Design of composite structures with extremal elastic properties in presence of technological constraints

Significance Statement

Modifying the topology of material microstructure can be a good way of improving the mechanical attributes of composite materials. For example, a method based on structural topology optimization is normally adopted in finding the best space distribution of material phases that constitute the microstructure. Realizing optimal distribution of periodic stress-strain fields existing on a microscale for a periodic elementary cell, normally termed as the base cell, is the main objective of designing composite material microstructure with periodic cells.

A base cell is normally studied adopting the finite element method, then a method of topological optimization of this periodically repeated cell can be analyzed instead of analyzing the entire composite structure. Normally, homogenization method is adopted in a bid to average complex micro-structural behavior of elastic materials and come up with macroscopic attributes of a unit cell.

The process of homogenization has been established as an appropriate modelling method for characterizing mechanical behavior of composites with periodic microstructures. Unfortunately, for complex microstructures of elastic material, determining analytically the stress-strain fields is a bit challenging. For this reason, to establish the most effective attributes of an elastic medium, the process of homogenization is applied by numerical method, like the finite element method.

Several researchers have made attempts in a number of topology optimization algorithms as well as interpolation schemes such as evolutionary structural optimization scheme, the level set method, and solid isotropic materials with penalization. These approaches have been adopted extensively in solving design problems for both microstructures and macroscopic structures.

All these recent studies have been made for composites with one or two materials for a homogeneous base cell.  Vadim Krys’ko, Sergey Pavlov, Maxim Zhigalov and Kseniya Bodyagina at Saratov State Technical University in Russia in collaboration with Jan Awrejcewicz at Łódz´ and Warsaw University of Technology investigated the maximization of static stiffness problem for a base cell composite material that it having maximum of shear modulus and bulk modulus. They solved, for the first time, the problem of topological optimization for the base cell of the composite with previously established technological holes and inclusions. Their work is published in peer-reviewed journal, Composite structures.

The authors had the objective of identifying the optimal spatial distribution of components within a composite material in order to realize a material with enhanced functional properties. They adopted the method of homogenization in a bid to establish the relationship between macro and micro-structural attributes of composite material. The researchers also investigated the problem of identifying optimal microstructures of a number of materials, while aiming at obtaining maximum rigidity for the base cell of a composite material. To validate and illustrate the proposed method, the authors provided numerical examples.

The approach of topology optimization was demonstrated and adopted in finding the optimal microstructure in a given composite structure. The results of the study indicated that the optimization aiming at obtaining the extreme bulk modulus and shear modulus allowed the finding of a composite microstructure being considerably reinforced. Therefore, the authors concluded that it was possible that micro-scale elastic attributes of a composite could be designed and defined through investigations done on a microscale.

Design of composite structures with extremal elastic properties in the presence of technological constraints. Advances in Engineering
Maximization of bulk modulus
Design of composite structures with extremal elastic properties in the presence of technological constraints. Advances in Engineering
The maximization of shear modulus

About the author

Jan Awrejcewicz  was born in Telesze, Poland on August 26, 1952. He received the M.Sc. and Ph.D. degrees in the field of Mechanics from the Technical University of Lodz in 1977 and 1981, respectively. He received also his bachelor’s degree in Philosophy in 1978 from the University of Lodz, and DSc. degree in Mechanics from the Technical University of Lodz in 1990. He is an author or co-author of 728 publications in scientific journals and conference proceedings, monographs (48), text books (2), edited volumes (22), conference proceedings (16), journal special issues (23), and other books (9) and other short communications and unpublished reports (381). He is now the Head of Department of Automatics and Biomechanics, and the Head of Ph.D. School on ‘Mechanics’ associated with the Faculty of Mechanical Engineering of the Technical University of Lodz. In 1994 he earned the title of Professor from the President of Poland, Lech Wałęsa, and in 1996 he obtained the golden cross of merit from the next President of Poland, Aleksander Kwaśniewski.

About the author

Vadim Krys’ko 1962 and works in the Saratov Polytechnic Institute. In 1978 he defended his doctoral thesis in the Moscow engineering and construction Institute (MISI). Since 1977 he is head of the Department “Mathematics and modeling”

He created the scientific field of construction, justification and numerical realization of new classes of equations of mathematical physics, hyperbolo-parabolic types, effective methods for their numerical solution. The last time he intensively develops a new direction associated with modeling in the field of biomechanics and stochastic dynamics. Under his leadership, has been defended 10 doctoral theses and 50 master’s theses. They published 9 books in English, 8 books in the Polish language, and 16 monographs in the Russian language. He is the author of 142 publications in Russian scientific journals, 86 publications in international journals, 101 publication in the proceedings of conferences and 154 in scientific text books.

About the author

Sergey P. Pavlov, Doctor of Technical Sciences, Professor of the Department “Mathematics and modeling” on the Institute of physics and technology at the Yuri Gagarin  State Technical University of Saratov. Scientific topics: Optimization problems with distributed parameters, proof of existence of solutions, numerical methods and algorithms. He had the grants (Russian Foundation for Basic Research, Russian Science Foundation) on these topics.

About the author

Dr. Maxim Zhigalov is a Professor of Yuri Gagarin  State Technical University of Saratov. He studied at Saratov state University from 1983 to 1990.  He received his PhD in 1996 at the Yuri Gagarin  State Technical University of Saratov.  He has served at the Department “Mathematics and modeling” on the Institute of physics and technology at the Yuri Gagarin  State Technical University of Saratov since 1990.

His research interests include chaotic dynamics in mechanical systems, taking into account size-dependent effects; methods of solving nonlinear partial differential equations; cliodynamics. He had the grants (Russian Foundation for Basic Research, Russian Science Foundation) on these topics.

About the author

Kseniya S. Bodyagina, Postgraduate Student, at the “Department Information Security of Automated Systems” the Yuri Gagarin  State Technical University of Saratov.

Reference

J. Awrejcewicz, S.P. Pavlov, K.S. Bodyagina, M.V. Zhigalov, V.A. Krysko. Design of composite structures with extremal elastic properties in the presence of technological constraints. Composite Structures, volume 174 (2017), pages 19–25.

 

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