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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.

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