Structural optimization of functionally graded materials with small concentration of inclusions

A. A. Diskovsky, O. I. Prudko

Abstract


Raising of problem.With an optimal design of inner structure of functionally graded material (FGM) based on the classical method of homogenization procedure, in cases of low concentration of inclusions, when the size of inclusions is essentially less than the distance between them, leads to computational difficulties.

Purpose – the research to develop a homogenization procedure, allowing solving effectively the problem of optimizing the internal structure of FGM at low concentrations of inclusions and illustration with specific examples.

Conclusion. The proposed method allows solving tasks of calculation and optimal design of the internal structure of FGM structures with variable inclusions and with a variable step between them using the same methodology. The optimization is performed using two mechanisms. The first allocation is fixed at the edges of the border areas in which inclusions are absent. The second optimization mechanism is the distribution of inclusions sizes under the law, coinciding with the distribution law of an external load. Alternate step for the step should be reduced in areas with greater intensity of the external load.


Keywords


functionally graded rod; homogenization method; functionally graded inclusion size; functionally graded step between inclusions

References


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GOST Style Citations


Ilschner B. and Cherradi N., eds. 3rd International Symposium on Structural and Functional Gradient Material: proceedings, 10-12 October 1994. Swiss Federal Institute of Technology of Lausanne. Switzerland: Presses polytechniques et universitaires romandes, 1995, 731 р.

 

Suresh S. and Mortensen A. Fundamentals of functionally graded materials: processing and thermomechancial behaviour of graded metals and metal-ceramic composites. London: IOM Communications Ltd., 1998, 165 р.

 

Hirai T. Functionally Graded Materials. Materials Science and Technology – A Comprehensive Treatment. Processing of Ceramics. Weinheim, 1996, vol. 17B, рart 2, pp. 293–363.

 

Bolshakov V.I. and Danishevs’kyy V. V Effective shear modulus and microscopic stresses in a fibred-reinforced composite materials with interphases. Stroitel’stvo, materialovedenie, mashinostruenie [Construction, Materials Science. Mechanical Engineering]. Prydniprovs’ka State Academy of Civil Engineering and Architecture. Dnepropetrovsk, 2006, iss. 36, part 3, pp. 167–173.

 

Bolshakov V.I. and Danishevs’kyy V. V. Asymptotic multiscale modelling of heat conduction in fibre-reinforced composite material with imperfect bonding. Aims for Future of Engineering Science: рroceedings the International Scientific Forum, 2006, 4-10 July. Davos, Switzerland, 2006, pp. 97–107.

 

Bolshakov V.I., Danishevs'kyy V.V. and Weichert D. Propagation of elastic waves in periodic composite structures. Stroitel’stvo, materialovedenie, mashinostruenie [Construction, Materials Science. Mechanical Engineering]. Prydniprovs’ka State Academy of Civil Engineering and Architecture. Dnepropetrovsk, 2008, iss. 45: Proceedings in memory of Starodubov, part 1, pp. 31–39.

 

Andrianov I.V., Awrejcewicz J. and Diskovsky A.A. Homogenization of the irregular cell-types constructions. 8th Conference on Dynamical Systems. Theory and Applications (DSTA 2005): proceedings. Technical University of Lodz. Poland, Lodz, December 12–15, 2005, vol. 2, pp. 871–876.

 

Andrianov I. V., Awrejcewicz J. and Diskovsky A.A. Homogenization of quasiperiodic structures. Journal of Vibration and Acoustics. Transactions of the ASME. 2006, vol. 128, iss. 4, pp. 532–534.

 

Andrianov I., Awrejcewicz J. and Diskovsky A. Asymptotic investigation of corrugated elements with quesi-periodic structures. 10th Conference on Dynamical Systems. Theory and Applications (DSTA 2009): рroceedings, December 7-10, 2009. Technical University of Lodz. Poland, 2009, vol. 2, pp. 523–532.

 

Andrianov I., Awrejcewicz J. and Diskovsky A. Homogenization of the functionally-graded materials. 11th Conference on Dynamical Systems. Theory and Applications (DSTA 2011): рroceedings, December 5-8, 2011. Technical University of Lodz. Poland, 2011, pp. 55–62. Available at: http://www.academia.edu/22581684/Homogenization_of_the_functionally-graded_materials.

 

Andrianov I. V., Awrejcewicz J. and Diskovsky A.A. Sensitivity analysis in design of constructions made of functionally-graded materials. Proceedings of the Institution of Mechanical Engineers. Part C: Journal of Mechanical Engineering Science. 2013, vol. 227, iss. 1, pp. 19–28.



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