A.P.Leschenko has offered a completely new approach to structural mechanics, which allowed for a unique technique for structural engineering to be developed. This new method is based on the following three discoveries made by the author:
--- Phenomenon of separating torsional strains of elastic bars;
--- Specific law of analogy in stability and oscillation of elastic systems;
--- Principle of force factors pairing in structural mechanics.
All actual approaches and theories of structural mechanics widely employ such an abstract concept as generalized force, neglecting, however, a definite and practical concept of external force factor. In author's opinion, this breaks the interrelations between the external and internal forces acting on structures and the strains occurring in the structures, which leads to an implicit violation of the classical mechanics laws, namely the law of energy conservation, the Lagrange principle, and Newton's laws. It should be stressed that Leschenko does not suggest that one concept should be simply replaced by the other, but interrelates the external action with other forces and factors concurrently acting on the structure.
Thus, the author has proposed to consider any elastic system as based on three permanently acting factors: 1) external forces; 2) internal forces; and 3) elastic strains; and indicated the principles linking the effects of these factors. Leschenko has developed a graphical scheme (the so-called triad) for an analysis of elastic systems. The triad analysis of elastic systems has enabled to reveal great contradictions in the available structural calculations of plates, shells and bars. On the other hand, the new method has allowed for an adequate model of stress-and-strain state of constructions to be developed, which, for the first time ever, has made it possible to predict with a high accuracy the moment of structural failure.
As main advantages of the new method we can list comparatively quick calculations of all types of structures, the examination and verification of design solutions, and`the detection of critical loads and weak points of constructions. All these result in a considerable saving of materials, which is accompanied by improving the safety of constructions.
|Conventional symbols used in the book|
|Chapter I. ||Analysis of modern conception of thin-walled structural strength|
| ||1.1.||Langrange-Castigliano's principle in elasticity theory|
| ||1.2.||Variational method in the structural mechanics|
| ||1.3.||Analysis of contradictions and errors of modern conceptions of thin-walled bars strength theory|
|Chapter II. ||The law of dividing torsional strains in the theory of thin-walled struts|
| ||2.1.||The law of dividing torsional strains|
| ||2.2.||Hypothesis and laws in the strength theory of thin-walled struts. The derivation of line differential equations system of strength|
| ||2.3.||Center of free torsion, center of ideal torsion and center of bending in the new conception of strength|
|Chapter III. ||The application of the law of dividing torsional strains to different engineering problems of strength|
| ||3.1.||Bending with torsion of a J-beam with the force applied in the middle of a span|
| ||3.2.||Bending with twisting a channel beam with the force in the middle of a span|
| ||3.3.||Bending with torsion of an eccentrically compressed double-T strut|
|Chapter IV. ||Experimental basis of the law of dividing torsional strains in strength theory of thin-walled bars|
| ||4.1.||Experiments on finding a center of bend of a beam of U-channel type|
| ||4.2.||Experiments on defining fibre strains (stresses) of a channel beam, fixed in the foundation and loaded with force at its end|
| ||4.3.||Experiments on designing strains and stresses of a double-T beam|
| ||4.4.||Experiments on analyzing strains and stresses under eccentrical compression of a double-T strut|
| ||4.5.||Experiments on determination of strains and stresses at eccentrically compression of a post of a channel type|
|Chapter V. ||Analysis of the conception of elastic system|
| ||5.1.||Analysis of a conception of elastic bars' strength|
| ||5.2.||The conclusions to the analysis of an elastic system's conception|
|Chapter VI. ||Strength of thin plates and gentle cylindrical shells|
| ||6.1.||Introduction into the theory of modern calculation of plates|
| ||6.2.||Calculation on thin plates's strength|
| ||6.3.||Calculation on thin gentle cylindrical shells on strength|
| ||6.4.||The analysis of the conception of elastic system of plates and gentle cyllindrical shells|
|Chapter VII. ||Description of the author's invention|
| ||7.1.||Calculation method to control catastrophic destruction|
| ||7.2.||Description of invention|
| || ||7.2.1.||Object -- phenomenon|
| || ||7.2.2.||Introduction|
| || ||7.2.3.||Justification of invention|
| || ||7.2.4.||Formula of invention|
| ||7.3.||Description of invention|
| || ||7.3.1.||Object -- law|
| || ||7.3.2.||Introduction|
| || ||7.3.3.||Justification of invention|
| || ||7.3.4.||Formula of invention|
| ||7.4.||Description of invention|
| || ||7.4.1.||Object -- law|
| || ||7.4.2.||Introduction|
| || ||7.4.3.||Justification of invention|
| || ||7.4.4.||Formula of invention|
The second half of the Twentieth century is characterized with
great progress in science and technique. Progress in science and
technique in Russia is coincided with changes in man's life and
with reforms of Russian society. Ideas of these reforms are
especially actual for such a field of man's activity as science.
This book might be considered as development and application to
another A. Leschenko's book -- "Building mechanics of
thin-walled constructions" (USSR, Moscow, 'Strojizdat', 1989),
in which the new conceptions of strength, stability and dynamics
of thin-walled constructions have been discussed.
The detail and deep theoretical analysis of building mechanics
theory, on which the modern methods of thin-walled constructions
are based, has allowed to the author to open the contradictions
in modern conceptions of strength, stability and dynamics of
The author has introduced the new law of dividing torsional
strains in theory of strength of thin-walled bars, and that has
allowed to get the new linear differential simultaneous
equations of strength. Besides, applying by the author the
specific law of analogy in theory of stability and oscillation
has allowed to develop linear theories of stability and
oscillations which are described with linear differential
simultaneous equations and based on the new criteria of
stability and dynamic balance:
Tr <= Tf.
Here for the first time the conception of elastic system has
been formulated as the view at the three fundamental physical
1) External force factor;
2) Internal force factor;
3) Elastic strains.
It has been shown their interactions in laws of physics and
mechanics. These models of interactions have allowed to show all
contradictions in modern theories of strength, stability and
dynamics of thin-walled constructions and to formulate the main
law of cross-section method (principle of pairing of force
At any cross-section loaded of elastic body being under load
there are always two force factors: 1) external force factor
which is the sum of projections (or moments) of all external
forces of the cut off part of elastic body and 2) internal force
factor (integral characteristics), which, due to condition of
equilibrium of the cut off part, equals to external force factor
and acts in opposite direction.
Ignoring this principle violates the main laws of mechanics (see
The developed new adequate theoretical models of strength,
stability and dynamics of the thin-walled constructions
considerably specify physics of the phenomena and simplify
Experimental proving of new ideas as the main criteria of truth
has been discussed a lot in the book.
The development of the new branches of technique such as
cosmonautics, missile manufacturing, researching hydrosphere
depths with the help of deepwater apparatus, etc. makes
engineers and designers to solve more and more complicated
problems concerning evaluation of constructions for strength,
stability and dynamics.
The main goal of this book is to help the practical engineers in
solution such problems.
The book consists of 7 chapters. In chapter I the analysis of
current conception of the strength of elastic systems, its
consistency harmony with Lagrange--Castigliano's principles and
variation mechanics principles have been discussed. Here the
analysis of contradictions in the current theory of thin-walled
bars are paid attention to.
In Chapter II the earlier unknown law of dividing torsional
strain is introduced in the strength theory and on its base
according to variation mechanics principles the new conception
of thin-walled construction strength is being developed. In
Chapter III the solution methods of various engineering problems
of strength evaluation of beams and bars are developed according
to methods suggested by the author.
The Chapter IV is devoted to the experimental proving of the law
of dividing torsional strains law. The new strength conceptions
are proved on the base of experiments of designing J-beam
bending center and fibre strains of beams and bars.
In Chapter V the detail analysis of the elastic system
conception is given, the current conception is corrected and
conclusions are made.
Chapter VI is devoted to the development of new conception of
bending thin plates and slanting cylindrical shells. Here
Karman's conception of bending plates in details, is discussed
its contradictions with mechanics laws are shown and the new
approach to solution of the problem of bending plates and shell
In Chapter VII mechatronic units and their using in analyzing
strength of J-beams are discribed.
The analysis of corrections says that the using of scientific
results introduced in the book in to practice of designing and
building means the reform of the whole science of structural
About the author
Prof. Alexander Petrovich Leschenko was born in 1939. He has got PhD degree
in Civil Engineering.
Prof. Leschenko has 3 Certificates on his discoveries in the field of
1) Certificate DO N 000008 on discovery Principle of pairing of force
2) Certificate DO N 000006 on discovery Phenomena of separating
torsional strains of elastic bars;
3) Certificate DO N 000007 on discovery Specific analogy law in
stability and oscillation of an elastic system;
and 2 patents on his inventions:
1) Patent N 2150098 of 27.05.2000 on invention Testing method for
buckling failure of metal constructions;
2) Patent N 542435 of 21.09.1978 on invention Breakdown controller of
His current research concerns various aspects of Civil Engeneering and
The publication list comprises the following books:
-- Structural mechanics of thin-walled structures (in Russian),
Moscow, Stroyizdat, 1989;
-- New principles in structural mechanics of thin-walled
structures (in Russian), Moscow, Stroyizdat, 1995;
-- Fundamental structural mechanics of elastic systems (in
Russian), Taganrog, Sphinx, 2003.