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Optimal control of a rotating body beam

Weijiu Liu (2002)

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 numerical...

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 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...

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.

Positive solutions to a class of elastic beam equations with semipositone nonlinearity

Qingliu Yao (2010)

Annales Polonici Mathematici

Let h ∈ L¹[0,1] ∩ C(0,1) be nonnegative and f(t,u,v) + h(t) ≥ 0. We study the existence and multiplicity of positive solutions for the nonlinear fourth-order two-point boundary value problem u ( 4 ) ( t ) = f ( t , u ( t ) , u ' ( t ) ) , 0 < t < 1, u(0) = u’(0) = u’(1) =u”’(1) =0, where the nonlinear term f(t,u,v) may be singular at t=0 and t=1. By constructing a suitable cone and integrating certain height functions of f(t,u,v) on some bounded sets, several new results are obtained. In mechanics, the problem models the deflection of...

Reliable solution of an elasto-plastic Reissner-Mindlin beam for Hencky's model with uncertain yield function

Ivan Hlaváček (1998)

Applications of Mathematics

We apply the method of reliable solutions to the bending problem for an elasto-plastic beam, considering the yield function of the von Mises type with uncertain coefficients. The compatibility method is used to find the moments and shear forces. Then we solve a maximization problem for these quantities with respect to the uncertain input data.

Currently displaying 141 – 160 of 213