Numerical Stability Criteria for Localized Post-buckling Solutions in a Strut-on-Foundation Model

2004 ◽  
Vol 71 (3) ◽  
pp. 334-341 ◽  
Author(s):  
M. Khurram Wadee ◽  
Ciprian D. Coman ◽  
Andrew P. Bassom
Keyword(s):  
Total Potential Energy ◽  
Stability Criteria ◽  
Total Potential ◽  
All Solutions ◽  
Static Solutions ◽  
Foundation Model ◽  
Post Buckling ◽  
The Stability ◽  
Dead Loading ◽  
Stability Results

Some stability results are established for localized buckling solutions of a strut-on-foundation model which has an initially unstable post-buckling path followed by a restabilizing property. These results are in stark contrast with those for models with non-restabilizing behavior for which all solutions are unstable under dead-loading conditions. By approximating solutions with a nonperiodic set of functions, the stability of these static solutions can be assessed by examining the nature of the equilibrium using total potential energy considerations.

scholarly journals Computation of elastic equilibria of complete Möbius bands and their stability

2018 ◽  
Vol 24 (4) ◽  
pp. 939-967 ◽  
Author(s):  
Alexander Moore ◽  
Timothy Healey
Keyword(s):  
Local Minimum ◽  
Systematic Approach ◽  
Equilibrium Configuration ◽  
Total Potential Energy ◽  
Surface Model ◽  
Challenging Problem ◽  
Total Potential ◽  
The Stability ◽  
Kirchhoff Theory ◽  
Stability Results

Determining the equilibrium configuration of an elastic Möbius band is a challenging problem. In recent years numerical results have been obtained by other investigators, employing first the Kirchhoff theory of rods and later the developable, ruled-surface model of Sadowsky–Wunderlich. In particular, one such strategy used does not deliver an equilibrium configuration for the complete unsupported strip. Here we present our own systematic approach to the same problem for each of these models, with the ultimate goal of assessing the stability of flip-symmetric configurations. The presence of point-wise constraints considerably complicates the latter step. We obtain the first stability results for the problem, numerically demonstrating that such equilibria render the total potential energy a local minimum. Along the way we introduce a novel regularization for the singular Wunderlich model that delivers equilibria for complete strips having sufficiently narrow widths, which can then be tested for stability.

Dilute Aqueous Dispersions of Zro2 And Al2O3

1985 ◽  
Vol 60 ◽  
Author(s):  
Evelyn M. De Liso ◽  
W. Roger Cannon ◽  
A. Srinivasa Rao
Keyword(s):  
Potential Energy ◽  
Total Potential Energy ◽  
Alumina Powder ◽  
Maximum Height ◽  
Colloidal Interactions ◽  
Total Potential ◽  
Particle Size Data ◽  
Theoretical Predictions ◽  
Alumina Composite ◽  
The Stability

AbstractColloidal interactions in a heteroparticulate mixture of zirconia and alumina in water were studied for use in a transformation toughened alumina composite. The microelectrophoresis technique was used to measure the mobility of three zirconia powders and an alumina powder. The electro-phoretic mobility and particle size data were used to calculate total potential energy curves. The maximum height of the total potential energy barrier was used to predict the stability of a zirconia/alumina mixture. Theoretical predictions were compared to experimental results obtained from sedimentation and rheology measurements carried out as a function of pH of the dispersion. For a 5 v/o aqueous zirconia/alumina system stable dispersions were made at pH 3 and pH 5.

MODEL OF BINDING ALPHA-PARTICLES AND APPLICATIONS TO SUPERHEAVY ELEMENTS

2005 ◽  
Vol 14 (04) ◽  
pp. 635-643 ◽  
Author(s):  
K. A. GRIDNEV ◽  
S. YU. TORILOV ◽  
D. K. GRIDNEV ◽  
V. G. KARTAVENKO ◽  
W. GREINER
Keyword(s):  
Pair Potential ◽  
Total Potential Energy ◽  
Binding Energies ◽  
Alpha Particles ◽  
Superheavy Nuclei ◽  
Lennard Jones ◽  
Total Potential ◽  
Stability Island ◽  
The Stability ◽  
Good Agreement

A model of nuclear matter built from alpha-particles is proposed. In this model, nuclei possess the molecular-like structure. Analyzing the numbers of bonds, one gets the formula for the binding energy of a nucleus. The structure is determined by the minimum of the total potential energy, where interaction between alpha-particles is pairwise and the pair-potential is of Lennard–Jones type. The calculated binding energies show a good agreement with experiment. Calculations predict the stability island for superheavy nuclei around Z=120.

Research of Safe Distance between Concealed Karst Cave and Tunnel

2013 ◽  
Vol 405-408 ◽  
pp. 1283-1287
Author(s):  
Yong Biao Lai ◽  
Chun Sheng Qiao ◽  
Chen Guang Bai
Keyword(s):  
Catastrophe Theory ◽  
Total Potential Energy ◽  
Karst Cave ◽  
Safe Distance ◽  
Rock Stratum ◽  
Distance Calculation ◽  
Total Potential ◽  
Concealed Karst Cave ◽  
The Stability ◽  
Rock Strata

Based on the catastrophe theory, a research method of safe distance between concealed karst cave and tunnel is put forward. The stability of rock stratum between concealed karst cave and tunnel is evaluated by the catastrophe theory, the catastrophe mode of rock strata system destabilization is established through the research of rock stratum total potential energy between karst cave and tunnel, then the safe distance calculation formula between concealed karst cave and tunnel are deduced, which is veried by an engineering example.

Stability Analysis of an Imperfect Slender Web Subjected to the Shear Load

2016 ◽  
Vol 837 ◽  
pp. 52-57
Author(s):  
Martin Psotny
Keyword(s):  
Stability Analysis ◽  
Potential Energy ◽  
Total Potential Energy ◽  
Iteration Algorithm ◽  
Buckling Mode ◽  
Total Potential ◽  
Nonlinear Equilibrium ◽  
The Stability ◽  
Ansys System ◽  
Raphson Iteration

The stability analysis of an imperfect slender web subjected to the shearing load is presented, a specialized code based on FEM has been created. The nonlinear finite element method equations are derived from the variational principle of minimum of total potential energy. To obtain the nonlinear equilibrium paths, the Newton-Raphson iteration algorithm is used. Corresponding levels of the total potential energy are defined. The peculiarities of the effects of the initial imperfections are investigated. Special attention is paid to the influence of imperfections on the post-critical buckling mode. Obtained results are compared with those gained using ANSYS system.

scholarly journals Buckling And Postbuckling Of An Imperfect Plate Subjected To The Shear Load

2015 ◽  
Vol 15 (2) ◽  
Author(s):  
Martin Psotný
Keyword(s):  
Potential Energy ◽  
Total Potential Energy ◽  
Iteration Algorithm ◽  
Shear Load ◽  
Buckling Mode ◽  
Total Potential ◽  
Nonlinear Equilibrium ◽  
The Stability ◽  
Ansys System ◽  
Raphson Iteration

Abstract The stability analysis of an imperfect plate subjected to the shear load is presented. To solve this problem, a specialized computer program based on FEM has been created. The nonlinear finite element method equations are derived from the variational principle of minimum of total potential energy. To obtain the nonlinear equilibrium paths, the Newton-Raphson iteration algorithm is used. Corresponding levels of the total potential energy are defined. Special attention is paid to the influence of imperfections on the post-critical buckling mode. Obtained results are compared with those gained using ANSYS system.

Stability Analysis for Descriptor Neutral Systems with Mixed Delays

2011 ◽  
Vol 228-229 ◽  
pp. 153-157
Author(s):  
Xiu Liu ◽  
Shou Ming Zhong ◽  
Xiu Yong Ding
Keyword(s):  
Descriptor System ◽  
Linear Matrix ◽  
Mixed Delays ◽  
Matrix Inequalities ◽  
Stability Criteria ◽  
Neutral Systems ◽  
The Stability ◽  
Delay Dependent ◽  
Delay Dependent Stability ◽  
Stability Results

Delay-dependent stability of descriptor neutral systems with mixed delays is investigated in this paper. Based on descriptor system approach, some new delay-dependent stability and robust stability criteria are established in terms of a operator and linear matrix inequalities(LMIs). Lyapunov-Krasovskii functional and Leibniz-Newton formula are applied to find the stability results.

scholarly journals Absolute Stability and Master-Slave Synchronization of Systems with State-Dependent Nonlinearities

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Rong Li ◽  
Bo Liu ◽  
Chao Liu
Keyword(s):  
Absolute Stability ◽  
Schur Complement ◽  
Stability Conditions ◽  
Stability Criteria ◽  
Numerical Example ◽  
Kyp Lemma ◽  
State Dependent ◽  
The Stability ◽  
Stability Results

This paper is concerned with the problems of absolute stability and master-slave synchronization of systems with state-dependent nonlinearities. The Kalman-Yakubovich-Popov (KYP) lemma and the Schur complement formula are applied to get novel and less conservative stability conditions. A numerical example is presented to illustrate the efficiency of the stability criteria. Furthermore, a synchronization criterion is developed based on the proposed stability results.

scholarly journals Stability of a Class of Hybrid Neutral Stochastic Differential Equations with Unbounded Delay

2017 ◽  
Vol 2017 ◽  
pp. 1-11
Author(s):  
Boliang Lu ◽  
Ruili Song
Keyword(s):  
Differential Equations ◽  
Exponential Stability ◽  
Stochastic Differential Equations ◽  
Lyapunov Functions ◽  
Stability Criteria ◽  
Bounded Delay ◽  
Unbounded Delay ◽  
The Stability ◽  
Generalized Itô Formula ◽  
Stability Results

This paper studies the stability of hybrid neutral stochastic differential equations with unbounded delay. Some novel exponential stability criteria and boundedness conditions are established based on the generalized Itô formula and Lyapunov functions. The factor e-εδ(t) is used to overcome the difficulties caused by the unbounded delay δ(t) effectively. In particular, our results generalize and improve some previous stability results from bounded delay to unbounded delay conditions. Finally, an example is presented to demonstrate the effectiveness of the proposed results.

scholarly journals Stabilization of systems of galaxies by subclustering

1978 ◽  
Vol 79 ◽  
pp. 98-100
Author(s):  
L. M. Ozernoy ◽  
M. Reinhardt
Keyword(s):  
Potential Energy ◽  
Velocity Dispersion ◽  
Total Potential Energy ◽  
Groups Of Galaxies ◽  
Total Potential ◽  
Group Members ◽  
The Mean ◽  
Mass Segregation ◽  
The Stability ◽  
Good Agreement

Subclustering might help to solve the virial theorem paradox for systems of galaxies by hiding a major part of the potential energy in gravitationally bound subsystems. We have shown (Ozernoy and Reinhardt 1976, Astr. Astrophys., 52, 31) that even in groups of galaxies there is mass segregation, in the sense that bright group members tend to be concentrated towards the centre. Recently Wesson and Lermann (1977, Astrophys. Sp. Sci., 46, 327), realizing the importance of subclustering, proposed a quantitative method for estimating its effect on the stability of systems of galaxies. However, their assumption about the frequency of subsystems of multiplicity n is not in accord with Holmberg's (1962) result. the mean frequency of galaxies in pairs is 0.37 for the Turner and Gott groups (1976) and 0.23 for the de Vauceulours groups (1976), in good agreement with the value of 0.25 required by Holmberg's distribution. Assuming Holmberg's frequency of gravitationally bound subsystems and that they are homogeneously distributed throughout the system, we have for the ratio of the total potential energy of a system of N equal masses Ω to the potential energy calculated in the usual way neglecting subclustering Ωs, Ω/Ωs≈ 1+(Rc)/(<r2>N), if the velocity dispersion <σr2(n)> = constant. Here Rc is the effective radius of the system and <r2> the mean distance of binaries. the assumption σr2(n) = const is reasonable for n ≤ 7, when Holmberg's distribution holds, since σr2(2) = 203 km s−1 according to Karachentsev (1974), and increases to only ≃ 1000 km s−1 for rich clusters. Since Karachentsev's data give an <r2> = 33 kpc for HO = 55 km s−1 Mpc−1, we have Ω/Ωs≈ 4 for groups of galaxies with Rc≈ 1 Mpc and N = 10. Thus it seems that subclustering cannot remove the mass discrepancy for rich clusters and for groups only in moderate cases.

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