the basic methods to represent surfaces in CAD

-       Apprehend a computational technique based on the exact geometric representation in CAD (NURBS-based isogeometric analysis).

-       Set up a mixed formulation to couple different elastic domains (Mortar coupling).

Needed prerequisite

Continuum mechanics

Fundamentals for geometric representation in CAD: B-Spline and NURBS curves.



Form of assessment

The evaluation of outcome prior learning is made as a continuous training during the semester. According ot the teaching, the assessment will be different: as a written exam, an oral exam, a record, a written report, peers review...