Handbook of mechanical stability in engineering.

Vol. 1. 1. Stability of equilibrium of systems that have a finite number of degrees of freedom. 1.1. Definition of the equilibrium stability -- 1.2. Elastic systems with a finite number of degrees of freedom. 1.3. Some general theorems of the equilibrium stability theory. 1.4. Characteristic curve of an elastic system. 1.5. Final notes to chapter 1 -- 2. Variational statement of the problem of equilibrium stability for elastic bodies. 2.1. Geometrically nonlinear problems of elasticity. 2.2. Stability of equilibrium of an elastic body. 2.3. Ritz method. 2.4. Mixed functionals in the equilibrium stability problems. 2.5. Timoshenko-type functionals. 2.6. Elastic systems in presence of constraints. 2.7. Elastic systems in presence of perfectly rigid bodies. 2.8. Continuous RB-bodies in application models of elasticity. 2.9. Final notes to chapter 2 -- 3. Asymptotic analysis of post-critical behavior. 3.1. Role played by initial imperfections. 3.2. Systems with multiple degrees of freedom. 3.3. Final notes to chapter 3 -- 4. Stability of equilibrium of straight bars. 4.1. Stability of equilibrium of a compressed bar. 4.2. Variational derivation of the equation of stability for a compressed bar. 4.3. Stability of equilibrium of a compressed spring. 4.4. Buckling of a bar in tension. 4.5. Spatial buckling modes of a compressed bar. 4.6. Does the critical force depend on the lateral load? 4.7. Rayleigh ratio and Timoshenko formula. 4.8. Spatial bar. 4.9. Stability of bars in torsion. 4.10. Final notes to chapter 4 -- 5. Stability of equilibrium of curved bars. 5.1. Basic equations for a curved bar in the linear model. 5.2. Variational derivation of the equilibrium stability equations for a curved bar. 5.3. Stability of equilibrium of an incompressible curved bar. 5.4. Stability of equilibrium of flat arches -- 6. Stability of equilibrium of thin-walled bars. 6.1. Open-profile thin-walled bar. 6.2. Lateral bending of thin-walled bars. 6.3. Thin-walled bars considered by the semi-shear theory -- 7. Conservative external forces and moments: paradoxes and misbeliefs. 7.1. Some cases of behavior of external forces. 7.2. Hydrostatic load. 7.3. Polar load. 7.4. Moment load. 7.5. Stability of bars in three-dimensional space. 7.6. Argyris paradox and accompanying myths. 7.7. Final notes to chapter 7 -- 8. Spatial curved bar -- Kirchhoff-Klebsch theory. 8.1. Basic knowledge about the geometry of a spatial curve. 8.2. Curved bar and its geometry. 8.3. Kinematic relationships for a bar. 8.4. Equations of equilibrium for a bar. 8.5. Physical equations. 8.6. Planar curved bar. 8.7. Rectilinear bar with an initial twist. 8.8. Final notes to the Kirchhoff-Klebsch theory.

Vol. 2. 9. Stability of equilibrium of plates -- Kirchhoff-Love and Reissner plates. 9.1. Stability of equilibrium of Kirchhoff-Love plates. 9.2. Stability of equilibrium of Reissner plates. 9.3. Slender plates -- von Karman theory. 9.4. Post-critical behavior of slender plates. 9.5. Final notes to chapter 9 -- 10. Systems with unilateral constraints. 10.1. Elements of the theory of systems with unilateral constraints. 10.2. Critical value of the load intensity. 10.3. Determining the upper critical load. 10.4. Illustrative examples. 10.5. High-rise building on a unilateral elastic bed. 10.6. Possible destabilization of systems with unilateral constraints. 10.7. Final notes to chapter 10 -- 11. Stability of equilibrium of planar bar structures. 11.1. Planar bar structures. 11.2. Deformed-shape-based analysis of a planar bar structure. 11.3. Final notes to chapter 11 -- 12. FEM in stability problems. 12.1. Basics of FEM. 12.2. Stiffness matrices of a bar in plane. 12.3. Stiffness matrix of a spatial bar. 12.4. Plate finite elements. 12.5. Perfectly rigid bodies as parts of discrete design models. 12.6. FEN relationships for geometrically nonlinear models. 12.7. Final notes to chapter 12 -- 13. Hinged bar systems. 13.1. Preliminaries. 13.2. Geometrical nonlinearity for truss-type bars. 13.3. Stable configurations of a substatic system. 13.4. Buckling of nodes out of a truss plane. 13.5. Estimation of forces in null bars. 13.6. Estimation of the node stiffness effect. 13.7. Compound bars -- 14. Dynamic criterion of stability and non-conservative systems. 14.1. Dynamic analysis of equilibrium stability. 14.2. Systems with multiple degrees of freedom. 14.3. Nikolai problem. 14.4. Continuous non-conservative systems. 14.5. Beck problem. 14.6. Flutter when fluid comes out of tube. 14.7. Models with a truncated number of inertial characteristics. 14.8. On the application of the static approach to non-conservative problems. 14.9. Final notes to chapter 14 -- 15. Post-critical deformation. 15.1. Post-critical behavior of bars. 15.2. Frame systems. 15.3. Using the post-critical behavior of plates. 15.4. Post-critical interaction between buckling modes. 15.5. Final notes to chapter 15 -- 16. Design models in stability problems: practical examples. 16.1. Stability of a multi-story building: the effect of rigidity of floor panels. 16.2. Finite element modeling of thin-walled bars. 16.3. Stability of masts with Guy ropes. 16.4. Energy-based estimation of roles of particular subsystems. 16.5. Sensitivity of the critical load to changes in the system's stiffness values. 16.6. Approximate estimation of Ferroconcrete behavior.

Vol. 3. 17. Stability of inelastic systems. 17.1. A long way to modern concepts. 17.2. Elastoplastic bar subjected to bending and compression. 17.3. Elastoplastic bar of I-section. 17.4. Bar systems method of two design sections. 17.5. Semi-empirical and approximate analytic formulas. 17.6. Lateral-torsional buckling of bars subjected to bending. 17.7. Final notes to chapter 17 -- 18. Stability at Creep 1273 18.1. Creep phenomenon: necessary general information. 18.2. Simplest problems of creep stability. 18.3. Other approaches and criteria. 18.4. Final notes to chapter 18 -- 19. Dynamic stability. 19.1. Dynamic longitudinal bending. 19.2. Parametric resonance. 19.3. Action of moving load. 19.4. Final notes to chapter 19 -- 20. Aerodynamic instability. 20.1. Vortex shedding oscillations. 20.2. Galloping. 20.3. Divergence and flutter. 20.4. Aeroelastic vibrations and instability of suspension bridge. 20.5. Buffeting. 20.6. Final notes to chapter 20 -- 21. Theory and experiment. 21.1. Introduction. 21.2. Challenges concerning experimental technique. 21.3. Interpretation of experimental results. 21.4. Vibration method of critical load identification. 21.5. Influence of testing machine compliance. 21.6. Description of certain experiments. 21.7. Final notes to chapter 21 -- 22. Stability check on design codes. 22.1. Buckling as a limit state. 22.2. Stability safety factor. 22.3. Traditions of standardization. 22.4. Effective length and stability analysis. 22.5. Allowance for initial imperfections. 22.6. Code requirements to general analysis. 22.7. Add-load on individual structural members. 22.8. More about second order analysis.

Handbook of Mechanical Stability in Engineering (in 3 volumes) is a systematic presentation of mathematical statements and methods of solution for problems of structural stability. It also presents a connection between the solutions of the problems and the actual design practice. This comprehensive multi-volume set with applications in Applied Mechanics, Structural, Civil and Mechanical Engineering and Applied Mathematics is useful for research engineers and developers of CAD/CAE software who investigate the stability of equilibrium of mechanical systems; practical engineers who use the software tools in their daily work and are interested in knowing more about the theoretical foundations of the strength analysis; and for advanced students and faculty of university departments where strength-related subjects of civil and mechanical engineering are taught.

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