Composite
materials are used in various fields, especially in aerospace field where high
performance such as high strength-to-density and stiffness-to-density is
required. The first advantage of composite materials is that they have high
kinetic and functional properties compared with metals by the same weight. The
second is that they have high design flexibility that can control their
properties by changing material constitution, types, and a mixture ratio. There
is no doubt about that advanced material properties are one of the most
important factors to determine the performance of a structure, so that a
material design with high properties is always demanded for the purpose of the
improvement of structural performance. In order to design such materials, it is
necessary to consider a micro-structural design as well as a macro-structural
one. A micro-structural design makes it possible to design composite materials
more flexibly, so that the design corresponding to more various uses will be
attained and it will lead to improve the performance of a structure.
The
aim of this paper is to find a distribution of material constitution consisting
two materials that improves elastic or thermal properties under the constraints
of elastic properties and volume fractions of constituent materials, within a
periodic microstructure. The elastic moduli and thermal expansion which are the
homogenized properties of an arbitrary microstructure are found using a
numerical homogenization method based on a finite element discretization of the
microstructure. The optimization problem is solved using sequential linear
programming. To avoid checkerboard pattern of materials constitution, a
filtering method is also used. Several examples of an optimal design such as the
maximization of Young’s modulus and the minimization of the thermal expansion
coefficient using the present method.
edited by Shusuke SANAI