Computational design of microstructure for the optimization of the temperature-dependent macroscopic response

V. FACHINOTTI; S. GIUSTI; F. BRE; A E. HUESPE

Buenos Aires

Congreso; 1st Pan-American Congress on Computational Mechanics - PANACM 2015; 2015

IACM

This work is addressed to the optimization of the steady-state, thermal response of a macroscopic body byaltering the parameters that define the macroscopic thermal conductivity, which is allowed to varythroughout the body. Mathematically speaking, it is an optimization problem where the goal functiondepends on the macroscopic temperature field and the design variables are the parameters defining themacroscopic thermal conductivity at a series of sampling points embedded in the body.Every evaluation of the goal function amounts to solve a macroscopic thermal problem using the finiteelement method, where each node of the mesh is allowed to have a different conductivity, characterized bya finite (usually few) number of parameters. The whole set of design variables consists of all the parametersdefining the thermal conductivity of all the nodes of the mesh.In this case, the macroscopic thermal conductivity is allowed to be, in general, orthotropic. Since only 2Dproblems are addressed in this work, the macroscopic conductivity is completely defined by three microparameters: its two principal values and the orientation of one of the principal axes.As an example of application, we solve an optimization problem in a given 2D domain with givenboundary conditions in order to determine the conductivity distribution that makes the temperature attains agiven value at a given point of the domain.