Optimization in multiscale thermoelastic problems

Optimization in multiscale thermoelastic problems

Adam Długosz

Silesian University of Technology, Institute of Computational Mechanics and Engineering, Division of Computational Mechanics and Applied Informatics, Gliwice, Poland.

DOI:

https://doi.org/10.7494/cmms.2014.1.0478

Abstract:

The paper is devoted to the optimization in two-scale thermoelastic problems. The problems are solved by means of evolutionary computation and direct analysis based on a numerical homogenization. Direct thermoelastic analysis with representative volume element (RVE) and finite element method (FEM) is performed. Design variables in optimization tasks describe micro-structure, whereas optimization functionals are formulated on the basis of the quantities derived from a macro scale. Numerical examples of the optimization are included.

Cite as:

Długosz, A. (2014). Optimization in multiscale thermoelastic problems. Computer Methods in Materials Science, 14(1), 86 – 93. https://doi.org/10.7494/cmms.2014.1.0478

Article (PDF):

Keywords:

Multi-scale modeling, Numerical homogenization, Thermoelasticity, Evolutionary algorithms, Multi-objective

Publication dates:

Received: 02.10.2013, accepted: 18.12.2013, published:

Publication type:

Original scientific paper

References:

Abraham, A., Jain, L., Goldberg, R., 2005, Evolutionary Multiobjective Optimization: Theoretical Advances and Applications, Springer-Verlag London Limited.

Andersson, J., 2000, A survey of multiobjective optimization in engineering design, Technical Report: LiTH-IKP-R-1097.

Carter, J., Booker, J., 1989, Finite Element Analysis of Coupled Thermoelasticity, Computer and Structures, 31, 1, 73- R ability to conduct heat and greater porosity. 80. A

Deb, K., 1999, Multi-objective Genetic Algorithms: Problem M 5. CONCLUSIONS Difficulties and Construction of Test Problems, Evolu- N tionary Computation, 7(3), 205-230.

Deb, K., Pratap, A, Agarwal, S., Meyarivan, T., 2002, A fast and O H elitist multi-objective genetic algorithm: NSGA-II, IEEE Transaction on Evolutionary Computation, 6(2), 181- 197.

Długosz, A., 2010, Multiobjective Evolutionary Optimization of MEMS Structures, Computer Assisted Mechanics and Engineering Sciences, 17(1), 41-50.

Długosz, A., Burczyński, T., 2012, Multiobjective shape optimization of selected coupled problems by means of evolutionary algorithms, Bulletin of the Polish Academy of Sciences, Technical Sciences, 60(2), 215-222.

Długosz, A., Burczyński, T., 2011, Shape optimization of electro-thermal-mechanical systems by using multiobjective evolutionary algorithms. Evolutionary and Deterministic Methods for Design, Optimization and Control, Applications to Industrial and Societal Problems, eds, Burczyński, T., Périaux, J., CIMNE, Barcelona, 162-169.

Fish, J., 2006, Bridging the scales in nano engineering and science, Journal of Nanoparticle Research, 8, 577-594.
Fish, J., 2008, Bridging the Scales in Science and Engineering, Oxford University Press, Oxford.

Kouznetsova, V., Geers, M., Brekelmans, W., 2004, Multi-scale second-order computational homogenization of multiphase materials: a nested finite element solution strategy, Computer Methods in Applied Mechanics and Engineering, 193, 5525-5550.

Madej, Ł., Mrozek, A., Kuś, W., Burczyński, T., Pietrzyk, M., 2008, Concurrent and upscaling methods in multi scale
modelling – case studies, Computer Methods in Material Science, 8 (1), 1-15.

MSC.MARC, 2010, Theory and user information, Vol. A-D, MSC Software Corporation.

Michalewicz, Z., 1996, Genetic algorithms + data structures = evolutionary algorithms, Springer-Verlag, Berlin.

Nowacki, W., 1970, Teoria sprężystości, PWN, Warszawa (in Polish).

Nowacki, W., 1972, Termosprężystość, Ossolineum, Wrocław (in Polish).

Piegl, L.A., Tiller W., 1996, The NURBS book, Springer; 2nd eds., 14.

Terada, K., Kurumatani M., Ushida T., Kikuchi N., 2010, A method of two-scale thermo-mechanical analysis for
porous solids with micro-scale heat transfer, Computional Mechanics, 46, 269-285.

Zhodi, T.I., Wriggers, P., 2008, Introduction to Computational Micromechanics, Springer-Verlag, Berlin Heidelberg.

Zienkiewicz, O.C., Taylor, R.L., 2000, The Finite Element Method, Butterworth-Heinemann, Oxford.

Zitzler, E., Thiele, L., 1999, Multiobjective evolutionary algorithms: A comparative case study and the strength Pareto
approach, IEEE Transactions on Evolutionary Computation, 3(4), 257-271.