The Fundamental Structural Mechanics of Elastic Systems

Argumento de The Fundamental Structural Mechanics of Elastic Systems

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.0Introduction.
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.