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 and a brief historical review.
Conventional symbols used in the book.

Chapter 1. Description of the author's invention
1.1. Calculation method to control catastrophic destruction
1.2. Description of invention
1.2.1. Object -- phenomenon
1.2.2. Introduction
1.2.3. Justification of invention
1.2.4. Formula of invention
1.3. Description of invention
1.3.1. Object -- law
1.3.2. Introduction
1.3.3. Justification of invention
1.3.4. Formula of invention
1.4. Description of invention
1.4.1. Object -- law
1.4.2. Introduction
1.4.3. Justification of invention
1.4.4. Formula of invention.

Chapter 2. The analogy method in oscillations of thin-walled constructions (a general linear theory of oscillations)
2.1. On some properties of constructions. A load coefficient. Statement of the problem on thin-walled bar oscillations
2.2. Classification of loads and symbols in the theory of oscillations
2.3. Possible forms of free oscillations of a thin-walled bar
2.4. Solution of differential equations of a bar's free oscillations
2.5. Criterions of dynamical balance, stability and instability in oscillations. A concept of analogy in a form of free oscillations
2.6. The theorem on analogy at elastic systems' oscillations
2.7. A qualitative method of solution of some equations of bars' free oscillations
2.8. The method of analogy in calculations on beam's oscillations loaded in the middle of the span with concentrated load
2.9. The analogy method in calculations on the oscillation of the pillar loaded by the load of eccentric compression
2.10. Experimental basis of the analogy method in oscillations of thin-walled constructions
2.11. The analogy method in calculations on oscillations of the beam loaded with the load evenly distributed along the span length
2.12. The analogy method in calculations of the beam's oscillations loaded by concentrated moments on supports
2.13. The analogy method in calculations on oscillations of thin-walled plates and gentle cylindrical shells.

Chapter 3. Application of the analogy method in calculations on oscillations of construction elements of bridges and aircrafts
3.1. Introduction
3.2. Calculation of a frame/beam bridge's span structure on oscillations
3.3. A calculation of a carrier-rocket body on oscillations
3.4. The calculations of aircraft construction elements on oscillations.

Chapter 4. The flutter theory as a particular case of general linear theory of oscillations
4.1. Introduction and analysis of modern concepts of the flutter theory
4.2. On some properties of consructions
4.3. Derivation of flutter's differential equations and their solutions
4.4. The flutter of the beam loaded by a concentrated load in the middle of a span
4.5. The flutter of the post loaded by the load of eccentric compression
4.6. Experimental basis of the flutter theory
4.7. The flutter of the beam loaded with the load evenly distributed along the span's length
4.8. The flutter of the beam loaded by concentrated moments on supports
4.9. The flutter of thin plates and gentle cylindrical shells.

Chapter 5. Aircrafts' flutter
5.1. Calculation of a carrier-rocket's body on flutter
5.2. Calculation on flutter of an aircraft's construction elements.

Conclusion.
References.