Shape Optimal Design Of Phases In Composites:
Harmonic Problem
Author(s)
P. P. Prochazka
Abstract
In the paper identification of phases micro-geometry is studied providing that the
overall properties are given as well as the intrinsic characteristics of the phases.
Harmonic problem is solved, so that the linear steady-state conductivity problem
is a typical application to be discussed. For example, overall change of
temperature and the temperature characteristics are given as well as the set of all
conductivities are prescribed. The objective of the solution is the shape of phases
fulfilling the condition that the homogenized and given values of the
conductivity tensors are as close as possible in some sense. This task appears as
non-solvable uniquely and even can exceed the realistic results. This is why
additional constraints have to be added. One of such reasonable conditions is the
restriction on the volume (in 2D the area) of phases involved in the composite
structure. Still, this cannot be sufficient to meet a realistic situation, since the
side condition is mostly formulated in integral form, i.e. positive and negative
signs can lead to non-realistic geometry. For this reason, restrictions on the shape
of phases should be introduced, such as the diameters or tangential inclination of
certain directions of the phase boundaries.
Practical effects are of great importance to engineers dealing with composite
materials (aerospace, civil, mechanical engineers, and similar). This optimization
is enabled by having one free property: the shape of the phases. The
mathematical formulation and subsequent numerical treatment utilizes this
opportunity and provides a reasonable, fully usable in practice, layout.
Keywords: composite structure, shape optimization, micro- and macro-levels.
Keywords
composite structure, shape optimization, micro- and macro-levels.
Related Book
Other papers in this volume
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