ifer workshop, barcelona, july 4-5, 2010 motivation...
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3.13 Nonsmooth - nonconvex analysis, optimalization and mechanics (short version)
Stavroulakis G., Greece
Nonsmooth-nonconvex analysis, optimization and
mechanicsGeorgios E. Stavroulakis,
Institute of Computational Mechanics and Optimizationwww.comeco.tuc.gr
Technical University of Crete, Chania, Greece and Dept. of Civil Engineering,
T.U. Braunschweig, Germany
IFER Workshop, Barcelona, July 4-5, 2010
Motivation: unilateral contact problem
• Nonpenetration relation
• Only compressive stresses are allowed (contact pressure)
• Complementarity relation
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G.E. Stavroulakis – IFER Barcelona July 2010
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Motivation: Frictional Stick-Slip problem(Tangential direction of the interfaces)
Coulomb friction model
• Two contacting surfaces start sliding when- Stick conditions: No sliding when τ < τcr
- τcr: Critical shear stress- µ: Friction coefficient- tn: Contact pressure
• Graphical representation
G.E. Stavroulakis – IFER Barcelona July 2010
Complementarity Problems
Linear Complementarity
Nonlinear Complementarity
G.E. Stavroulakis – IFER Barcelona July 2010
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Unilateral Contact Interface
Linear Complementarity Interface, Variational Inequalities, Nonsmooth Mechanics G.E. Stavroulakis – IFER Barcelona July 2010
Complementarity Problems(other applications)
Flow in Networks (e.g. transportation)
Equilibrium in the sense of Nash – Walrasch
Financial Mathematics
Price analysis of derivatives and options
Flow in porous media
Multiphase flow, salt water front analysis etc
G.E. Stavroulakis – IFER Barcelona July 2010
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Monotone Laws and Convex Nonsmooth Superpotentials
G.E. Stavroulakis – IFER Barcelona July 2010
Monotone Laws
G.E. Stavroulakis – IFER Barcelona July 2010
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Monotone Laws
G.E. Stavroulakis – IFER Barcelona July 2010
Monotone Laws
G.E. Stavroulakis – IFER Barcelona July 2010
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Monotone Laws
G.E. Stavroulakis – IFER Barcelona July 2010
Conclusions
• Nonsmooth-nonconvex potentials in mechanics and thermomechanics allow us extend classical approaches
• Algorithms are expanded with the help of nonsmooth – nonconvex optimization
• Inverse and parameter identification problems can be solved by classical optimization or soft computing.
G.E. Stavroulakis – IFER Barcelona July 2010
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