Planar Equilibrium Problems for Elastic Rods

1995 ◽  
pp. 85-123
Author(s):  
Stuart S. Antman
Keyword(s):  
Equilibrium Problems ◽  
Elastic Rods ◽  
Planar Equilibrium

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.

Variational Theory of Motion of Curved, Twisted and Extensible Elastic Rods

1993 ◽  
Author(s):  
Iradj Tadjbakhsh ◽  
Dimitris C. Lagoudas
Keyword(s):  
Elastic Rods ◽  
Variational Theory ◽  
Theory Of Motion

Two new extragradient methods for solving equilibrium problems

2021 ◽  
Vol 115 (2) ◽  
Author(s):  
Habib ur Rehman ◽  
Aviv Gibali ◽  
Poom Kumam ◽  
Kanokwan Sitthithakerngkiet
Keyword(s):  
Equilibrium Problems ◽  
Extragradient Methods

scholarly journals Inducing strong convergence of trajectories in dynamical systems associated to monotone inclusions with composite structure

2020 ◽  
Vol 10 (1) ◽  
pp. 450-476
Author(s):  
Radu Ioan Boţ ◽  
Sorin-Mihai Grad ◽  
Dennis Meier ◽  
Mathias Staudigl
Keyword(s):  
Dynamical Systems ◽  
Strong Convergence ◽  
Equilibrium Problems ◽  
Monotone Operators ◽  
Inclusion Problem ◽  
Minimum Norm ◽  
Monotone Inclusion ◽  
Inclusion Problems ◽  
Monotone Inclusion Problem ◽  
Maximally Monotone Operators

Abstract In this work we investigate dynamical systems designed to approach the solution sets of inclusion problems involving the sum of two maximally monotone operators. Our aim is to design methods which guarantee strong convergence of trajectories towards the minimum norm solution of the underlying monotone inclusion problem. To that end, we investigate in detail the asymptotic behavior of dynamical systems perturbed by a Tikhonov regularization where either the maximally monotone operators themselves, or the vector field of the dynamical system is regularized. In both cases we prove strong convergence of the trajectories towards minimum norm solutions to an underlying monotone inclusion problem, and we illustrate numerically qualitative differences between these two complementary regularization strategies. The so-constructed dynamical systems are either of Krasnoselskiĭ-Mann, of forward-backward type or of forward-backward-forward type, and with the help of injected regularization we demonstrate seminal results on the strong convergence of Hilbert space valued evolutions designed to solve monotone inclusion and equilibrium problems.

scholarly journals Common Solution for a Finite Family of Equilibrium Problems, Quasi-Variational Inclusion Problems and Fixed Points on Hadamard Manifolds

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1161
Author(s):  
Jinhua Zhu ◽  
Jinfang Tang ◽  
Shih-sen Chang ◽  
Min Liu ◽  
Liangcai Zhao
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Equilibrium Problems ◽  
Fixed Point Problem ◽  
Finite Family ◽  
Variational Inclusion ◽  
Point Problem ◽  
Hadamard Manifolds ◽  
Inclusion Problems ◽  
Common Solution

In this paper, we introduce an iterative algorithm for finding a common solution of a finite family of the equilibrium problems, quasi-variational inclusion problems and fixed point problem on Hadamard manifolds. Under suitable conditions, some strong convergence theorems are proved. Our results extend some recent results in literature.

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