Variation Principles and Bounds for the Approximate Analysis of Plane Membranes Under Lateral Pressure

1983 ◽  
Vol 50 (4a) ◽  
pp. 743-749 ◽  
Author(s):  
B. Stora˚kers
Keyword(s):  
Lateral Pressure ◽  
Practical Interest ◽  
Upper Bounds ◽  
Approximate Analysis ◽  
Lower And Upper Bounds ◽  
First Order ◽  
Linear Elastic ◽  
Consistent Approximation ◽  
Elastic Membranes ◽  
Variational Formulations

A first-order consistent approximation for the analysis of small deflections of membranes is given several variational formulations. Lower and upper bounds are derived for the volume enclosed by deformed and undeformed membranes. The power of the principles is discussed and their application is illustrated by some cases of practical interest. Explicit analytical results are given for linear elastic membranes having circular, elliptic, and rectangular contours.

A Viscoelastic Correspondence Principle for Plane Membranes Subjected to Lateral Pressure

1983 ◽  
Vol 50 (4a) ◽  
pp. 740-742 ◽  
Author(s):  
B. Stora˚kers
Keyword(s):  
Time Dependence ◽  
Viscoelastic Material ◽  
Lateral Pressure ◽  
Correspondence Principle ◽  
Material Model ◽  
Material Behavior ◽  
Linear Elastic Material ◽  
First Order ◽  
Linear Elastic ◽  
Consistent Approximation

The classical Fo¨ppl equations, governing the deflection of plane membranes, constitute the first-order consistent approximation in the case of linear elastic material behavior. It is shown that despite the static and kinematic nonlinearities present, for arbitrary load histories a correspondence principle for viscoelastic material behavior exists if all relevant relaxation moduli are of uniform time dependence. Application of the principle is illustrated by means of a popular material model.

Elastic Modulus Adjustment Improved Convergement Schemes Using Variable Local Constraints

2005 ◽  
Author(s):  
R. Adibi-Asl ◽  
Ihab F. Z. Fanous ◽  
R. Seshadri
Keyword(s):  
Finite Element Analysis ◽  
Elastic Modulus ◽  
Simple Procedure ◽  
Upper Bounds ◽  
Lower And Upper Bounds ◽  
Element Analysis ◽  
Local Constraints ◽  
Limit Loads ◽  
Linear Elastic ◽  
Degree Of Convergence

Elastic modulus adjustment procedures (EMAP) have been employed to determine limit loads of pressure components. On the basis of linear elastic Finite Element Analysis (FEA) with non-hardening elastic properties, i.e., by specifying spatial variations in the elastic modulus, numerous set of statically admissible and kinematically admissible distributions can be generated, and both lower and upper bounds on limit loads can be obtained. Some methods such as the classical, r-node and mα methods provide limit loads on the basis of partly-converged distributions, whereas the accuracy of linear matching procedures rely on fully converged distributions. In this paper, a criterion for establishing the degree of convergence of EMAP is developed, and a simple procedure for achieving improved convergence is described. The procedure is applied to some practical pressure component configurations.

scholarly journals Piecewise linear lower and upper bounds for the standard normal first order loss function

2014 ◽  
Vol 231 ◽  
pp. 489-502 ◽  
Author(s):  
Roberto Rossi ◽  
S. Armagan Tarim ◽  
Steven Prestwich ◽  
Brahim Hnich
Keyword(s):  
Loss Function ◽  
Piecewise Linear ◽  
Upper Bounds ◽  
Lower And Upper Bounds ◽  
First Order ◽  
Standard Normal

Small Deflections of Linear Elastic Circular Membranes Under Lateral Pressure

1983 ◽  
Vol 50 (4a) ◽  
pp. 735-739 ◽  
Author(s):  
B. Stora˚kers
Keyword(s):  
Numerical Analysis ◽  
Lateral Pressure ◽  
Computer Method ◽  
Uniform Pressure ◽  
Linear Elastic ◽  
Pressure Load ◽  
Elastic Membranes ◽  
Quantitative Results ◽  
Circular Contour ◽  
Considerable Detail

The classical Fo¨ppl equations, governing the deflection of plane elastic membranes, are cast in a form convenient for numerical analysis in the case of a circular contour. A solution based on a standard computer method is given for uniform pressure load. Quantitative results within determined accuracy are reported in considerable detail together with a discussion of the physical range of validity.

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
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