Shape Optimal Design Of Phases In Composites: Harmonic Problem
Free (open access)
197 - 208
P. P. Prochazka
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.
composite structure, shape optimization, micro- and macro-levels.