Elastic stability

The classic example of failure due to elastic instability is the buckling of tall thin columns (struts), which is described in any elementary text on the Strength of Materials . 

For a structure that is likely to fail by buckling there will be a certain critical value of load below which the structure is stable if this value is exceeded catastrophic failure through buckling can occur. 

The walls of pressure vessels are usually relatively thin compared with the other dimensions and can fail by buckling under compressive loads. 

Elastic buckling is the decisive criterion in the design of thin-walled vessels under external pressure. 

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S. P. Timoshenko and J. M. Gere, Theory of Elastic Stability, 2nd edition, McGraw-Hill, New York, 1961. 

Southwell, R. V. (1913) Phil. Trans. 213A, 187. On the general theory of elastic stability. 

Tobias, I., Swigon, D., and Coleman, B.D. (2000) Elastic stability of DNA configurations. I. General theory. Physical Review E 61, 747-758. 

W.C. Johnson. On the elastic stabilization of precipitates against coarsening under applied load. Acta Metall., 32(3) 465-475, 1984. 

Southwell, R. V (1913) Phil Trans. 213A, 187. On the general theory of elastic stability. Tang, S. S. (1968) Hyd Proc. 47 (November) 230. Shortcut methods for calculating tower... 

Two fundamentally different types of failure may occur in vessels operated under vacuum (as opposed to high pressure). The problem in vacuum operation is the elastic stability of the vessel shell when it is under an external pressure loading. In general, elastic instability is a problem that must be considered in all structures having limited rigidity when subjected to bending, torsion, compression or a combination of these loadings. In failure by elastic instability, the structure buckles or collapses like an evacuated thin-shelled vessel. 

One satisfactory procedure for combining the compressive loads is to add together all the compressive stresses. However, the design problem is still one of elastic stability. The elastic stability... 

In using this equation, check to assure that the combined compressive stress does not exceed that allowed for simple compression (taken as 1/3 the yield point in tension) and that it is within the safe limits of elastic stability (taken as 1.5 times 10 t/r). 

Experimental evidence for elastic steric stabilization There is a paucity of experimental studies of elastic steric stabilization. Smitham and Napper (1976a,b) have shown that it is possible to prepare polystyrene latex particles stabilized by poIy(oxyethylene) and dispersed in molten poly(oxyethylene). These experiments suggested that the maximum particle size that could be elastically stabilized was dependent upon the molecular weight of the stabilizing moieties, as would be expected intuitively. Everett and Stageman (1978a) have also reported the elastic stabilization of poly(methyl methacrylate) particles stabilized by poly(dimethylsiloxane) in liquid poly(dimethylsiloxane). 

Potier-Ferry, M. On the mathematical foundations of elastic stability theory I. Arch. Ration. Mech. Anal. 78(1), 55-72 (1982)... 

Elastic-stability criteria are usually determined entirely by elastic constants and geometry. Elastic constants are the controlling factors for failure modes such as buckling and jamming [ ]. 

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