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SUMMARY:Optimal reliability: Stochastic failure time processes and geometr
 y optimization
DTSTART:20150602T100000
DTEND:20150603T120000
DTSTAMP:20260407T020841Z
UID:9277b91842b25effa24b659b264f7535c109d00ef2bafa8ca1246a93
CATEGORIES:Conferences - Seminars
DESCRIPTION:Hanno Gottschalk\n1.    The first lecture gives an outline 
 on the engineering practice of fatigue life calculation for mechanical com
 ponents under cyclic loading. The elasticity PDE and the weak solution the
 ory are developed\, physical failure mechanisms as Low Cycle Fatigue are r
 eviewed. The combination of Neuber- and Glinker shake-down\, Ramberg Osgoo
 d equantion and Coffin-Manson Basquin equation are explained with an empha
 sis to mathematical properties. Stochastic failure time processes are intr
 oduced on the basis of the first occurrence time of spatio-temporal point 
 processes. A specific failure time model is introduced based on the Weibul
 l distribution. It is explained\, how the demand for optimal reliability\,
  i.e. the choice of a form that minimizes failure probabilities\, in a nat
 ural way leads to a problem in the field of shape optimization. \n2.  
   The second lecture reviews the fundamentals of shape optimization inclu
 ding  definitions of admissible shapes\, shape compactness\, the relation
  to the state equation and the requirement of lower semicontinuity. These 
 features are combined into an abstract proof of the existence of optimal s
 hapes. The role of regularity theory in the existence proof of shapes with
  optimal reliability properties is explained. We shortly introduce the the
 ory of strong solutions and boundary regularity (Schauder esimates) that a
 llow to show the crucial graph compactness properties needed in the abstra
 ct existence proofs. Uniform Schauder estimates are provided and the proof
  of existence of forms with minimal failure probabilities is completed.\n3
 .    In the last lecture\, an exposition of the notion of shape derivat
 ives and shape gradients is given. We sketch a proof\, how the existence o
 f shape derivatives for very singular objective functionals\, motivated by
  failure probabilities\, can actually be constructed. Implications to opti
 mization on the infinite dimensional manifold of shapes are given.
LOCATION:BI A0 448 https://plan.epfl.ch/?room==BI%20A0%20448
STATUS:CONFIRMED
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