The Fundamental Structural Mechanics of Elastic Systems: Stability

Argumento de The Fundamental Structural Mechanics of Elastic Systems: Stability

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.0
Introduction and a brief historical review
Conventional symbols used in the book

Chapter I. 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 II. The method of analogy in stability of thin walled constructions (a general linear theory of stability)
2.1. Setting of the problem on stability of eccentrically compressed bar and ways of its solution
2.2. Loss of stability "in small" and "in big"
2.3. Possible forms of stability loss "in big". Solution of differential equation of the form
2.4. Classification of load combination in stability. A concept of analogy
2.5. The theorem on analogy in stability
2.6. The analogy method in calculations on stability of centrally and eccentrically compressed thin walled bars. Calculation of the examples was performed using a computer
2.7. Experimental grounding of the analogy method and correction provided by the experiment for the calculations on normative technique
2.8. The analogy method in calculations on stability of the beam loaded with a concentrated load in the middle of the span
2.9. The analogy method in calculations on stability of the beam loaded with the load evenly distributed by the length
2.10. The analogy method in calculations on stability of the beam loaded with concentrated moments at bearings
2.11. Method of analogy in calculations on stability of thin plates and gentle cylindrical shells

Chapter III. Application of the method of analogy in calculation on stability of construction elements of bridges and flying apparatus
3.1. Introduction
3.2. Solution of the sets of differential equations of stability of the analogy method for thin walled bars with rigidity variable by the length
3.3. The qualitative method of solution of some equations on stability of bars
3.4. General informations about frame/beam bridges and description of their constructions
3.5. Calculation on stability of the span structure of the frame/beam bridge
3.6. The computer programs at calculation of the bridge's girder on stability
3.7. The forces effecting for carrier rocket in flight
3.8. The forces effecting an aircraft in flight
3.9. On selection of the design model of construction elements of flying apparatus at calculation on stability
3.10. The calculation on stability of a carrier rocket
3.11. Calculation on stability of construction elements of the aircraft

Chapter IV. Corrections provided by new concepts on state of the problems on strength, stability and dynamics of thin-walled constructions
4.1. LaGrange-Castiliano's principle in the theory of elasticity
4.2. A variational method in construction mechanics
4.3. The corrections provided by new concepts to a state of the problem on strength of thin walled constructions
4.4. The corrections provided by new concepts to the state of a problem on stability and oscillations of thin walled constructions

Conclusion
References