scholarly journals On stretch-limited elastic strings

2021 ◽  
Vol 477 (2249) ◽  
pp. 20210181
Author(s):  
Casey Rodriguez
Keyword(s):  
Constitutive Relations ◽  
Degenerate Case ◽  
Equilibrium States ◽  
Elastic Strings ◽  
Existence And Multiplicity ◽  
Cauchy Elasticity

Motivated by the increased interest in modelling non-dissipative materials by constitutive relations more general than those from Cauchy elasticity, we initiate the study of a class of stretch-limited elastic strings : the string cannot be compressed smaller than a certain length less than its natural length nor elongated larger than a certain length greater than its natural length. In particular, we consider equilibrium states for a string suspended between two points under the force of gravity (catenaries). We study the locations of the supports resulting in tensile states containing both extensible and inextensible segments in two situations: the degenerate case when the string is vertical and the non-degenerate case when the supports are at the same height. We then study the existence and multiplicity of equilibrium states in general with multiplicity differing markedly from strings satisfying classical constitutive relations.

Thermodynamics of Infinitesimally Constrained Equilibrium States

2008 ◽  
Vol 76 (1) ◽  
Author(s):  
Q. Yang ◽  
L. J. Xue ◽  
Y. R. Liu
Keyword(s):  
Constitutive Relations ◽  
Hessian Matrix ◽  
Coefficient Matrix ◽  
Internal Variable ◽  
Irreversible Thermodynamics ◽  
Equilibrium States ◽  
Variable Theory ◽  
Constrained Equilibrium ◽  
Flow Potential ◽  
Nonequilibrium States

This paper is concerned with infinitesimally constrained equilibrium states, which are nonequilibrium states and infinitesimally close to equilibrium states. The corresponding thermodynamics is established in this paper within the thermodynamic framework of Rice (1971, “Inelastic Constitutive Relations for Solids: An Internal Variable Theory and Its Application to Metal Plasticity,” J. Mech. Phys. Solids, 19, pp. 433–455). It is shown that the thermodynamics of infinitesimally constrained equilibrium states belongs to linear irreversible thermodynamics. The coefficient matrix is the Hessian matrix of the flow potential function at the equilibrium state. The process of a state change induced by an infinitesimal stress increment in time-independent plasticity can be viewed as a sequence of infinitesimally constrained equilibrium states. The thermodynamic counterpart of yield functions are flow potential functions, and their convexity is required by intrinsic dissipation inequality. Drucker and Il’yushin’s inequalities are not essential thermodynamic requirements.

5.—Qualitative Aspects of the Spatial Deformation of Non-linearly Elastic Rods.

1975 ◽  
Vol 73 ◽  
pp. 85-105 ◽  
Author(s):  
Stuart S. Antman ◽  
Kathleen B. Jordan
Keyword(s):  
Boundary Value Problem ◽  
Geometric Structure ◽  
Constitutive Relations ◽  
Equilibrium States ◽  
Linear Functions ◽  
Order System ◽  
Elastic Rods ◽  
Qualitative Behaviour ◽  
Spatial Deformation ◽  
Planar Equilibrium

In this article we examine the qualitative behaviour of non-planar equilibrium states ofnon-linearly elastic rods subject to terminal loads. In our geometrically exact theory, a rod is endowed with enough geometric structure for it to undergo flexure, torsion, axial extension, and shear. The constitutive equations give appropriate stress resultants and couples as non-linear functions of appropriate strains. These constitutive relations must meet minimal conditions ensuring that they be physically reasonable. It turns out that the equilibrium states of such a rod are governed by a boundary value problem for a quasilinear fifteenth-order system of ordinary differential equations.

Exotic equilibrium states of the elastic string

1984 ◽  
Vol 96 (3-4) ◽  
pp. 289-302 ◽  
Author(s):  
Michael Reeken
Keyword(s):  
Equilibrium States ◽  
Elastic Strings ◽  
Elastic String ◽  
Distributional Solutions ◽  
Nonlinear Elastic ◽  
Catenary Problem

SynopsisA detailed description of the totality of distributional solutions of the catenary problem for nonlinear elastic strings is given.

Macroeconomic Equilibrium Theory in the Context of Methodological Problems of Contemporary Economic Science

2008 ◽  
pp. 77-88
Author(s):  
M. Likhachev
Keyword(s):  
Empirical Analysis ◽  
Equilibrium States ◽  
Equilibrium Theory ◽  
Economic Systems ◽  
Economic Science ◽  
The Real ◽  
Theoretical Status ◽  
Methodological Problems ◽  
Real Stability

The article is devoted to the analysis of methodological problems in using the conception of macroeconomic equilibrium in contemporary economics. The author considers theoretical status and relevance of equilibrium conception and discusses different areas and limits of applicability of the equilibrium theory. Special attention is paid to different epistemological criteria for this theory taking into account both empirical analysis of the real stability of economic systems and the problem of unobservability of equilibrium states.

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