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Optimal Control of a Rotating Body Beam

Weijiu Liu (2010)

ESAIM: Control, Optimisation and Calculus of Variations

In this paper we consider the problem of optimal control of the model for a rotating body beam, which describes the dynamics of motion of a beam attached perpendicularly to the center of a rigid cylinder and rotating with the cylinder. The control is applied on the cylinder via a torque to suppress the vibrations of the beam. We prove that there exists at least one optimal control and derive a necessary condition for the control. Furthermore, on the basis of iteration method, we propose ...

Optimal control of variational inequality with applications to axisymmetric shells

Ján Lovíšek (1987)

Aplikace matematiky

The optimal control problem of variational inequality with applications to axisymmetric shells is discussed. First an existence result for the solution of the optimal control problem is given. Next is presented the formulation of first order necessary conditionas of optimality for the control problem governed by a variational inequality with its coefficients as control variables.

Optimal control problems for variational inequalities with controls in coefficients and in unilateral constraints

Igor Bock, Ján Lovíšek (1987)

Aplikace matematiky

We deal with an optimal control problem for variational inequalities, where the monotone operators as well as the convex sets of possible states depend on the control parameter. The existence theorem for the optimal control will be applied to the optimal design problems for an elasto-plastic beam and an elastic plate, where a variable thickness appears as a control variable.

Optimal design of an elastic beam on an elastic basis

Jan Chleboun (1986)

Aplikace matematiky

An elastic simply supported beam of given volume and of constant width and length, fixed on an elastic base, is considered. The design variable is taken to be the thickness of the beam; its derivatives of the first order are bounded both above and below. The load consists of concentrated forces and moments, the weight of the beam and of the so called continuous load. The cost functional is either the H 2 -norm of the deflection curve or the L 2 -norm of the normal stress in the extemr fibre of the beam. Existence...

Optimal design of an elastic beam with a unilateral elastic foundation: semicoercive state problem

Roman Šimeček (2013)

Applications of Mathematics

A design optimization problem for an elastic beam with a unilateral elastic foundation is analyzed. Euler-Bernoulli's model for the beam and Winkler's model for the foundation are considered. The state problem is represented by a nonlinear semicoercive problem of 4th order with mixed boundary conditions. The thickness of the beam and the stiffness of the foundation are optimized with respect to a cost functional. We establish solvability conditions for the state problem and study the existence of...

Optimal design of cylindrical shell with a rigid obstacle

Ján Lovíšek (1989)

Aplikace matematiky

The aim of the present paper is to study problems of optimal design in mechanics, whose variational form are inequalities expressing the principle of virtual power in its inequality form. We consider an optimal control problem in whixh the state of the system (involving an elliptic, linear symmetric operator, the coefficients of which are chosen as the design - control variables) is defined as the (unique) solution of stationary variational inequalities. The existence result proved in Section 1...

Optimal design of laminated plate with obstacle

Ján Lovíšek (1992)

Applications of Mathematics

The aim of the present paper is to study problems of optimal design in mechanics, whose variational form is given by inequalities expressing the principle of virtual power in its inequality form. The elliptic, linear symmetric operators as well as convex sets of possible states depend on the control parameter. The existence theorem for the optimal control is applied to design problems for an elastic laminated plate whose variable thickness appears as a control variable.

Optimal error estimates for FEM approximations of dynamic nonlinear shallow shells

Irena Lasiecka, Rich Marchand (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

Finite element semidiscrete approximations on nonlinear dynamic shallow shell models in considered. It is shown that the algorithm leads to global, optimal rates of convergence. The result presented in the paper improves upon the existing literature where the rates of convergence were derived for small initial data only [19].

Optimization of the shape of axisymmetric shells

Ivan Hlaváček (1983)

Aplikace matematiky

Axisymmetric thin elastic shells of constant thickness are considered and the meridian curves of their middle surfaces taken for the design variable. Admissible functions are smooth curves of a given length, which are uniformly bounded together with their first and second derivatives, and such that the shell contains a given volume. The loading consists of the hydrostatic pressure of a liquid, the shell's own weight and the internal or external pressure. As the cost functional, the integral of the...

Optimum beam design via stochastic programming

Eva Žampachová, Pavel Popela, Michal Mrázek (2010)

Kybernetika

The purpose of the paper is to discuss the applicability of stochastic programming models and methods to civil engineering design problems. In cooperation with experts in civil engineering, the problem concerning an optimal design of beam dimensions has been chosen. The corresponding mathematical model involves an ODE-type constraint, uncertain parameter related to the material characteristics and multiple criteria. As a~result, a~multi-criteria stochastic nonlinear optimization model is obtained....

Oscillations of a nonlinearly damped extensible beam

Eduard Feireisl, Leopold Herrmann (1992)

Applications of Mathematics

It is proved that any weak solution to a nonlinear beam equation is eventually globally oscillatory, i.e., there is a uniform oscillatory interval for large times.

Pointwise and spectral control of plate vibrations.

Alain Haraux, Stéphane Jaffard (1991)

Revista Matemática Iberoamericana

We consider the problem of controlling pointwise (by means of a time dependent Dirac measure supported by a given point) the motion of a vibrating plate Ω. Under general boundary conditions, including the special cases of simply supported or clamped plates, but of course excluding the cases where multiple eigenvalues exist for the biharmonic operator, we show the controlability of finite linear combinations of the eigenfunctions at any point of Ω where no eigenfunction vanishes at any time greater...

Currently displaying 421 – 440 of 684