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Sensitivity analysis of a nonlinear obstacle plate problem

Isabel N. Figueiredo, Carlos F. Leal (2002)

ESAIM: Control, Optimisation and Calculus of Variations

We analyse the sensitivity of the solution of a nonlinear obstacle plate problem, with respect to small perturbations of the middle plane of the plate. This analysis, which generalizes the results of [9, 10] for the linear case, is done by application of an abstract variational result [6], where the sensitivity of parameterized variational inequalities in Banach spaces, without uniqueness of solution, is quantified in terms of a generalized derivative, that is the proto-derivative. We prove that...

Sensitivity Analysis of a Nonlinear Obstacle Plate Problem

Isabel N. Figueiredo, Carlos F. Leal (2010)

ESAIM: Control, Optimisation and Calculus of Variations

We analyse the sensitivity of the solution of a nonlinear obstacle plate problem, with respect to small perturbations of the middle plane of the plate. This analysis, which generalizes the results of [9,10] for the linear case, is done by application of an abstract variational result [6], where the sensitivity of parameterized variational inequalities in Banach spaces, without uniqueness of solution, is quantified in terms of a generalized derivative, that is the proto-derivative. We prove that...

Shape and topological sensitivity analysis in domains with cracks

Alexander Khludnev, Jan Sokołowski, Katarzyna Szulc (2010)

Applications of Mathematics

The framework for shape and topology sensitivity analysis in geometrical domains with cracks is established for elastic bodies in two spatial dimensions. The equilibrium problem for the elastic body with cracks is considered. Inequality type boundary conditions are prescribed at the crack faces providing a non-penetration between the crack faces. Modelling of such problems in two spatial dimensions is presented with all necessary details for further applications in shape optimization in structural...

Shape optimization for dynamic contact problems

Andrzej Myśliński (2000)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

The paper deals with shape optimization of dynamic contact problem with Coulomb friction for viscoelastic bodies. The mass nonpenetrability condition is formulated in velocities. The friction coefficient is assumed to be bounded. Using material derivative method as well as the results concerning the regularity of solution to dynamic variational inequality the directional derivative of the cost functional is calculated and the necessary optimality condition is formulated.

Shape optimization in contact problems based on penalization of the state inequality

Jaroslav Haslinger, Pekka Neittaanmäki, Timo Tiihonen (1986)

Aplikace matematiky

The paper deals with the approximation of optimal shape of elastic bodies, unilaterally supported by a rigid, frictionless foundation. Original state inequality, describing the behaviour of such a body is replaced by a family of penalized state problems. The relation between optimal shapes for the original state inequality and those for penalized state equations is established.

Shape optimization of piezoelectric sensors or actuators for the control of plates

Emmanuel Degryse, Stéphane Mottelet (2005)

ESAIM: Control, Optimisation and Calculus of Variations

This paper deals with a new method to control flexible structures by designing non-collocated sensors and actuators satisfying a pseudo-collocation criterion in the low-frequency domain. This technique is applied to a simply supported plate with a point force actuator and a piezoelectric sensor, for which we give some theoretical and numerical results. We also compute low-order controllers which stabilize pseudo-collocated systems and the closed-loop behavior show that this approach is very promising....

Shape optimization of piezoelectric sensors or actuators for the control of plates

Emmanuel Degryse, Stéphane Mottelet (2010)

ESAIM: Control, Optimisation and Calculus of Variations

This paper deals with a new method to control flexible structures by designing non-collocated sensors and actuators satisfying a pseudo-collocation criterion in the low-frequency domain. This technique is applied to a simply supported plate with a point force actuator and a piezoelectric sensor, for which we give some theoretical and numerical results. We also compute low-order controllers which stabilize pseudo-collocated systems and the closed-loop behavior show that this approach is very promising. ...

Signorini problem with a solution dependent coefficient of friction (model with given friction): Approximation and numerical realization

Jaroslav Haslinger, Oldřich Vlach (2005)

Applications of Mathematics

Contact problems with given friction and the coefficient of friction depending on their solutions are studied. We prove the existence of at least one solution; uniqueness is obtained under additional assumptions on the coefficient of friction. The method of successive approximations combined with the dual formulation of each iterative step is used for numerical realization. Numerical results of model examples are shown.

Simulation and design of extraction and separation fluidic devices

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.

Simulation and design of extraction and separation fluidic devices

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.

Solution of 3D contact shape optimization problems with Coulomb friction based on TFETI

Alexandros Markopoulos, Petr Beremlijski, Oldřich Vlach, Marie Sadowská (2023)

Applications of Mathematics

The present paper deals with the numerical solution of 3D shape optimization problems in frictional contact mechanics. Mathematical modelling of the Coulomb friction problem leads to an implicit variational inequality which can be written as a fixed point problem. Furthermore, it is known that the discretized problem is uniquely solvable for small coefficients of friction. Since the considered problem is nonsmooth, we exploit the generalized Mordukhovich’s differential calculus to compute the needed...

Solution of Signorini's contact problem in the deformation theory of plasticity by secant modules method

Jindřich Nečas, Ivan Hlaváček (1983)

Aplikace matematiky

A problem of unilateral contact between an elasto-plastic body and a rigid frictionless foundation is solved within the range of the so called deformation theory of plasticity. The weak solution is defined by means of a variational inequality. Then the so called secant module (Kačanov's) iterative method is introduced, each step of which corresponds to a Signorini's problem of elastoplastics. The convergence of the method is proved on an abstract level.

Solvability of a dynamic rational contact with limited interpenetration for viscoelastic plates

Jiří Jarušek (2020)

Applications of Mathematics

Solvability of the rational contact with limited interpenetration of different kind of viscolastic plates is proved. The biharmonic plates, von Kármán plates, Reissner-Mindlin plates, and full von Kármán systems are treated. The viscoelasticity can have the classical (``short memory'') form or the form of a certain singular memory. For all models some convergence of the solutions to the solutions of the Signorini contact is proved provided the thickness of the interpenetration tends to zero.

Special exact curved finite elements

Jitka Křížková (1991)

Applications of Mathematics

Special exact curved finite elements useful for solving contact problems of the second order in domains boundaries of which consist of a finite number of circular ares and a finite number of line segments are introduced and the interpolation estimates are proved.

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