Shape optimization in contact problems. Approximation and numerical realization
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J. Haslinger, P. Neittaanmäki (1987)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
I. Hlaváček (1987)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
Ivan Hlaváček (1987)
Aplikace matematiky
Within the range of Prandtl-Reuss model of elasto-plasticity the following optimal design problem is solved. Given body forces and surface tractions, a part of the boundary, where the (two-dimensional) body is fixed, is to be found, so as to minimize an integral of the squared yield function. The state problem is formulated in terms of stresses by means of a time-dependent variational inequality. For approximate solutions piecewise linear approximations of the unknown boundary, piecewise constant...
Vladislav Pištora (1990)
Aplikace matematiky
The state problem of elasto-plasticity (for the model with strain-hardening) is formulated in terms of stresses and hardening parameters by means of a time-dependent variational inequality. The optimal design problem is to find the shape of a part of the boundary such that a given cost functional is minimized. For the approximate solutions piecewise linear approximations of the unknown boundary, piecewise constant triangular elements for the stress and the hardening parameter, and backward differences...
Ivan Hlaváček (1989)
Aplikace matematiky
The shape of the meridian curve of an elastic body is optimized within a class of Lipschitz functions. Only axisymmetric mixed boundary value problems are considered. Four different cost functionals are used and approximate piecewise linear solutions defined on the basis of a finite element technique. Some convergence and existence results are derived by means of the theory of the appropriate weighted Sobolev spaces.
Ivan Hlaváček (1991)
Applications of Mathematics
A minimization of a cost functional with respect to a part of a boundary is considered for an elasto-plastic axisymmetric body obeying Hencky's law. The principle of Haar-Kármán and piecewise linear stress approximations are used to solve the state problem. A convergence result and the existence of an optimal boundary is proved.
Ivan Hlaváček (1986)
Aplikace matematiky
A minimization of a cost functional with respect to a part of the boundary, where the body is fixed, is considered. The criterion is defined by an integral of a yield function. The principle of Haar-Kármán and piecewise constant stress approximations are used to solve the state problem. A convergence result and the existence of an optimal boundary is proved.
Bijan Mohammadi, Juan G. Santiago (2001)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
We present the combination of a state control and shape design approaches for the optimization of micro-fluidic channels used for sample extraction and separation of chemical species existing in a buffer solution. The aim is to improve the extraction and identification capacities of electroosmotic micro-fluidic devices by avoiding dispersion of the extracted advected band.
Bijan Mohammadi, Juan G. Santiago (2010)
ESAIM: Mathematical Modelling and Numerical Analysis
We present the combination of a state control and shape design approaches for the optimization of micro-fluidic channels used for sample extraction and separation of chemical species existing in a buffer solution. The aim is to improve the extraction and identification capacities of electroosmotic micro-fluidic devices by avoiding dispersion of the extracted advected band.
Beneš, M., Mikula, K. (1998)
Acta Mathematica Universitatis Comenianae. New Series
Fernando Reitich (1991)
Numerische Mathematik
Bruno Carbonaro, Remigio Russo (1991)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
Miroslav Vondrák (1985)
Aplikace matematiky
The fundamental problem in the application of the principle of complementary energy is the construction of suitable subsets that approximate the set of all statically admissible fields satisfying both the conditions of equilibrium inside the body and the static boundary conditions. The notion “slab analogy” is motivated and the interface conditions for the Airy stress function are established at the contact of two domains. Some spaces of types of conforming equilibrium stress elements, which can...
Stein A. Berggren, Dag Lukkassen, Annette Meidell, Leon Simula (2003)
Applications of Mathematics
We present a general numerical method for calculating effective elastic properties of periodic structures based on the homogenization method. Some concrete numerical examples are presented.
Dario Graffi, Mauro Fabrizio (1989)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
Si considera un materiale viscoelastico lineare in cui la funzione di rilassamento è la somma di esponenziali. Lo stato di questi sistemi non è necessariamente assegnato dalla storia passata di , ma è sufficiente fornire il valore iniziale del tensore di deformazione , del tensore degli sforzi e delle sue derivate. Infine per questi materiali abbiamo ottenuto una espressione dell'energia libera come una funzione dello stato di dimensione finita .
Antonio Claudio Grioli (1983)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
In the present work an extension of a classical Menabrea’s theorem on a variational principle of the second potential energy is considered. Such extension deals with hyperelastic micropolar media without constraints.
Tajeddine Guennouni (1988)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
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