# Advanced modeling in computational structural mechanics

## Presentation

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

Organization:

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

 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...

## Bibliography

Bischoff, M., Ramm, E., & Irslinger, J. (2018). Models and finite elements for thinâ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.