[Seminario] INVITACIÓN SEMINARIO MECÁNICA MATEMÁTICA Y PROBLEMAS INVERSOS MARTES 12 DE JULIO DEL 2016.

Maria Ines mrivera en dim.uchile.cl
Lun Jun 20 11:20:55 CLT 2016


Estimados Académicos y Alumnos,

se les invita para el próximo /*Martes 12 de Julio a las 15:00 hrs*/,  a 
una nueva sesión del /*Seminario  Mecánica Matemática y Problemas 
Inversos*/, este seminario se realizará en la sala de seminarios John  
Von Nuemann CMM, séptimo Piso, Torre Norte de Beauchef 851.

*
SEMINARIO

MECÁNICA MATEMÁTICA Y PROBLEMAS INVERSOS

EXPOSITOR
*
*Prof. Grégoire Allaire*
*Centre de Mathématiques Appliquées*
*Ecole Polytechnique de Paris*
*Unité Mixte de Recherche du C.N.R.S. - 7641 *
*91128 Palaiseau (FRANCE) *

*TITULO*
Robust shape optimisation with small uncertainties

*Abstract*

In this talk we propose two approaches for dealing with small uncertainties
in geometry and topology optimisation of structures. Uncertainties occur in
the loadings, the material properties, the geometry or the imposed vibration
frequency.

A first approach, in a worst-case scenario, amounts to linearise
the considered cost function with respect to the uncertain parameters, then
to consider the supremum function of the obtained linear approximation, 
which
can be rewritten as a more `classical’ function of the design, owing to 
standard
adjoint techniques from optimal control theory.

The resulting `linearised worst-case’ objective function turns out to be 
the sum
of the initial cost and of a norm of an adjoint state function, which is 
dual with
respect to the considered norm over perturbations.

A second approach considers objective functions which are mean values, 
variances or
failure probabilities of standard cost functions under random 
uncertainties.
By assuming that the uncertainties are small and generated by a finite 
number
N of random variables, and using first - or second-order Taylor expansions,
we propose a deterministic approach to optimise approximate objective 
functions.
The computational cost is similar to that of a multiple load problems 
where the
number of loads is N.

We demonstrate the effectiveness of both approaches on various 
parametric and
geometric optimisation problems for elastic structures in two space 
dimensions.

The talk is based on joint work with Charles Dapogny (LJK, Grenoble).


Martes 12 de Julio a las 15:00 hrs, sala de Seminarios John Von Neumann 
CMM, séptimo piso, torre norte de Beauchef 851.

Esperando contar con su presencia, les saluda,

Ma.  Inés Rivera


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