Quasiconvexity and Uniqueness of Equilibrium Solutions in Nonlinear Elasticity

1986 ◽  
pp. 473-489
Author(s):  
R. J. Knops ◽  
C. A. Stuart
Keyword(s):  
Nonlinear Elasticity ◽  
Equilibrium Solutions ◽  
Uniqueness Of Equilibrium

scholarly journals Stability Analysis of the Rhomboidal Restricted Six-Body Problem

2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
M. A. R. Siddique ◽  
A. R. Kahsif ◽  
M. Shoaib ◽  
S. Hussain
Keyword(s):  
Body Problem ◽  
Equilibrium Points ◽  
First Integral ◽  
Small Mass ◽  
Equilibrium Solutions ◽  
Integral Of Motion ◽  
Jacobian Constant ◽  
Zero Velocity Curves ◽  
The Masses ◽  
Uniqueness Of Equilibrium

We discuss the restricted rhomboidal six-body problem (RR6BP), which has four positive masses at the vertices of the rhombus, and the fifth mass is at the intersection of the two diagonals. These masses always move in rhomboidal CC with diagonals 2 a and 2 b . The sixth body, having a very small mass, does not influence the motion of the five masses, also called primaries. The masses of the primaries are m 1 = m 2 = m 0 = m and m 3 = m 4 = m ˜ . The masses m and m ˜ are written as functions of parameters a and b such that they always form a rhomboidal central configuration. The evolution of zero velocity curves is discussed for fixed values of positive masses. Using the first integral of motion, we derive the region of possible motion of test particle m 5 and identify the value of Jacobian constant C for different energy intervals at which these regions become disconnected. Using semianalytical techniques, we show the existence and uniqueness of equilibrium solutions on the axes and off the axes. We show that, for b ∈ 1 / 3 , 1.1394282249562009 , there always exist 12 equilibrium points. We also show that all 12 equilibrium points are unstable.

scholarly journals BMO and Elasticity: Korn’s Inequality; Local Uniqueness in Tension

2021 ◽  
Author(s):  
Daniel E. Spector ◽  
Scott J. Spector
Keyword(s):  
Positive Definite ◽  
Second Variation ◽  
Local Uniqueness ◽  
Equilibrium Solutions ◽  
Principal Stresses ◽  
Korn’S Inequality ◽  
The Second Variation ◽  
Strain Space ◽  
Vector Valued ◽  
Uniqueness Of Equilibrium

AbstractIn this manuscript two BMO estimates are obtained, one for Linear Elasticity and one for Nonlinear Elasticity. It is first shown that the BMO-seminorm of the gradient of a vector-valued mapping is bounded above by a constant times the BMO-seminorm of the symmetric part of its gradient, that is, a Korn inequality in BMO. The uniqueness of equilibrium for a finite deformation whose principal stresses are everywhere nonnegative is then considered. It is shown that when the second variation of the energy, when considered as a function of the strain, is uniformly positive definite at such an equilibrium solution, then there is a BMO-neighborhood in strain space where there are no other equilibrium solutions.

NUMERICAL AND STABILITY ANALYSIS OF THE TRANSMISSION DYNAMICS OF SVIR EPIDEMIC MODEL WITH STANDARD INCIDENCE RATE

2019 ◽  
Vol 4 (2) ◽  
pp. 349 ◽  
Author(s):  
Oluwatayo Michael Ogunmiloro ◽  
Fatima Ohunene Abedo ◽  
Hammed Kareem
Keyword(s):  
Reproduction Number ◽  
Disease Spread ◽  
Asymptotically Stable ◽  
Equilibrium Solutions ◽  
Transform Method ◽  
Globally Asymptotically Stable ◽  
Differential Transform ◽  
Mathematical Techniques ◽  
Fourth Order Method ◽  
Theoretical Results

In this article, a Susceptible – Vaccinated – Infected – Recovered (SVIR) model is formulated and analysed using comprehensive mathematical techniques. The vaccination class is primarily considered as means of controlling the disease spread. The basic reproduction number (Ro) of the model is obtained, where it was shown that if Ro<1, at the model equilibrium solutions when infection is present and absent, the infection- free equilibrium is both locally and globally asymptotically stable. Also, if Ro>1, the endemic equilibrium solution is locally asymptotically stable. Furthermore, the analytical solution of the model was carried out using the Differential Transform Method (DTM) and Runge - Kutta fourth-order method. Numerical simulations were carried out to validate the theoretical results. 

Variant of Nonlinear Elasticity Relations

2019 ◽  
Vol 54 (8) ◽  
pp. 1182-1188
Author(s):  
A. A. Markin ◽  
M. Yu. Sokolova
Keyword(s):  
Nonlinear Elasticity

Exploration of trabecular bone nonlinear elasticity using time of flight modulation

2007 ◽  
Author(s):  
Guillaume Renaud ◽  
Samuel Callé ◽  
Jean-Pierre Remenieras ◽  
Marielle Defontaine
Keyword(s):  
Trabecular Bone ◽  
Nonlinear Elasticity ◽  
Time Of Flight

scholarly journals Decision and Coordination in a Dual-Channel Three-Layered Green Supply Chain

Symmetry ◽  
2018 ◽  
Vol 10 (11) ◽  
pp. 549 ◽  
Author(s):  
Zilong Song ◽  
Shiwei He ◽  
Baifeng An
Keyword(s):  
Sustainable Development ◽  
Supply Chain ◽  
Environmental Performance ◽  
Fresh Produce ◽  
Green Supply Chain ◽  
Market Demand ◽  
Equilibrium Solutions ◽  
Sustainable Performance ◽  
Dual Channel ◽  
Social And Environmental Performance

This paper investigated, for the first time, the game and coordination of a dual-channel, three-layered, green fresh produce supply chain, with regard to its economic, social, and environmental performance. Considering that the market demand is dual-channel priced and sensitive to the degree of greenness and the freshness-level, four game models, under different scenarios have been established. These included a centralized scenario, a decentralized scenario, and two contractual scenarios. The equilibrium solutions under the four scenarios were characterized. From the perspective of a sustainable development, the economic, social, and environmental performance of the supply chain was analyzed. To enhance the supply chain performance, two contract mechanisms were designed and the conditions for a multi-win outcome were obtained. Accordingly, many propositions and management implications were provided. The results showed that, (1) compared to the centralized supply chain case, the performance of the decentralized supply chain case is inferior; (2) in addition to increasing the concentration of the supply chain decisions, the two contracts proposed can effectively coordinate the green supply chain and improve its sustainable performance; and (3) the performance of the supply chain is positively driven by the consumers’ sensitivity to greenness degree and the freshness level of fresh produce. This paper fills a research gap and helps the participants of the channel recognize the operational decision principle of a complex green supply chain, in order to achieve a higher and a long-term sustainable-development performance.

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