Original scientific paper
Optimality criteria method for optimal design in hyperbolic problems
Marko Vrdoljak
; Department of Mathematics, University of Zagreb, Zagreb, Croatia
Abstract
We consider an optimal design problem with a hyperbolic initial boundary value problem as the state equation.
As a possible application consider a body made from a mixture of different materials which is vibrating under the
given external force, subject to a prescribed boundary
and initial values.
The control function (the distribution of given materials in the given domain) uniquely determines the response (the state function) of the vibrating material.
Our goal is to find a distribution of materials minimising given integral functional depending on state and control functions.
We derive the necessary condition of optimality, which enables us to formulate an optimality criteria method for a numerical solution. Two numerical examples are presented.
The same procedure can be applied in the case of multiple state equations as well.
Keywords
optimal design; wave equation; homogenisation; optimality criteria method
Hrčak ID:
61879
URI
Publication date:
8.12.2010.
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