Variational formulation of a contact problem for linearly elastic and physically nonlinear shallow shells

1982 ◽  
Vol 46 (5) ◽  
pp. 674-678
Author(s):  
G.I. L'Vov
Keyword(s):  
Contact Problem ◽  
Variational Formulation ◽  
Shallow Shells

A piezoelectric contact problem with slip dependent friction and damage

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Abderrezak Kasri
Keyword(s):  
Weak Solution ◽  
Contact Problem ◽  
Dry Friction ◽  
Existence And Uniqueness ◽  
Variational Formulation ◽  
Normal Compliance ◽  
Electrically Conductive ◽  
Coulomb’S Law ◽  
Electrical Condition ◽  
Coulomb's Law

Abstract The aim of this paper is to study a quasistatic contact problem between an electro-elastic viscoplastic body with damage and an electrically conductive foundation. The contact is modelled with an electrical condition, normal compliance and the associated version of Coulomb’s law of dry friction in which slip dependent friction is included. We derive a variational formulation for the model and, under a smallness assumption, we prove the existence and uniqueness of a weak solution.

Tykhonov well-posedness of a frictionless unilateral contact problem

2019 ◽  
Vol 25 (6) ◽  
pp. 1294-1311 ◽  
Author(s):  
Zhenhai Liu ◽  
Mircea Sofonea ◽  
Yi-bin Xiao
Keyword(s):  
Contact Problem ◽  
Variational Formulation ◽  
Unilateral Contact ◽  
Well Posedness ◽  
Unilateral Constraints ◽  
The Family ◽  
Contact Models ◽  
Mechanical Interpretation ◽  
Well Posed ◽  
Natural Way

We consider a frictionless contact problem, Problem [Formula: see text], for elastic materials. The process is assumed to be static and the contact is modelled with unilateral constraints. We list the assumptions on the data and derive a variational formulation of the problem, Problem [Formula: see text]. Then we consider a perturbation of Problem [Formula: see text], which could be frictional, governed by a small parameter [Formula: see text]. This perturbation leads in a natural way to a family of sets [Formula: see text]. We prove that Problem [Formula: see text] is well-posed in the sense of Tykhonov with respect to the family [Formula: see text]. The proof is based on arguments of monotonicity, pseudomonotonicity and various estimates. We extend these results to a time-dependent version of Problem [Formula: see text]. Finally, we provide examples and mechanical interpretation of our well-posedness results, which, in particular, allow us to establish the link between the weak solutions of different contact models.

Influence of Surface Waviness and Roughness on the Normal Pressure Distribution in the Hertzian Contact

1987 ◽  
Vol 109 (3) ◽  
pp. 462-469 ◽  
Author(s):  
J. Seabra ◽  
D. Berthe
Keyword(s):  
Surface Roughness ◽  
Contact Problem ◽  
Pressure Distribution ◽  
Variational Formulation ◽  
Virtual Work ◽  
Normal Pressure ◽  
Hertzian Contact ◽  
Surface Waviness ◽  
Normal Contact ◽  
Surface Imperfections

Contact stresses are one of the most important parameters in the analysis of a contact problem found for instance, in the design of gears and roller bearings. In this work the influence of geometrical surface imperfections on the normal pressure distribution in the contact is studied. A variational formulation based on the principle of complementary virtual work is used to solve the normal contact problem. The normal contact between two elastic half-spaces is considered, as the contact surface is small when compared to the dimensions of the contacting bodies. Results are presented to determine the influence of surface roughness, wavelength, and amplitude on the normal pressure distribution.

A traction contact problem governed by hemivariational inequalities for a mixed formulation of Stokes equation

2016 ◽  
Vol 22 (3) ◽  
pp. 420-433 ◽  
Author(s):  
T Sluzalec
Keyword(s):  
Weak Solution ◽  
Velocity Field ◽  
Contact Problem ◽  
Stokes Equation ◽  
Existence And Uniqueness ◽  
Variational Formulation ◽  
Contact Problems ◽  
Mixed Formulation ◽  
Hemivariational Inequalities ◽  
The Stokes Equation

In this paper the traction contact problems for Stokes equation are discussed and the Stokes equation is considered in a mixed formulation. We prove the existence and uniqueness of the weak solution for a mixed formulation of Stokes equation with traction contact. The traction contact is described by subdifferential boundary conditions. For this problem we present a variational formulation in a form of a hemivariational inequality for the velocity field.

scholarly journals A HISTORY-DEPENDENT FRICTIONAL CONTACT PROBLEM WITH WEAR FOR THERMOVISCOELASTIC MATERIALS

2019 ◽  
Vol 24 (3) ◽  
pp. 351-371
Author(s):  
Lamia Chouchane ◽  
Lynda Selmani
Keyword(s):  
Contact Problem ◽  
Thermal Effects ◽  
Variational Formulation ◽  
Frictional Contact ◽  
Viscoelastic Body ◽  
Perturbation Parameter ◽  
Convergence Result ◽  
Uniqueness Result ◽  
Quasivariational Inequalities ◽  
Wear And Friction

In this manuscript we study a contact problem between a deformable viscoelastic body and a rigid foundation. Thermal effects, wear and friction between surfaces are taken into account. A variational formulation of the problem is supplied and an existence and uniqueness result is proved. The idea of the proof rested on a recent result on history-dependent quasivariational inequalities. Finally, a perturbation of the data is initiated and a convergence result is demonstrated when the perturbation parameter converges to zero.

A Variational Formulation of Shallow Shells

1991 ◽  
pp. 68-79 ◽  
Author(s):  
A. Ibrahimbegovic ◽  
F. Frey ◽  
G. Fonder ◽  
C. Massonnet
Keyword(s):  
Variational Formulation ◽  
Shallow Shells
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