Open AccessThe paper suggests an algorithm for solving the problems of optimal design of multicomponent disperse-reinforced composite materials, which properties are defined by filler concentrations and are independent of their shape. It formulates the problem of conditional optimization of a composite with restrictions on its effective parameters - the elasticity modulus, tension and compression strengths, and heat-conductivity coefficient with minimized composite density. The effective characteristics of a composite were computed by finite-element solving the auxiliary local problems of elasticity and heat-conductivity theories appearing when the asymptotic averaging method is applied.
The algorithm suggested to solve the optimization problem includes the following main stages:
1) finding a set of solutions for direct problem to calculate the effective characteristics;
2) constructing the curves of effective characteristics versus filler concentrations by means of approximating functions, which are offered for use as a thin plate spline with smoothing;
3) constructing a set of points to satisfy restrictions and a boundary of the point set to satisfy restrictions obtaining, as a result, a contour which can be parameterized;
4) defining a global density minimum over the contour through psi-transformation.
A numerical example of solving the optimization problem was given for a dispersereinforced composite with two types of fillers being hollow microspheres: glass and phenolic. It was shown that the suggested algorithm allows us to find optimal filler concentrations efficiently enough.