Determination of the Buckling Load for Columns of Variable Stiffness

1949 ◽  
Vol 16 (4) ◽  
pp. 406-410
Author(s):  
C. C. Miesse
Keyword(s):  
Lower Bounds ◽  
Axial Loading ◽  
Variable Stiffness ◽  
Buckling Load ◽  
Upper And Lower Bounds ◽  
Variable Section ◽  
Rayleigh Principle

Abstract A method is given for determining both upper and lower bounds on the critical or buckling load for variable-section columns with axial loading. This method, which is an extension of the Rayleigh principle, is illustrated by three examples.

Upper and Lower Bounds for Special Eigenvalues

1959 ◽  
Vol 26 (2) ◽  
pp. 246-250
Author(s):  
F. C. Appl ◽  
C. F. Zorowski
Keyword(s):  
Exact Solution ◽  
Power Series ◽  
Lower Bounds ◽  
Comparison Theorem ◽  
Eigenvalue Problems ◽  
Buckling Load ◽  
Upper And Lower Bounds ◽  
Elastic Buckling ◽  
Variable Section ◽  
Exact Eigenvalue

Abstract A method for finding upper and lower bounds for the fundamental eigenvalue in special eigenvalue problems is presented. The method is systematic and is shown to provide convergence from above and below to the exact eigenvalue under certain conditions. The method is based on the relatively well-known enclosure or comparison theorem of Collatz, and makes use of a power series to approximate the eigenfunction. The method is applied to two examples concerning the critical-elastic buckling load of variable-section columns with pinned ends. Results for the first example compare well with the exact solution, which is known; the second example is presented as an addition to the literature.

scholarly journals Ramsey numbers for certain k-graphs

1981 ◽  
Vol 30 (3) ◽  
pp. 284-296 ◽  
Author(s):  
Stefan A. Burr ◽  
Richard A. Duke
Keyword(s):  
Lower Bounds ◽  
Complete Solution ◽  
Ramsey Number ◽  
Upper And Lower Bounds ◽  
Uniform Hypergraph ◽  
Steiner Systems ◽  
Ramsey Numbers ◽  
Existence Question

AbstractWe are interested here in the Ramsey number r(T, C), where C is a complete k-uniform hypergraph and T is a “tree-like” k-graph. Upper and lower bounds are found for these numbers which lead, in some cases, to the exact value for r(T, C) and to a generalization of a theorem of Chváta1 on Ramsey numbers for graphs. In other cases we show that a determination of the exact values of r(T, C) would be equivalent to obtaining a complete solution to existence question for a certain class of Steiner systems.

Probability of Scuffing in Lubricated Contacts

1989 ◽  
Vol 203 (6) ◽  
pp. 361-369 ◽  
Author(s):  
T A Stolarski
Keyword(s):  
Computer Program ◽  
Lower Bounds ◽  
Plasticity Index ◽  
Upper And Lower Bounds ◽  
Analytical Determination ◽  
Asperity Contact ◽  
Flash Temperature ◽  
Lubricated Contacts ◽  
The Subject

An analytical determination of the probability of scuffing is presented and used to modify and extend a computer program that was the subject of earlier work. The program identifies conditions that produce boundary or mixed lubrication with asperity overlaps for which the plasticity index is greater than 0.6. It then imposes, as a necessary prerequisite for scuffing, the condition that the surface bulk plus flash temperature is high enough to cause significant desorption of adsorbed lubricant film. For such conditions determination of the probabilities of asperity contact and of plastic asperity contact provide upper and lower bounds respectively to the probability of scuffing. It is shown that in this way critical ranges of conditions can be clearly distinguished from ranges for which scuffing is unlikely.

Numerical Methods for the Limit Analysis of Plates

1968 ◽  
Vol 35 (4) ◽  
pp. 796-802 ◽  
Author(s):  
P. G. Hodge ◽  
T. Belytschko
Keyword(s):  
Finite Element ◽  
Numerical Methods ◽  
Mathematical Programming ◽  
Rectangular Plate ◽  
Yield Point ◽  
Lower Bounds ◽  
Limit Analysis ◽  
Upper And Lower Bounds ◽  
Mathematical Programming Problems

The determination of upper and lower bounds on the yield-point loads of plates are formulated as mathematical programming problems by using finite element representations for the velocity and moment fields. Results are presented for a variety of square and rectangular plate problems and are compared to other available solutions.

On the Determination of Stresses and Deflections for Anisotropic Homogeneous Cantilever Beams

1976 ◽  
Vol 43 (1) ◽  
pp. 75-80 ◽  
Author(s):  
S. Nair ◽  
E. Reissner
Keyword(s):  
Cross Section ◽  
Lower Bounds ◽  
Basic Assumption ◽  
Rectangular Cross Section ◽  
Upper And Lower Bounds ◽  
Cantilever Beams ◽  
Normal Stresses ◽  
Complementary Energy ◽  
Minimum Potential

We analyze the effect of anisotropy on beam flexibility by the derivation of upper and lower bounds, through use of the principles of minimum potential and complementary energy, for the load-deflection ratios of narrow rectangular cross-section cantilever beams. The basic assumption is a class of stress-strain relations of such nature that normal strains are caused not only by normal stresses but also by shearing stresses, and shearing strains are caused not only by shearing stresses but also by normal stresses.

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