scholarly journals Bounds for the Collapse Load of a Beam Compressed by Three Dies

1956 ◽  
Vol 9 (4) ◽  
pp. 419
Author(s):  
W Freiberger
Keyword(s):  
Plastic Deformation ◽  
Plastic Flow ◽  
Lower Bounds ◽  
Limit Analysis ◽  
Velocity Fields ◽  
The Other ◽  
Upper And Lower Bounds ◽  
Collapse Load ◽  
Plastic Yielding ◽  
Plane Plastic

This paper deals with the problem of the plastic deformation of a beam under the action of three perfectly rough rigid dies, two dies applied to one side, one die to the other side of the beam, the single die being situated between the two others. It is treated as a problem of plane plastic flow. Discontinuous stress and velocity fields are assumed and upper and lower bounds for the pressure sufficient to cause pronounced plastic yielding determined by limit analysis.

Limit Analysis of Flow Through Inclined Converging Planes

1980 ◽  
Vol 102 (2) ◽  
pp. 109-117 ◽  
Author(s):  
M. Kiuchi ◽  
B. Avitzur
Keyword(s):  
Lower Bound ◽  
Plane Strain ◽  
Upper Bound ◽  
Limit Analysis ◽  
Velocity Fields ◽  
The Body ◽  
Design Flow ◽  
Upper And Lower Bounds ◽  
Lower Upper ◽  
Flow Through

A variety of mathematical models may be used to analyze plastic deformation during a metal-forming process. One of these methods—limit analysis—places the estimate of required power between an upper bound and a lower bound. The upper- and lower-bound analysis are designed so that the actual power or forming stress requirement is less than that predicted by the upper bound and greater than that predicted by the lower bound. Finding a lower upper-bound and a higher lower-bound reduces the uncertainty of the actual power requirement. Upper and lower bounds will permit the determination of such quantities as required forces, limitations on the process, optimal die design, flow patterns, and prediction and prevention of defects. Fundamental to the development of both upper-bound and lower-bound solutions is the division of the body into zones. For each of the zones there is written either a velocity field (upper bound) or a stress field (lower bound). A better choice of zones and fields brings the calculated values closer to actual values. In the present work, both upper- and lower-bound solutions are presented for plane-strain flow through inclined converging dies. For the upper bound, trapezoidal velocity fields, uni-triangular velocity fields, and multi-triangular velocity fields have been dealt with and the solutions compared to previously published work on cylindrical velocity fields. It was found that in different domains of the various combinations of the process parameters, different patterns of flow (cylindrical, triangular, etc.) provide lower upper-bound solutions. The lower-bound solution for plane-strain flow through inclined converging planes is newly developed.

The Limit Design of a Transversely Loaded Square Grid

1952 ◽  
Vol 19 (2) ◽  
pp. 153-158
Author(s):  
Jacques Heyman
Keyword(s):  
Exact Solutions ◽  
Lower Bounds ◽  
Upper And Lower Bounds ◽  
Collapse Load ◽  
Transverse Loading ◽  
Square Grid ◽  
Modes Of Failure ◽  
Combined Actions

Abstract An earlier paper discussed the derivation of a breakdown criterion for beams subjected to combined bending and torsion. The present paper deals with the limit design of grids, formed by two sets of parallel beams intersecting at right angles, subjected to transverse loading at the joints. This form of loading introduces both bending and twisting moments in the beams, and modes of failure under these combined actions are investigated. Exact solutions are determined for some simple grids, but general methods are demonstrated which lead to upper and lower bounds on the collapse load.

Review of Lower-Bound Limit Analysis for Pressure Vessel Intersections

1977 ◽  
Vol 99 (3) ◽  
pp. 413-418 ◽  
Author(s):  
A. Biron
Keyword(s):  
Lower Bound ◽  
Lower Bounds ◽  
Limit Analysis ◽  
Pressure Vessel ◽  
General Purpose ◽  
Collapse Load ◽  
Rotationally Symmetric ◽  
Bound Theorem ◽  
Symmetric Structures ◽  
Lower Bound Limit Analysis

On the basis of a study of several recent papers concerned with the lower-bound computation of the collapse load of pressure vessel intersections, a review is made of the satisfaction, or nonsatisfaction, of the requirements of the lower-bound theorem of limit analysis. It is shown that, whereas for rotationally symmetric structures true lower bounds have been obtained, for a nonsymmetric case such as a right cylinder-cylinder intersection it is difficult to avoid so me approximations. If attempts are to be made to develop general purpose limit analysis programs, the consequences of approximations of the type used so far must be evaluated with care if significant results are to be obtained.

Limit Analysis of Nonsymmetrically Loaded Spherical Shells

1972 ◽  
Vol 39 (2) ◽  
pp. 422-430 ◽  
Author(s):  
S. Palusamy ◽  
N. C. Lind
Keyword(s):  
Lower Bounds ◽  
Limit Analysis ◽  
Upper And Lower Bounds ◽  
Spherical Shells ◽  
Limit Loads ◽  
Analytical Results

Upper and lower bounds are found for limit loads on nonsymmetrically loaded spherical shells. The influence of geometrical and load parameters are discussed. The analytical results are compared with the results of tests on four steel models.

scholarly journals ON THE REMAK HEIGHT, THE MAHLER MEASURE AND CONJUGATE SETS OF ALGEBRAIC NUMBERS LYING ON TWO CIRCLES

2001 ◽  
Vol 44 (1) ◽  
pp. 1-17 ◽  
Author(s):  
A. Dubickas ◽  
C. J. Smyth
Keyword(s):  
Lower Bounds ◽  
Height Function ◽  
Complete Characterization ◽  
Mahler Measure ◽  
The Other ◽  
Upper And Lower Bounds ◽  
Algebraic Numbers ◽  
Salem Numbers ◽  
Primary 11R06

AbstractWe define a new height function $\mathcal{R}(\alpha)$, the Remak height of an algebraic number $\alpha$. We give sharp upper and lower bounds for $\mathcal{R}(\alpha)$ in terms of the classical Mahler measure $M(\alpha)$. Study of when one of these bounds is exact leads us to consideration of conjugate sets of algebraic numbers of norm $\pm 1$ lying on two circles centred at 0. We give a complete characterization of such conjugate sets. They turn out to be of two types: one related to certain cubic algebraic numbers, and the other related to a non-integer generalization of Salem numbers which we call extended Salem numbers.AMS 2000 Mathematics subject classification: Primary 11R06

Upper and Lower Bounds for the Number of Conjugated Patterns in Carbocyclic and Heterocyclic Compounds

1994 ◽  
Vol 49 (10) ◽  
pp. 973-976
Author(s):  
Tetsuo Morikawa
Keyword(s):  
Lower Bounds ◽  
Special Class ◽  
Heterocyclic Compounds ◽  
The Other ◽  
Upper And Lower Bounds ◽  
The One

Abstract It is possible to regard two polygonal skeletons as the same in a special class of carbocyclic and heterocyclic compounds, if the one is reducible to the other by means of the contraction of cyclic subskeletons, and if the numbers of conjugated patterns in them are equal to each other. In such polygonal skeletons, three forms of cyclic subskeletons are defined; the one is called “alternate”, and the others, involving the one called “inclusive”, have a path (b, b), where (b) is a conjugated vertex connecting with three vertices. Successive eliminations of the cyclic subskeletons enable to estimate the upper and lower bounds for the number of conjugated patterns in a given polygonal skeleton.

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.

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