EXISTENCE AND UNIQUENESS OF SOLUTIONS OF THE DISCRETIZED CONTACT ELASTO-PLASTIC PROBLEM WITH ISOTROPIC HARDENING

2000 ◽  
Vol 10 (08) ◽  
pp. 1151-1179 ◽  
Author(s):  
EDUARD ROHAN
Keyword(s):  
Variational Inequalities ◽  
Fundamental Theorem ◽  
Existence And Uniqueness ◽  
Contact Problems ◽  
Isotropic Hardening ◽  
Plastic Strains ◽  
Uniqueness Of Solutions ◽  
Operator Equations

A class of quasistatic contact problems for elasto-plastic bodies with isotropic hardening is considered. The problems involve displacements, plastic strains and plastic multipliers. In the framework of multi-valued operator equations, the existence and uniqueness assertions for discretized reduced subproblems are proved using a fundamental theorem on variational inequalities.

Existence and Uniqueness of Solutions in Strain Space of Elastoplastic Problems with Isotropic Hardening

1997 ◽  
Vol 07 (01) ◽  
pp. 31-48 ◽  
Author(s):  
Ivan Hlaváček ◽  
John R. Whiteman
Keyword(s):  
Existence And Uniqueness ◽  
Mixed Boundary ◽  
Maximal Monotone ◽  
Maximal Monotone Operators ◽  
Mixed Boundary Conditions ◽  
Monotone Operators ◽  
Isotropic Hardening ◽  
Uniqueness Of Solutions ◽  
Quasistatic Problem ◽  
Strain Space

The flow theory of elasto-plastic bodies with isotropic strain hardening is formulated in strain space by means of a time-dependent variational inequality. Using concepts of subdifferential and multivalued maximal monotone operators, we prove the existence and uniqueness of a solution of the quasistatic problem in ℝn, (n = 2,3), with mixed boundary conditions.

scholarly journals Subdifferential inclusions and quasi-static hemivariational inequalities for frictional viscoelastic contact problems

2012 ◽  
Vol 10 (6) ◽  
Author(s):  
Stanisław Migórski
Keyword(s):  
Mathematical Modeling ◽  
Boundary Conditions ◽  
Existence And Uniqueness ◽  
Contact Problems ◽  
Hemivariational Inequality ◽  
Hemivariational Inequalities ◽  
Uniqueness Of Solutions ◽  
Viscoelastic Contact

AbstractWe survey recent results on the mathematical modeling of nonconvex and nonsmooth contact problems arising in mechanics and engineering. The approach to such problems is based on the notions of an operator subdifferential inclusion and a hemivariational inequality, and focuses on three aspects. First we report on results on the existence and uniqueness of solutions to subdifferential inclusions. Then we discuss two classes of quasi-static hemivariational ineqaulities, and finally, we present ideas leading to inequality problems with multivalued and nonmonotone boundary conditions encountered in mechanics.

scholarly journals On the existence and uniqueness problems of solutions for set-valued and single-valued nonlinear operator equations in probabilistic normed spaces

1994 ◽  
Vol 17 (2) ◽  
pp. 389-396 ◽  
Author(s):  
Shih-Sen Chang ◽  
Yeol Je Cho ◽  
Fan Wang
Keyword(s):  
Existence And Uniqueness ◽  
Nonlinear Operator ◽  
Normed Spaces ◽  
Uniqueness Of Solutions ◽  
Operator Equations ◽  
Nonlinear Operator Equations ◽  
Probabilistic Normed Spaces

In this paper, we introduce the concept of more general probabilistic contractors in probabilistic normed spaces and show the existence and uniqueness of solutions for set-valued and single-valued nonlinear operator equations in Menger probabilistic normed spaces.

Integral Representations for the Solution of Dynamic Bending of a Plate with Displacement-Traction Boundary Data

2003 ◽  
Vol 10 (3) ◽  
pp. 467-480
Author(s):  
Igor Chudinovich ◽  
Christian Constanda
Keyword(s):  
Existence And Uniqueness ◽  
Boundary Data ◽  
Boundary Integral Equations ◽  
Mixed Boundary ◽  
Mixed Boundary Conditions ◽  
Boundary Integral ◽  
Integral Representations ◽  
Transverse Shear Deformation ◽  
Uniqueness Of Solutions ◽  
Nonstationary Boundary

Abstract The existence of distributional solutions is investigated for the time-dependent bending of a plate with transverse shear deformation under mixed boundary conditions. The problem is then reduced to nonstationary boundary integral equations and the existence and uniqueness of solutions to the latter are studied in appropriate Sobolev spaces.

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