About: Nonsmooth analysis in problems of continuum mechanics

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rdfs:seeAlso	http://www.isvav.cz/projectDetail.do?rowId=IAA1075707
Description	The main aim of the project is the application of some recent strong results of nonsmooth analysis to selected classes of complex nonlinear problems of continuum mechanics such as dynamic contact problems (mainly with friction), shape optimization by the fictitious domain method, optimum design problems with monotone variational inequalities., effective numerical algorithms for relaxed vectorial variational problems, and optimal design of truss constructions. The results of their investigation will range from new achievements in theoretical analysis via numerical analysis to computational solutions. Conversely, stimulating impulses in nonsmooth analysis itself are expected from this research. (en) Hlavním cílem projektu je využití některých účinných nástrojů nehladké analýzy k řešení vybraných tříd složitých problémů mechaniky kontinua. Jde o dynamické kontaktní problémy (uvažované se třením), tvarovou optimalizaci pomocí metody fiktivních oblastí, úlohy optimálního návrhu s monotonními variačními nerovnicemi, numerické algoritmy pro relaxované vektorové variační problémy a optimální návrh rámových konstrukcí. Výzkum zasahuje od teoretické analýzy přes numerickou analýzu až k vývoji efektivních výpočetních programů. Od zkoumaných mechanických problémů očekáváme nadto stimulující náměty pro další rozvoj nehladké analýzy.
Title	Nonsmooth analysis in problems of continuum mechanics (en) Nehladká analýza v úlohách mechaniky kontinua
skos:notation	IAA1075707
http://linked.open...avai/cep/aktivita	Grants of distinctly investigative character focused on the sphere of research pursued at present particularly in the Academy of Sciences of the Czech Republic
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http://linked.open...ep/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open.../cep/fazeProjektu	501616
http://linked.open...ai/cep/hlavniObor	BA - Obecná matematika
http://linked.open...hodnoceniProjektu	V - Vynikající výsledky (s mezinárodním významem apod.). Zároveň byly splněny cíle a předpokládané výsledky uvedené ve smlouvě / rozhodnutí o poskytnutí podpory.
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http://linked.open...iciPoslednihoRoku	2000
http://linked.open...atUdajeProjZameru	2000
http://linked.open...usZobrazovaneFaze	DUU
http://linked.open...ai/cep/typPojektu	P - Projekt výzkumu a vývoje financovaný ze státního rozpočtu
http://linked.open...jektu+dodavatelem	Existenční věty pro kontaktní úlohy s třením, aproximace hemivariačních nerovnic, optimalizace tvarová, -- úloh s ekvilibriálními omezeními, -- konstrukcí s technologickými omezeními, nové metody řešení relaxovaných variačních a optimalizačních úloh. (cs)
http://linked.open...tniCyklusProjektu	ZBKU
is http://linked.open...vavai/riv/projekt of	Unilateral dynamic contact problems with Coulomb friction. A survey on existence of solutions for viscoelastic bodies. Existence of solutions for the dynamic frictional contact problem of isotropic viscoelastic bodies. DiPerna-Majda measures and uniform integrability. Dynamic contact problem with Coulomb friction for viscoelastic bodies, existence of solutions for a general body. Existence results for the static contact problem with Coulomb friction. Mechanical design problems with unilateral contact. Remark to dynamic contact problems for bodies with a singular memory. Convex locally compact extensions of Lebesgue spaces and their applications. Dynamic contact problems with small Coulomb friction for viscoelastic bodies. Existence of solutions. Dynamic contact problems with Coulomb friction for viscoelastic bodies. A survey about existence of solutions. Cascading - an approach to robust material optimization. Bauer's maximum principle and hulls of sets. Existence results for the semicoercive static contact problem with Coulomb friction. On constraint qualifications for mathematical programs with mixed complementarity constraints. Recent existence theorems for unilateral dynamic contact problems with Coulomb friction. An Iterative Two-Step Algorithm for American Option Pricing. Young measure approximation in micromagnetics. Free material optimization. Optimal truss design by interior-point methods. Nonsmooth Approach to Optimization Problems with Equilibrium Constraints. Numerical treatment of microstructure evolution modeling. Nonlinear heat equation with L^1-data. Free material design via semidefinite programming: The multiload case with contact conditions. Existence of solutions to a nonlinear coupled thermo-viscoelastic contact problem with small Coulomb friction. Optimal Design of Trusses under a Nonconvex Global Buckling Constraint. On the Modelling and Solving of the Truss Design Problem with Global Stability Constraints. Optimality conditions for a class of mathematical programs with equilibrium constraints: Strongly regular case. On the composition of quasiconvex functions and the transposition. Optimization problems with concentration and oscillation effects: Relaxation theory and numerical approximation. Optimality conditions for a class of mathematical programs with equilibrium constraints. Optimization of steady flows for incompressible viscous fluids. Noncooperative games with elliptic systems. Some geometric properties of the set of generalized Young functionals. The solvability of a coupled thermoviscoelastic contact problem with small friction and linearized growth of frictional heat. A generalized mathematical program with equilibrium constraints. An iterative two-step algorithm for American option pricing. A Survey on Dynamic Contact Problems with Coulomb Friction. On mathematical programs with complementarity constraints. Optimal design of trusses under a nonconvex global buckling constraint. Weierstrass-type maximum principle for microstructure in micromagnetics. Buoyancy-driven viscous flow with L 1-data. Optimality Conditions for a Class of Mathematical Programs with Equilibrium Constraints. On exterior penalties in equilibrium problems. On a special class of mathematical programs with equilibrium constraints. On the measures of DiPerna and Majda.
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