scholarly journals Energy theorems and critical load approximations in the general theory of elastic stability

1952 ◽  
Vol 9 (4) ◽  
pp. 371-380 ◽  
Author(s):  
J. N. Goodier ◽  
H. J. Plass
Keyword(s):  
General Theory ◽  
Critical Load ◽  
Elastic Stability

The effect of finite deformations in the elastic stability of plane frames

1962 ◽  
Vol 266 (1324) ◽  
pp. 47-67 ◽  
Keyword(s):  
Critical Load ◽  
Failure Load ◽  
Elastic Stability ◽  
Load Level ◽  
Load Factor ◽  
Proportional Loading ◽  
Arbitrary Load ◽  
Plane Frames ◽  
The Difference ◽  
Rigid Joints

The circumstances are discussed under which orthogonal relations exist between the elastic critical modes of plane frames subjected to proportional loading. Orthogonal relations may be obtained provided the loading does not produce any components of deformation associated with any of the critical modes at arbitrary levels of the load factor, and provided no part of the structure remains statically indeterminate due to bar forces when all rigid joints are replaced by pin joints. When at arbitrary load factors, the structure deforms with components associated with any of the buckling modes, the elastic failure load is not identical with the lowest elastic critical load, although for many frames the two loads may be very close. A general expression is obtained which reveals the relation between the deformations at an arbitrary load level and the deflexions given by linear analysis. The difference between the elastic failure load and the elastic critical load is discussed, and an approximate treatment applicable to certain types of frame and associated loading is developed.

Follower forces: Leipholz's early researches in elastic stability

1990 ◽  
Vol 17 (3) ◽  
pp. 277-286 ◽  
Author(s):  
G. M. L. Gladwell
Keyword(s):  
Critical Load ◽  
Key Words ◽  
Lower Bounds ◽  
Critical Loads ◽  
Elastic Stability ◽  
Follower Force ◽  
Historical Account ◽  
Nonconservative Systems ◽  
Flutter Instability ◽  
Force Systems

This paper provides an historical account of Leipholz's research into elastic stability. Emphasis is placed on divergence and flutter instability of follower force systems, the derivation of lower bounds for the critical load for divergence, and estimates for critical loads for flutter. Key words: elastic stability, divergence, flutter, lower bounds, nonconservative systems, symmetrisable matrix.

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

Elastic Stability of Two-Span Continuous Beams under Moving Loads

2005 ◽  
Vol 8 (2) ◽  
pp. 157-172 ◽  
Author(s):  
Lei Zhang ◽  
Gengshu Tong
Keyword(s):  
Critical Load ◽  
Linear Approximation ◽  
Critical Loads ◽  
Elastic Stability ◽  
The Other ◽  
Moving Loads ◽  
Absolute Moment ◽  
Load Combination ◽  
Continuous Beams ◽  
Shear Centre

The elastic stability of two span continuous beams has been studied using FEA methods. Two formulae for estimating the critical loads are proposed, one is suitable for two-span beams with one span loaded, while the other is suitable for two-span beams with both spans equally loaded. Two identical concentrated loads symmetrically located about the mid-span of each loaded span were considered in the derivation of both formulae, and the effect of the height of loaded points for doubly symmetric beams was included. The formulae presented are also accurate enough in calculating the critical loads for two-span continuous beams with the mono-symmetric sections used in practice if the point of load application is at or above the shear centre. A linear approximation is suggested for the interaction of two spans when the two spans of the beam are not equally loaded. For a two-span continuous runway girder supporting moving cranes, the minimum critical load and the maximum absolute moment were investigated, some possible combination of wheel forces on beams considered, and approaches to calculating the critical load for each load combination are suggested when the girder has either one or two cranes moving along it.

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