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Advanced modeling in computational structural mechanics


Program (detailed contents):


Numerical modeling of thin structures (10h : 5CM + 3TD)

-       Construction of a beam model from standard 3D solid elasticity

-       Variational formulation, connection with energy minimization and numerical resolution by the finite element method.


CAD-analysis relation (10h : 4CM + 2TP)

-       Fundamentals for describing geometries in CAD.

-       Isogeometric analysis: spline finite elements

-       Application for the computation of beam models.


Model and computation of contact problem (7,5h = 3CM + 1TD + 1TP)

-       Frictionless contact between elastic bodies, Signorini conditions

-       Introduction to variational inequalities

-       Numerical methods for contact problems : penalty, regularization, duality


Image registration using the FE modeling (7,5h : 4CM + 1TP)

-       Digital image correlation

-       Data-model combination in experimental mechanics




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.


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


A few advanced modelling methods in structural mechanics to tackle current real applications such as:

-       computation of shell-type structures;

-       use of CAD data for the computation;

-       model and computation of contact problems between elastic bodies;

-       image registration in view of performing data – model comparison in experimental mechanics.


The student will be able to:


On simple cases:


-       Formulate and solve by the FEM beam models.

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

-       Formulate and solve using various finite elements algorithms a frictionless contact problem

-       Identify material properties by image data - model comparison.


Needed prerequisite

-       Continuum mechanics.

-       Elasticity modelling.

-       Finite element method.

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...


Bischoff, M., Ramm, E., & Irslinger, J. (2018). Models and finite elements for thin‐walled structures. Encyclopedia of Computational Mechanics Second Edition, 1-86.


J. Austin Cottrell, Thomas J. R Hughes, Yuri Bazilevs, Isogeometric Analysis: Toward Integration of CAD and FEA, Wiley , 2009, ISBN: 978-0-470-74873-2


SUTTON, Michael A., ORTEU, Jean Jose, et SCHREIER, Hubert. Image correlation for shape, motion and deformation measurements: basic concepts, theory and applications. Springer Science & Business Media, 2009.


Kikuchi, N. and Oden, J.T. Contact problems in elasticity. A study of variational inequalities and finite element methods. SIAM, 1988.