Minimum weight bars for given lower bounds on euler buckling load and frequency of longitudinal vibration

1987 ◽  
Vol 23 (8) ◽  
pp. 1163-1178
Author(s):  
Richard D. Parbery
Keyword(s):  
Lower Bounds ◽  
Longitudinal Vibration ◽  
Minimum Weight ◽  
Buckling Load ◽  
Euler Buckling

Tubular Conical Columns for Offshore Structures

1993 ◽  
Vol 115 (4) ◽  
pp. 219-222
Author(s):  
S. J. Cox
Keyword(s):  
Hydrostatic Pressure ◽  
Offshore Structures ◽  
Buckling Load ◽  
Tubular Columns ◽  
Euler Buckling ◽  
Effect Of Hydrostatic Pressure ◽  
Volume Preserving

We examine submerged nonlinear tubular columns with slenderness ratios between 40 and 160 and ratios of diameter to thickness between 20 and 50. We demonstrate that the column’s Euler buckling load can be increased nearly 30 percent by a volume preserving taper of only a few degrees. We determine the effect of hydrostatic pressure and self-weight on such conical columns and offer some preliminary remarks on the role played by model imperfections.

Wrinkling of Wide Sandwich Panels∕Beams With Orthotropic Phases by an Elasticity Approach

2004 ◽  
Vol 72 (6) ◽  
pp. 818-825 ◽  
Author(s):  
G. A. Kardomateas
Keyword(s):  
Compressive Loading ◽  
Sandwich Panels ◽  
Wave Mode ◽  
Buckling Load ◽  
Face Sheet ◽  
Beam Model ◽  
Elasticity Solution ◽  
Short Side ◽  
Euler Buckling ◽  
Sandwich Construction

There exist many formulas for the critical compression of sandwich plates, each based on a specific set of assumptions and a specific plate or beam model. It is not easy to determine the accuracy and range of validity of these rather simple formulas unless an elasticity solution exists. In this paper, we present an elasticity solution to the problem of buckling of sandwich beams or wide sandwich panels subjected to axially compressive loading (along the short side). The emphasis on this study is on the wrinkling (multi-wave) mode. The sandwich section is symmetric and all constituent phases, i.e., the facings and the core, are assumed to be orthotropic. First, the pre-buckling elasticity solution for the compressed sandwich structure is derived. Subsequently, the buckling problem is formulated as an eigen-boundary-value problem for differential equations, with the axial load being the eigenvalue. For a given configuration, two cases, namely symmetric and anti-symmetric buckling, are considered separately, and the one that dominates is accordingly determined. The complication in the sandwich construction arises due to the existence of additional “internal” conditions at the face sheet∕core interfaces. Results are produced first for isotropic phases (for which the simple formulas in the literature hold) and for different ratios of face-sheet vs core modulus and face-sheet vs core thickness. The results are compared with the different wrinkling formulas in the literature, as well as with the Euler buckling load and the Euler buckling load with transverse shear correction. Subsequently, results are produced for one or both phases being orthotropic, namely a typical sandwich made of glass∕polyester or graphite∕epoxy faces and polymeric foam or glass∕phenolic honeycomb core. The solution presented herein provides a means of accurately assessing the limitations of simplifying analyses in predicting wrinkling and global buckling in wide sandwich panels∕beams.

Optimally Directed Truss Topology Generation Using Shape Annealing

1995 ◽  
Vol 117 (1) ◽  
pp. 206-209 ◽  
Author(s):  
G. M. Reddy ◽  
J. Cagan
Keyword(s):  
Simulated Annealing ◽  
Minimum Weight ◽  
Truss Structure ◽  
Shape Grammar ◽  
Euler Buckling ◽  
Topology Generation ◽  
Truss Topology ◽  
Buckling Constraints ◽  
Annealing Algorithm

This paper presents a technique for the generation and optimization of truss structure topologies based on the shape annealing algorithm. Feasible truss topologies are generated through a shape grammar in an optimally directed manner using simulated annealing for minimum weight, subject to stress and Euler buckling constraints.

Full-Strength Reinforcement of a Cutout in a Cylindrical Shell

1964 ◽  
Vol 31 (4) ◽  
pp. 667-675 ◽  
Author(s):  
Philip G. Hodge
Keyword(s):  
Cylindrical Shell ◽  
Lower Bounds ◽  
Upper Bound ◽  
Circular Cylindrical Shell ◽  
Minimum Weight ◽  
Upper And Lower Bounds ◽  
Minimum Weight Design ◽  
Initial Strength ◽  
Weight Design ◽  
Circular Cutout

A long circular cylindrical shell is to be pierced with a circular cutout, and it is desired to design a plane annular reinforcing ring which will restore the shell to its initial strength. Upper and lower bounds on the design of the reinforcement are obtained. Although these bounds are far a part, it is conjectured that the upper bound, in addition to being safe, is reasonably close to the minimum weight design. Some suggestions for further work on the problem are advanced.

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 Lower bounds on the Roman and independent Roman domination numbers

2016 ◽  
Vol 10 (1) ◽  
pp. 65-72 ◽  
Author(s):  
Mustapha Chellali ◽  
Teresa Haynes ◽  
Stephen Hedetniemi
Keyword(s):  
Lower Bound ◽  
Lower Bounds ◽  
Minimum Weight ◽  
Domination Number ◽  
Roman Domination ◽  
Roman Domination Number ◽  
Roman Dominating Function ◽  
Independent Domination ◽  
Dominating Function ◽  
Domination Numbers

A Roman dominating function (RDF) on a graph G is a function f : V (G) ? {0,1,2} satisfying the condition that every vertex u with f(u) = 0 is adjacent to at least one vertex v of G for which f(v) = 2. The weight of a Roman dominating function is the sum f(V) = ?v?V f(v), and the minimum weight of a Roman dominating function f is the Roman domination number ?R(G). An RDF f is called an independent Roman dominating function (IRDF) if the set of vertices assigned positive values under f is independent. The independent Roman domination number iR(G) is the minimum weight of an IRDF on G. We show that for every nontrivial connected graph G with maximum degree ?, ?R(G)? ?+1/??(G) and iR(G) ? i(G) + ?(G)/?, where ?(G) and i(G) are, respectively, the domination and independent domination numbers of G. Moreover, we characterize the connected graphs attaining each lower bound. We give an additional lower bound for ?R(G) and compare our two new bounds on ?R(G) with some known lower bounds.

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