Collapse Strength of Redundant Beams After Lateral Buckling

1957 ◽  
Vol 24 (2) ◽  
pp. 283-288
Author(s):  
E. F. Masur ◽  
K. P. Milbradt
Keyword(s):  
Upper Bounds ◽  
Lower And Upper Bounds ◽  
Postbuckling Behavior ◽  
Collapse Strength ◽  
Neutral Equilibrium ◽  
Slender Beams ◽  
End Restraint ◽  
Limiting Values ◽  
Increasing Load ◽  
Good Agreement

Abstract According to classical linear theory, slender beams buckle laterally under vertical loads which remain constant as the buckling amplitude increases. Unless prior yielding takes place, the loads corresponding to neutral equilibrium represent therefore the collapse strength of the beam. However, the inclusion of nonlinear terms in the strain-displacement relations modifies the predicted postbuckling behavior of redundant beams. If continued elasticity is postulated, increasing amplitudes are associated with increasing load magnitudes, which generally approach limiting values. These “ultimate loads” may be estimated by means of two principles establishing lower and upper bounds. Tests performed on a single-span beam of varying degrees of end restraint show good agreement with the proposed theory.

Optimal control and anti-control of the nonlinear dynamics of a rigid block

2006 ◽  
Vol 364 (1846) ◽  
pp. 2353-2381 ◽  
Author(s):  
Stefano Lenci ◽  
Giuseppe Rega
Keyword(s):  
Nonlinear Dynamics ◽  
Optimal Control ◽  
Upper Bounds ◽  
Rigid Block ◽  
Periodic Excitation ◽  
Heteroclinic Bifurcation ◽  
Lower And Upper Bounds ◽  
Good Agreement

This paper deals with control and anti-control of overturning of a rigid block subjected to a generic periodic excitation. Attention is focused on two relevant thresholds, corresponding to heteroclinic bifurcation and immediate overturning, and representing lower and upper bounds of the region where toppling can occur. The two opposite problems of increasing (control) or decreasing (anti-control) of these two curves by properly modifying the shape of the excitation are investigated in depth and the optimal excitations permitting their maximum variations are determined. The notions of ‘global’ and ‘one-side’ control (anti-control) are utilized and their different importance for the various cases is discussed. The effects of control (anti-control) of one curve on the uncontrolled (non-anti-controlled) curve are also investigated, both analytically and with numerical overturning charts. A good agreement is seen to occur.

scholarly journals Asymptotic behavior of spanning forests and connected spanning subgraphs on two-dimensional lattices

2020 ◽  
Vol 34 (27) ◽  
pp. 2050249
Author(s):  
Shu-Chiuan Chang ◽  
Robert Shrock
Keyword(s):  
Asymptotic Behavior ◽  
Exponential Growth ◽  
Upper Bounds ◽  
Great Length ◽  
Two Dimensional ◽  
Lower And Upper Bounds ◽  
Spanning Subgraphs ◽  
Spanning Forests ◽  
Growth Constants ◽  
Limiting Values

We calculate exponential growth constants [Formula: see text] and [Formula: see text] describing the asymptotic behavior of spanning forests and connected spanning subgraphs on strip graphs, with arbitrarily great length, of several two-dimensional lattices, including square, triangular, honeycomb, and certain heteropolygonal Archimedean lattices. By studying the limiting values as the strip widths get large, we infer lower and upper bounds on these exponential growth constants for the respective infinite lattices. Since our lower and upper bounds are quite close to each other, we can infer very accurate approximate values for these exponential growth constants, with fractional uncertainties ranging from [Formula: see text] to [Formula: see text]. We show that [Formula: see text] and [Formula: see text] are monotonically increasing functions of vertex degree for these lattices.

Extension of the Spatial PDI Model to Three Dimensions

1997 ◽  
Vol 84 (1) ◽  
pp. 176-178
Author(s):  
Frank O'Brien
Keyword(s):  
Population Density ◽  
Dimensional Space ◽  
Finite Lattice ◽  
Three Dimensional ◽  
Upper Bounds ◽  
Three Dimensions ◽  
Lower And Upper Bounds ◽  
Density Index ◽  
Three Dimensional Space

The author's population density index ( PDI) model is extended to three-dimensional distributions. A derived formula is presented that allows for the calculation of the lower and upper bounds of density in three-dimensional space for any finite lattice.

Energy of spherical fuzzy graphs

2020 ◽  
pp. 321-332
Author(s):  
S. Yahya Mohamed ◽  
A. Mohamed Ali
Keyword(s):  
Adjacency Matrix ◽  
Upper Bounds ◽  
Fuzzy Graph ◽  
Lower And Upper Bounds ◽  
Fuzzy Graphs

In this paper, the notion of energy extended to spherical fuzzy graph. The adjacency matrix of a spherical fuzzy graph is defined and we compute the energy of a spherical fuzzy graph as the sum of absolute values of eigenvalues of the adjacency matrix of the spherical fuzzy graph. Also, the lower and upper bounds for the energy of spherical fuzzy graphs are obtained.

scholarly journals Relationship between Age and Value of Information for a Noisy Ornstein–Uhlenbeck Process

Entropy ◽  
2021 ◽  
Vol 23 (8) ◽  
pp. 940
Author(s):  
Zijing Wang ◽  
Mihai-Alin Badiu ◽  
Justin P. Coon
Keyword(s):  
Value Of Information ◽  
Markov Models ◽  
Upper Bounds ◽  
Distribution Functions ◽  
Lower And Upper Bounds ◽  
Uhlenbeck Process ◽  
Source Data ◽  
Non Linear ◽  
Queue Model ◽  
Selection Of

The age of information (AoI) has been widely used to quantify the information freshness in real-time status update systems. As the AoI is independent of the inherent property of the source data and the context, we introduce a mutual information-based value of information (VoI) framework for hidden Markov models. In this paper, we investigate the VoI and its relationship to the AoI for a noisy Ornstein–Uhlenbeck (OU) process. We explore the effects of correlation and noise on their relationship, and find logarithmic, exponential and linear dependencies between the two in three different regimes. This gives the formal justification for the selection of non-linear AoI functions previously reported in other works. Moreover, we study the statistical properties of the VoI in the example of a queue model, deriving its distribution functions and moments. The lower and upper bounds of the average VoI are also analysed, which can be used for the design and optimisation of freshness-aware networks. Numerical results are presented and further show that, compared with the traditional linear age and some basic non-linear age functions, the proposed VoI framework is more general and suitable for various contexts.

The Lower and Upper Bounds of Turán Number for Odd Wheels

2021 ◽  
Vol 37 (3) ◽  
pp. 919-932
Author(s):  
Byeong Moon Kim ◽  
Byung Chul Song ◽  
Woonjae Hwang
Keyword(s):  
Upper Bounds ◽  
Lower And Upper Bounds ◽  
Turán Number

scholarly journals Lower and upper bounds of quantum battery power in multiple central spin systems

2021 ◽  
Vol 103 (5) ◽  
Author(s):  
Li Peng ◽  
Wen-Bin He ◽  
Stefano Chesi ◽  
Hai-Qing Lin ◽  
Xi-Wen Guan
Keyword(s):  
Upper Bounds ◽  
Spin Systems ◽  
Lower And Upper Bounds ◽  
Battery Power
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