Some static and dynamic implications of of the general theory of elastic stability

1965 ◽  
Vol 19 (3) ◽  
pp. 167-188 ◽  
Author(s):  
Millard F. Beatty
Keyword(s):  
General Theory ◽  
Elastic Stability

scholarly journals General theory of elastic stability

1956 ◽  
Vol 14 (2) ◽  
pp. 133-144 ◽  
Author(s):  
Carl E. Pearson
Keyword(s):  
General Theory ◽  
Elastic Stability

scholarly journals V. On the general theory of elastic stability

1914 ◽  
Vol 213 (497-508) ◽  
pp. 187-244 ◽  
Keyword(s):  
General Theory ◽  
Boundary Conditions ◽  
Radial Pressure ◽  
Elastic Stability ◽  
Circular Ring ◽  
Theory Of Elasticity ◽  
Comprehensive Theory ◽  
The Subject ◽  
The Stability ◽  
Straight Rod

Problems which deal with the stability of bodies in equilibrium under stress are so distinct from the ordinary applications of the theory of elasticity that it is legitimate to regard them as forming a special branch of the subject. In every other case we are concerned with the integration of certain differential equations, fundamentally the same for all problems, and the satisfaction of certain boundary conditions; and by a theorem due to Kiechiioff we are entitled to assume that any solution which we may discover is unique. In these problems we are confronted with the possibility of two or more configurations of equilibrium , and we have to determine the conditions which must be satisfied in order that the equilibrium of any given configuration may be stable. The development of both branches has proceeded upon similar lines. That is to say, the earliest discussions were concerned with the solution of isolated examples rather than with the formulation of general ideas. In the case of elastic stability, a comprehensive theory was not propounded until the problem of the straight strut had been investigated by Euler, that of the circular ring under radial pressure by M. Lévy and G. H. Halphen, and A. G. Greenhill had discussed the stability of a straight rod in equilibrium under its own weight, under twisting couples, and when rotating.

Imperfection-sensitivity of semi-symmetric branching

1977 ◽  
Vol 357 (1689) ◽  
pp. 193-211 ◽  
Keyword(s):  
General Theory ◽  
Potential Function ◽  
Catastrophe Theory ◽  
Bifurcation Theory ◽  
Elastic Stability ◽  
Structural Systems ◽  
Stiffened Plate ◽  
Imperfection Sensitivity ◽  
Branching Points ◽  
Symmetric Points

The general theory of elastic stability is extended to include the imperfection-sensitivity of twofold compound branching points with symmetry of the potential function in one of the critical modes (semi-symmetric points of bifurcation). Three very different forms of imperfection-sensitivity can result, so a subclassification into monoclinal, anticlinal and homeoclinal semi-symmetric branching is introduced. Relating this bifurcation theory to René Thom’s catastrophe theory, it is found that the anticlinal point of bifurcation generates an elliptic umbilic catastrophe, while the monoclinal and homeoclinal points of bifurcation lead to differing forms of the hyperbolic umbilic catastrophe. Practical structural systems which can exhibit this form of branching include an optimum stiffened plate with free edges loaded longitudinally, and an analysis of this problem is presented leading to a complete description of the imperfection-sensitivity. The paper concludes with some general remarks concerning the nature of the optimization process in design as a generator of symmetries, instabilities and possible compound bifurcations.

Elastic stability of DNA configurations. I. General theory

2000 ◽  
Vol 61 (1) ◽  
pp. 747-758 ◽  
Author(s):  
Irwin Tobias ◽  
David Swigon ◽  
Bernard D. Coleman
Keyword(s):  
General Theory ◽  
Elastic Stability

THE GENERAL THEORY OF ELASTIC STABILITY AT THE END OF THE 19th CENTURY

2011 ◽  
Vol 11 (03) ◽  
pp. 401-410
Author(s):  
LUIS A. GODOY
Keyword(s):  
General Theory ◽  
19Th Century ◽  
Structural Stability ◽  
Elastic Stability ◽  
Rigid Bodies ◽  
The Other ◽  
General Stability ◽  
The 19Th Century ◽  
The Impact ◽  
Energy Principles

This paper reviews the research on the theory of elastic stability published at the end of the 19th century, with emphasis on the work by G. H. Bryan in Cambridge. The state of the studies on structural stability previous to Bryan is reviewed, and two lines of work are identified: one is a general stability of rigid bodies and the other is a collection of case studies of elastic stability. Bryan's theory is discussed next, presenting his arguments based on first energy principles, which led him to strong conclusions. The importance of the word "general" and the idea of having solved the problem in each case are explained. The impact of the contributions made by Bryan, together with the critiques that this generated, is also discussed.

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