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Russian Academy of Sciences | | Founded
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| "Lev Aleksandrovich Galin (On the 100th anniversary of his birth)," J. Appl. Math. Mech. 76 (5), 631-633 (2012) |
| Year |
2012 |
Volume |
76 |
Issue |
5 |
Pages |
631-633 |
| Title |
Lev Aleksandrovich Galin (On the 100th anniversary of his birth) |
| Author(s) |
|
| Abstract |
On 28 September 2012 an outstanding academic in the field of mechanics, Lev Aleksandrovich Galin (1912-1981), who headed the editorial board of the journal Prikladnaya Matematika i Mekhanika for more than 20 years (1959-1981), would have been 100 years old. His classic results in the area of the mechanics of contact interaction, the theory of elastoplastic problems, gas dynamics, subsurface fluid mechanics, cavitation theory, and the mechanics of fracture started new trends in the development of these branches of mechanics.
He was born in Bogorodsk, Nizhny Novgorod region, into a family of an engineer. After leaving school, he worked as a librarian and was then admitted to study Hardware and Energy Management of Light Industry Enterprises at the Moscow Technological Institute of Light Industry, from which he graduated in 1939, specializing in footwear enterprises. At the Institute, he studied on an individual programme, since the lecturers immediately noticed his unusual talent. In his graduation year, his first scientific paper, "The solution of boundary-value problems of elasticity theory by point interpolation", was published in the journal Prikladnaya Matematika i Mekhanika. From then on, his scientific activity was connected with the Institute of Mechanics of the USSR Academy of Sciences, which he entered as a post-graduate student in 1939. His great interest in research, his devotion to science and his highly distinctive talent determined the future direction of his life. In 1942 he successfully defended his Master's thesis, devoted to methods of solving mixed problems of elasticity theory and problems the elastoplastic torsion of rods of polygonal cross-section, and, after only three years, his Doctoral thesis. Kochin and Muskhelishvili, who were his scientific tutors during his doctoral studies, rated his results very highly, noting the complete independence of the young scientist in his scientific research. In 1946, Galin was awarded the scientific degree of Doctor of Sciences in Physics and Mathematics, in 1951 he became a Professor, and in 1953 he was elected a corresponding member of the USSR Academy of Sciences.
His scientific work was devoted to a variety of problems of continuum mechanics as well as to some related problems.
He was one of the creators of an important area of mechanics of solids - contact mechanics. He investigated a large number of two- and three-dimensional problems concerning the interaction of elastic bodies with complicated boundary conditions, taking into account anisotropy, the forces of inertia, etc. For example, he obtained an elegant solution of the problem of the indentation of a punch into an elastic half-plane when there are regions of adhesion and slip in the contact area ("Galin's problem"), based on reducing Hilbert's problem for two functions to a problem of conformal mapping. He suggested methods for solving three-dimensional contact problems on the indentation of an elastic half-space by bodies of round, elliptical, wedge and rectangular plan form, he obtained a general expression for the pressure under a smooth punch of circular cross-section, he investigated the effect of an additional load applied outside the contact area on the contact pressure distribution, and he solved the problem of the indentation of a punch into an elastic plate. On the basis of the solution of the problem of an elastic half-space indented by a narrow punch, the limits of applicability of the Zimmermann - Winkler hypothesis were established. These results were collected together in his book "Contact Problems of Elasticity" published in Russian in 1953 and later translated into English, Japanese and Chinese.
It should be noted that some of the problems he formulated in the area of mechanics of contact interactions and the methods of solving them that he developed formed the foundation for new directions in this branch of science. In particular, the presently rapidly advancing mechanics of discrete contact is largely based on the results he obtained when solving three-dimensional contact problems of elasticity.
The wide introduction of polymer materials into industry prompted him to examine a number of important contact problems, taking into account the rheological properties of the contacting bodies. He studied some contact problems for a viscoplastic half-plane, taking into account the motion of a punch and inertia forces,and also the anisotropic properties of the material. Furthermore, he studied the action of a vibrating load on structural elements (suchs as rods and beams) made of polymer materials, and he solved the inverse problem of choosing the contour of a hole in a plate made of a glass fibre reinforced plastic.
He created a new scientific area in the theory of mixed problems - contact wear problems, in the formulation of which the change in the shape of the surface during the wear process is taken into account. Solutions of these problems are widely used in tribology, and also in wear and durability calculations for various joints.
The formulation and solution of novel contact problems taking into account inperfect elasticity, the surface microstructure and wear of interacting bodies were included in a new monograph by Galin "Contact Problems of Elasticity and Viscoelasticity" (1980). Recently (in 2008) it was published in English by Springer in the series "Solid Mechanics with Applications" edited by Prof. G. Gladwell. The works of other authors on the mechanics of contact interactions in which Galin's ideas and formulations of contact problems were further developed, were also included in the monograph.
A large number of his studies were devoted to investigating elastoplastic problems. He was among the first to switch from an examination of one-dimensional elastoplastic problems, mainly for thick-walled cylinders and spheres, to two-dimensional problems, expertly using methods of the theory of functions of a complex variable to solve them. He found remarkable solutions of plane elastoplastic problems for a plate with a circular hole subjected to tension, and also for a beam with a circular hole subjected to bending. An analogy for the plane elastoplastic problem (similar to the Prandtl - Nadai analogy) was also proposed, enabling many elastoplastic problems to be solved experimentally. His main papers on the theory of elastoplastic problems were included in his monograph "Elasoplastic Problems" which was published posthumously in 1984 (Moscow, "Nauka").
Together with colleagues, he proposed a theory of self-sustaining fracture, which describes the fracture dynamics of overstressed high-strength glasses, rock bursts, and other phenomena. In such processes, the fracture wave is similar to a detonation wave, and its steady propagation is sustained by converting the potential energy resourse into kinetic energy.
The range of his scientific interests was very broad. His work on fluid mechanics mostly covered cavitation, impact theory, and bubbling theory. The initial stage of cavitation - for fluid flow arround a body of polygonal contour - was studied, the size of the cavitation zone was established, and the conditions for its onset were investigated. He investigated the process of bubbling, where the motion of bubbles occurs in a certain reactor, accompanied by chemical reactions and the release of heat.
In the area of subsurface fluid mechanics, the problem of the displacement of the oil zone contour is of considerable importance. He obtained a brilliant solution of this problem in a two-dimensional formulation. It was reduced to the problem of finding the function of a complex variable satisfying the non-linear boundary equation on the contour of a unit circle. He also examined the problem of the motion of ground waters, taking into account the deformation of the boundary of the region occupied by ground waters, and he solved the important problem of the spreading of a lens of fresh water over the surface of a saline region.
The gas dynamics problems he dealt with concerned the case of hypersonic flow arround a wing of rectangular plan form, and mainly unsteady motions were analysed. He also solved some important problems related to the application of wave potentials to solving three-dimensional problems on the flow arround a foil.
He obtained interesting results in cybernetics, in research on the spreading of radiation in a scattering medium, and also in a medium whose optical properties vary as a function of the absorbed radiation.
While working on the development of thermonuclear weapon, he obtained important results (unfortunately, not published). For his scientific research and selfless work on strengthening the defence capability of his country, he was awarded the Order of Lenin, three Orders of Red Banner of Labour and five medals.
In the last years of his life he tackled problems of the application of mathematical methods in biology, and in particular in ecology, physiology and genetics. He presented a special lecture course on these topics at the Lomonosov Moscow State University that attracted undergraduate and post-graduate students of various departments.
Being a pupil of Kochin and Muskhelishvili, he established his own scientific school in mechanics, the main features of which are fine methods of analytical research on the most complicated problems in mechanics and applied mathematics. Many of his students have become prominent scholars.
Professor Galin published about 100 scientific works. His monograph "Contact Problems of Elasticity" (1953) is well known throughout the world and has become a textbook and a source of ideas for younger scholars who take the first steps in scientific research as well as for specialists in the area of mechanics of contact interactions. For this monograph and for the monograph "Elastoplastic Problems" (1984) he was posthumously awarded the State Prize of the USSR in 1986. The result of many years of activity by him and his successors and pupils in the field of contact problems was the review monograph published in 1976 under his editorship "The Development of the Theory of Contact Problems in the USSR".
He devoted considerable attention to the journal Prikladnaya Matematika i Mekhanika; from 1950 he was its Executive Secretary and from 1959 its Editor-in-Chief. His teaching and organizational activity was connected with the Institute of Mechanics and the Institute for Problems in Mechanics of the USSR Academy of Sciences, where he worked for over 30 years, with the N. Ye. Zhukovskii Airforce Engineering Academy, and with Lomonosov Moscow State University, where he was a Professor from 1956 onwards. He was a member of the Praesidium of the National Committee of the USSR in Mechanics.
Those who were fortunate to know him will remember him not only as a gifted scientist but also as a man of great kindness and principle. Apart from science, he was fond of poetry, history and literature; he himself wrote poetry. The scientific areas opened up by his work are being developed by his pupils, colleagues and successors, who treasure his memory. The scientific legacy of Professor Lev Galin will always be a source of inspiration and creativity and will promote advances in science. |
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