Optimization of space-time material layout for 1D wave propagation with varying mass and stiffness parameters

Results are presented for optimal layout of materials in the spatial and temporal domains for a ID structure subjected to transient wave propagation. A general optimization procedure is outlined including derivation of design sensitivities for the case when the mass density and stiffness vary in time. The outlined optimization procedure is exemplified on a ID wave propagation problem in which a single gaussian pulse is compressed when propagating through the optimized structure. Special emphasis is put on the use of a time-discontinuous Galerkin integration scheme that facilitates analysis of a system with a time-varying mass matrix

Optimality criteria method for optimal design in hyperbolic problems

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

A spatio-temporal design problem for a damped wave equation

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