Leschenko A.P. The fundamental structural mechanics of elastic systems:
Strength

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Introduction
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
Conclusion
References

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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 thin-walled constructions.

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:

T_r <= T_f.

Here for the first time the conception of elastic system has been formulated as the view at the three fundamental physical factors:

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 factors).

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 triads).

The developed new adequate theoretical models of strength, stability and dynamics of the thin-walled constructions considerably specify physics of the phenomena and simplify designing.

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 is proved.

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 mechanics.

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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 Structural Mechanics:

1) Certificate DO N 000008 on discovery Principle of pairing of force factors;

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 pile driver.

His current research concerns various aspects of Civil Engeneering and Structural Mechanics.

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.