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Computational structural mechanics

Presentation

  • Back to variational analysis in elasticity 

Mathematical analysis, Korn inequality

  • 2D linear computational structural mechanics 

In plane elasticity, finite element problem

  • Mixed formulations and coupling of computational models
  • Elastodynamic problem: modal 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

Objectives

At the end of this module, the student will have understood and be able to explain (main concepts):

 

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...