COMPARATIVE ANALYSIS OF STRUCTURE STABILITY. SYSTEMS WITH ONE DEGREE OF FREEDOM. PART 1

The paper considers the loss of structure stability as one of the most important marginal states. Though this type of limit conditions has been closely studied, there is still no agreement on their causes, hence, there is no uniform approach to defining the criteria that determine the critical state. The most popular criteria known in the structural analysis and the theory of structural stability are energy criteria of stability in the form of Timoshenko or Bryan. In the first case the analysis covers total work of all forces affecting the system at the moment of collapse. In the second the analysis deals with the system internal energy, which allows us to solve the problems considering thermal and similar effects. In spite of the simplicity of the first approach and general character of the second one, it is hardly possible to assert that they can be sufficient to cover the total scope of stability problems that may arise in engineering. The criterion of critical energy critical level permits us to formulate and solve stability problems without any limitations related with the smallness of displacements or the types of impacts affecting a system, so it can be applied to formulate boundary conditions. For better understanding of the said criteria and their illustration the paper presents some simple problems in the form of systems with lumped parameters. Structure stability criteria are studied as in case of the systems with one degree of freedom. The analysis covers the statements and solutions of stability problems in the form of Timoshenko, Bryan and the criterion of energy critical levels. These approaches are reviewed in terms of their advantages and disadvantages using the example of the model of a structure with one degree of freedom.

устойчивость конструкций, системы с распределенными параметрами, критическая сила, критерий устойчивости в форме Тимошенко, критерий устойчивости в форме Брайана, критерий критических уровней энергии, structure stability, systems with distributed parameters, critical load, criterion of stability in the form of Timoshenko, criterion of stability in the form of Bryan, criterion of energy critical levels

1. Алфутов Н.А. Основы расчёта на устойчивость упругих систем. - М.: Машиностроение, 1991. - 336 с.

2. Ржаницын А.Р. Устойчивость равновесия упругих систем. - М.: Гостехиздат, 1955. - 475 с.

3. Пановко Я.Г., Губанова И.И. Устойчивость и колебания упругих систем: Современные концепции, ошибки и парадоксы. - М.: Наука, 1979. - 384 с.

4. Ступишин Л.Ю. Вариационный критерий критических уровней внутренней энергии деформируемого тела // Промышленное и гражданское строительство. - 2011. - № 8. - С. 21-23.

5. Ступишин Л.Ю. Никитин К.Е. Методика оптимального проектирования ребристых оболочек // Известия Юго-Запад-ного государственного университета. - 2011. - № 5 (38). Ч. 2. - С. 227-232.

6. Stupishin L.U. Variational Criteria for Critical Levels of Internal Energy of a Deformable Solids//Applied Mechanics and Materials. - Vols. 578-579 (2014), pp. 1584-1587.

7. Stupishin L.U. & Kolesnikov A.G. 2014a. Geometric Nonlinear Orthotropic Shallow Shells Investigation //Applied Mechanics and Materials. - Vols. 501-504 (2014), pp. 766-769.

8. Stupishin L.U. & Kolesnikov A.G. 2014b. Geometric Non-linear Shallow Shells for Variable Thickness Investigation // Advanced Materials Research Vols. 919-921 (2014), pp. 144-147© (2014) Trans Tech Publications, Switzerland doi:10.4028/ www.scientific.net/AMR.919-921.144

9. Stupishin L.U. & Kolesnikov, A.G. 2014c. Reconstruction of Shallow Shells for increase Bearing Capacities and Operating Characteristics// Applied Mechanics and Materials Vols. 580-583 (2014), pp. 3062-3065 © (2014) Trans Tech Publications, Switzerland doi:10.4028/ www.scientific.net/ AMM.580-583.3062

10. Stupishin, L.U. & Nikitin, K.E. 2014. Mixed finite element of geometrically nonlinear shallow shells of revolution // Applied Mechanics and Materials. Vols. 501-504 (2014), pp. 514-517© (2014) Trans Tech Publications, Switzerland doi: 10.4028/ www.scientific.net/ AMM.501-504.514.