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Elastic Analysis of Inhomogeneous Solids: History and Development in Brief

Published online by Cambridge University Press:  18 July 2019

Yuriy Tokovyy Open the ORCID record for Yuriy Tokovyy [Opens in a new window]  and
Chien-Ching Ma
Yuriy Tokovyy*
Affiliation:
Pidstryhach Institute for Applied Problems of Mechanics and Mathematics National Academy of Sciences of Ukraine 3-b Naukova St., 79060Lviv, Ukraine
Chien-Ching Ma
Affiliation:
Department of Mechanical Engineering National Taiwan University No 1 Roosevelt Rd., Sec. 4, 10617Taipei, Taiwan ROC
*
*Corresponding author (tokovyy@gmail.com)
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Abstract

Inhomogeneous materials (the ones exhibiting spatial variations in their, all or specific, material properties) present a great deal of interest for scientists and engineers in both academia and industry. For over a hundred years, the mechanical behavior of inhomogeneous materials excites numerous attempts in mathematical modeling and development of methods for proper analysis and verification. With this concern, the reach experience was gained by scientists of different scientific schools in many countries. Despite numerous significant achievements, some results, unfortunately, remain unnoticed by the wide scientific community. On the other hand, one can observe a growing number of publications which repeatedly publish the solutions reported years ago or deal with the similar problems with slight modifications. The main objective of this paper is to: i) present a brief survey of the development history of the elastic analysis of inhomogeneous solids and ii) characterize some dominant analytical and semi-analytical methods. It was not our intent here to provide a comprehensive list of references on the topic, which is nearly impossible to make in view of rapidly growing number of publications and other restrictions, but to emphasize some important, in our opinion, stages of the development, methods and results.

Keywords

inhomogeneous materialselastic analysisdevelopment historyanalytical methods
Type
Research Article
Information
Journal of Mechanics , Volume 35 , Issue 5 , October 2019 , pp. 613 - 626
Copyright
© The Society of Theoretical and Applied Mechanics 2019 

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