scholarly journals Modified duality methods for solving an elastic crack problem with Coulomb friction on the crack faces

2020 ◽  
Vol 10 (1) ◽  
pp. 276-282
Author(s):  
Robert V. Namm ◽  
Georgiy I. Tsoy
Keyword(s):  
Variational Inequality ◽  
Elastic Body ◽  
Approximation Method ◽  
Coulomb Friction ◽  
Auxiliary Problem ◽  
Crack Problem ◽  
Successive Approximation Method ◽  
Elastic Crack ◽  
Quasi Variational Inequality ◽  
Crack Faces

AbstractWe consider an equilibrium problem for an elastic body with a crack, on the faces of which unilateral non-penetration conditions and Coulomb friction are realized. This problem can be formulated as quasi-variational inequality. To solve it, the successive approximation method is applied. On each outer step of this method, we solve an auxiliary problem with given friction. We solve the auxiliary problem by using modified Lagrange functionals. Numerical results are presented.

Some numerical graphs with successive approximation method of fractional integro–differential equation

2019 ◽  
Vol 8 (4) ◽  
pp. 36
Author(s):  
Samir H. Abbas
Keyword(s):  
Differential Equation ◽  
Successive Approximation ◽  
Approximation Method ◽  
Existence And Uniqueness ◽  
Successive Approximation Method ◽  
Integro Differential Equation

This paper studies the existence and uniqueness solution of fractional integro-differential equation, by using some numerical graphs with successive approximation method of fractional integro –differential equation. The results of written new program in Mat-Lab show that the method is very interested and efficient. Also we extend the results of Butris [3].

scholarly journals Ulam-Hyers Stability and Ulam-Hyers-Rassias Stability for Fuzzy Integrodifferential Equation

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-10 ◽  
Author(s):  
Nguyen Ngoc Phung ◽  
Bao Quoc Ta ◽  
Ho Vu
Keyword(s):  
Fixed Point ◽  
Successive Approximation ◽  
Integrodifferential Equation ◽  
Approximation Method ◽  
Fixed Point Method ◽  
Integrodifferential Equations ◽  
Point Method ◽  
Successive Approximation Method ◽  
Rassias Stability

In this paper, we establish the Ulam-Hyers stability and Ulam-Hyers-Rassias stability for fuzzy integrodifferential equations by using the fixed point method and the successive approximation method.

A Crack Model of a Bone Cement Interface

1984 ◽  
Vol 106 (3) ◽  
pp. 235-243 ◽  
Author(s):  
J. P. Clech ◽  
L. M. Keer ◽  
J. L. Lewis
Keyword(s):  
Bone Cement ◽  
Cohesive Zone ◽  
Edge Crack ◽  
Crack Problem ◽  
Bimaterial Interface ◽  
Fracture Mechanisms ◽  
Homogeneous Material ◽  
Crack Model ◽  
Cement Interface ◽  
Crack Faces

This paper is concerned with the fracture mechanics of a bone-cement interface that includes a cohesive zone effect on the crack faces. This accounts for the experimentally observed strengthening mechanism due to the mechanical interlock between the crack faces. Edge crack models are developed where the cohesive zone is simulated by a continuous or a discrete distribution of linear or nonlinear springs. It is shown that the solution obtained by assuming a homogeneous material is fairly close to the exact solution for the bimaterial interface edge crack problem. On the basis of that approximation, the analysis is conducted for the problem of two interacting edge cracks, one at the interface, and the other one in the cement. The small crack that was observed to initiate in the cement, close to the bone-cement interface, does not affect much the mode I stress-intensity factor at the tip of the interface crack. However it may grow, leading to a catastrophic breakdown of the cement. The analysis and following discussion point out an interdependency between bone-cement interface strength and cement strength not previously appreciated. The suggested crack models provide a framework for quantifying the fracture mechanisms at the bone-cement interface.

scholarly journals Strong Convergence Theorems for Asymptotically WeakG-Pseudo-Ψ-Contractive Non-Self-Mappings with the Generalized Projection in Banach Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
Yuanheng Wang
Keyword(s):  
Banach Space ◽  
Strong Convergence ◽  
Approximation Method ◽  
Generalized Projection ◽  
Iterative Sequence ◽  
Successive Approximation Method ◽  
Convergence Theorems ◽  
Mann Iterative Sequence ◽  
Sequence Method ◽  
Generalized Projection Method

A new concept of the asymptotically weakG-pseudo-Ψ-contractive non-self-mappingT:G↦Bis introduced and some strong convergence theorems for the mapping are proved by using the generalized projection method combined with the modified successive approximation method or with the modified Mann iterative sequence method in a uniformly and smooth Banach space. The proof methods are also different from some past common methods.

SAMPLE AVERAGE APPROXIMATION METHOD FOR SOLVING A DETERMINISTIC FORMULATION FOR BOX CONSTRAINED STOCHASTIC VARIATIONAL INEQUALITY PROBLEMS

2012 ◽  
Vol 29 (02) ◽  
pp. 1250014
Author(s):  
MEI-JU LUO ◽  
GUI-HUA LIN
Keyword(s):  
Variational Inequality ◽  
Approximation Method ◽  
Deterministic Model ◽  
Random Parameter ◽  
Sample Average Approximation ◽  
Variational Inequality Problems ◽  
Stochastic Variational Inequality ◽  
Sample Average ◽  
Sample Average Approximation Method ◽  
Average Approximation

In this paper, we discuss the Expected Residual Minimization (ERM) method, which is to minimize the expected residue of some merit function for box constrained stochastic variational inequality problems (BSVIPs). This method provides a deterministic model, which formulates BSVIPs as an optimization problem. We first study the conditions under which the level sets of the ERM problem are bounded. Then, we show that solutions of the ERM formulation are robust in the sense that they may have a minimum sensitivity with respect to random parameter variations in BSVIPs. Since the integrality involved in the ERM problem is difficult to compute generally, we then employ sample average approximation method to solve it. Finally, we show that the global optimal solutions and generalized KKT points of the approximate problems converge to their counterparts of the ERM problem. On the other hand, as an application, we consider the model of European natural gas market under price uncertainty. Preliminary numerical experiments indicate that the proposed approach is applicable.

scholarly journals Error bounds for generalized vector inverse quasi-variational inequality Problems with point to set mappings

2021 ◽  
Vol 6 (2) ◽  
pp. 1800-1815
Author(s):  
S. S. Chang ◽  
◽  
Salahuddin ◽  
M. Liu ◽  
X. R. Wang ◽  
...  
Keyword(s):  
Variational Inequality ◽  
Error Bounds ◽  
Variational Inequality Problems ◽  
Quasi Variational Inequality ◽  
Set Mappings
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