HOMOGENIZATION AND SENSITIVITY ANALYSIS FOR OPTIMAL THERMOELASTIC DESIGN OF METAL-CERAMIC COMPOSITES

摘要

The purpose of this investigation is solution of thermoelastic topology optimization problem for orthotropic materials (e.g. metal-ceramics composites, MCC [1]). The goal of the optimization is to find the optimal material (lamella) orientation that results in minimal compliance energy. Optimization for pure elastic microstructure behavior is described in works [2-6]. In this paper we consider two kinds of thermoelastic models: the model with constant temperature over the specimen region and the model with temperature distribution obtained from the solution of heat conductivity problem (coupled problem). Solution of the optimization problem where the temperature field is independent of the material orientation is presented in [7, 8]. In the present work the problem is solved using the stress-based method (principal stress direction method) [3, 4]. The mathematical foundation of the methodology for finding optimal orientation of orthotropic materials is discussed in [5]. The application of the stress-based method for topology optimization of the metal-ceramic composites (MCC) specimen subjected to mechanical loads only is presented in [6]. Current study demonstrates the application of the stress-based methodology [5, 6] for coupled problem combining heat conduction and elastic loads. This paper is organized as follows: thermoelastic homogenization procedure for orthotropic MCC is given in Sect. 2; the optimization problem is described in Sect. 3; Sect. 4 and Sect. 5 present sensitivity analysis for two kinds of models (problem with constant temperature and coupled problem); in Sect. 6 the results of numerical calculations are discussed. Finally, some concluding remarks are presented.