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Zagadnienia optymalizacji w modelowaniu wieloskalowym

Tadeusz Burczyński1,2, Wacław Kuś1

Optimization problems in multiscale modelling

The multiscale modelling of materials and structures is a very important and challenging area of research. It allows us to design new materials and products with better quality, strength and performance parameters and create reliable models taking into account products and material properties and topology in different length scales.
Optimization problems, and generally speaking inverse problems, considered in the paper, are much more complicated than direct problems. Challenging problems which appear in multiscale modelling in the context of optimization and identification are considered in this paper.
Optimization in multiscale modelling allows us in the rational way to find new materials and structures with the best performance or strength in one scale with respect to design variables in another scale. The identification problem is formulated as evaluation of some geometrical, material or topological parameters of structures in one scale having measured information in another scale. This last problem is formulated and considered as a special task of the minimization problem.
Problems considered in the paper tackle optimization and identification of microstructure parameters on the base of objective functionals and measured data (displacements, strains or natural frequencies) obtained for the macroscale level.
The proposed approach of identification is one of the most important stage of multiscale modelling because it enables to find some geometrical and/or material parameters of a micro-model in the rational and efficient way. Such parameters are necessary to formulate and solve the direct problems, in framework of the multiscale methodology, for engineering analysis of existed structures.
Special important problem of searching the stable configuration of an atom cluster in the nano and nano-micro scales is also considered in the paper. This problem is considered in the framework of optimization problems.
Optimization and identification performed with the use of the evolutionary and immune algorithms and multiscale FEM models based on the computational homogenization are considered.
Several numerical examples of optimization of composites and functionally graded engineering materials are presented. Identification of trabeculae material parameters of bone on the micro-level and material and shape of micro-parameters of composites are also presented.

1Institute of Computational Mechanics and Engineering, Silesian University of Technology
2Institute of Computer Science, Cracow University of Technology
© Realizacja Zbigniew Kacprzyk