Hi everyone,
I started last year my PhD in mechanical engineering in the University of Seville (Spain). After attending a lecture on Stroh and Lekhnitskii formalism I wanted to know more about this two mechanicians. It was easy to find a brief Stroh's biography in Ting's Anisotropic Elasticity, but I was unable to find anything about Lekhnitskii. My lecturer had also tried to find out something about him, asking even to russian engineers in international conferences, but not even his fellow countrymen knew anything. This lack of records increase even more my curiosity.
Would anyone have any information on Lekhnitskii's life?
Thank you very much in advance.
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Sergei Gheorgievich Lekhnitskii
I have an Englishe edition of his book, Theory of Elasticity of an Anisotropic Body, translated from the revised 1977 Russian edition, published in 1981 by Mir Publishers. The dust jacket of the book has the following blurb:
Professor Sergei Gheorgievich Lekhnitskii is a Doctor of Physical and Mathematical Sciences and a State Prize Winner. A leading scientist in the field of the theory of elasticity and particularly the elasticity of anisotropic bodies, Professor Lekhnitskii graduated from the Physics and Mathematics Faculty of Leningrad State University in 1931, specializing in "Mechanics". He completed a candidate's degree in the same faculty in 1934, his subject being the theory of elasticity. Professor Lekhnitskii has published, sometimes in a number of editions, several books, including Stability of Anisotropic Plates, Theory of Elasticity of Anisotropic Bodies, and Torsion of Anisotropic and Non-homogeneous Bars. He also has more than 60 articles to his credit, appearing in the journals of the Soviet Academy of Sciences, the proceedings of various congresses and conferences, and collections issued by Leningrad and Saratov Universities. A number of his works have been translated into foreign languages.
Regarding Likhnitskii Formalism for Anisotropic Elasticity
Prof. Suo
I was looking for a proof of Likhnitskii formalism for anisotropic material as briefly stated in your paper "Singularities, Interfaces and Cracks in Dissimilar Anisotropic Media". I have Likhnitskii book "The Theory of Elasticity of an Anisotropic Body" but I cannot find any articles in the book regarding the formalism.
Can you point out to me where I can find the formalism and its full proof, whether from the book or from any other source ?
Regards
In reply to Regarding Likhnitskii Formalism for Anisotropic Elasticity by ahmed.hussein
Orthotropic Elasticity
I would love to get a copy of Lehknitskii's work, too. I was playing around with the an orthotropic, elastic, axisymmetric problem and came across the resulting singularity on my own (over 40 years later). I think it's fascinating that the singularity of the geometry of the constitutive response makes what in an isotropic problem is nonsingular into a problem with a singular stress/strain field. Is anyone interested in how this might intersect the forum on cavitation?
Matt Lewis
Los Alamos, New Mexico
In reply to Regarding Likhnitskii Formalism for Anisotropic Elasticity by ahmed.hussein
RE: LEKHNITSKII'S TEXT BOOK.
To Ahmed Hussein
you say you have a copy of Leknitskii's text book. Please is it the 1963 holden-day copy or the 1981 Mir Version ?
I am not sure what you mean by "full proof" if not his book, but
Try also these references
Lekhnitskii’s Formalism for Stress Concentrations Around
Irregularities in Anisotropic Plates: Solutions for Arbitrary Boundary
Conditions
Optimization and Its Applications
Analysis and Aerospace Engineering
New York
(Print) 978-0-387-95857-6 (Online)
and Statistics
August 21, 2009
2) Deconstructing plane anisotropic elasticity Part I: The
latent structure of Lekhnitskii's formalism
WL Yin - International Journal of Solids
and Structures, 2000 - Elsevier
3)
A
proof of the equivalence of the Stroh and Lekhnitskii sextic
equations for plane anisotropic elastostatics
DM Barnett, HOK Kirchner - Philosophical
Magazine A, 1997 - informaworld.com
4)
An exact correspondence between plane piezoelectricity and
generalized plane strain in elasticity
T Chen, D Lai - Proceedings: Mathematical, Physical and
Engineering …, 1997 - JSTOR
Michele Ciavarella, Politecnico di BARI - Italy, Rector's delegate.
http://poliba.academia.edu/micheleciavarella
Editor, Italian Science Debate, www.sciencedebate.it
Associate Editor, Ferrari Millechili Journal, http://imechanica.org/node/7878
RE: PURCHASE OF LEKHNITSKII'S TEXT BOOK
COULD SOME ONE TELL ME WHERE I CAN PURCHASE A USED COPY OF LEKHNITSKII'S TEXT BOOK ON LINE
S. G. LEKNITSKII (1963) THEORY OF ELASTICITY OF OF AN ANISOTROPIC ELASTIC BODY, HOLDEN-DAY, SAN FRANCISCO
I TRIED TO PURCHASE IT FROM AMAZON.COM BUT IT SAID IT DOES NOT SHIP MATERIALS TO NIGERIA
get the book
You can download it from
http://en.bookfi.org/
It is in djvu format (deja vu). This seems to be a less known format. There is a link to a djvu program in Wikipedia, at least in the german version.
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Ruhr-University
Bochum
Germany