Asymptotic modeling of Signorini problem with Coulomb friction for a linearly elastostatic shallow shell

2015 ◽  
Vol 39 (6) ◽  
pp. 1410-1424 ◽  
Author(s):  
Abdallah Bensayah ◽  
Djamel Ahmed Chacha ◽  
Abderrezak Ghezal
Keyword(s):  
Coulomb Friction ◽  
Shallow Shell ◽  
Signorini Problem ◽  
Asymptotic Modeling

The reciprocal variational approach to the Signorini problem with friction. Approximation results

1984 ◽  
Vol 98 (3-4) ◽  
pp. 365-383 ◽  
Author(s):  
J. Haslinger ◽  
P. D. Panagiotopoulos
Keyword(s):  
Coulomb Friction ◽  
Numerical Results ◽  
Contact Boundary ◽  
Minimum Problem ◽  
Approximation Procedure ◽  
Signorini Problem ◽  
Direct Integral ◽  
Mixed Problems ◽  
Convergence Results ◽  
Integral Equation Approach

SynopsisIn this paper, a new variational formulation of the Signorini problem with friction is given in terms of the contact stresses. The method corresponds to the direct integral equation approach in classical elastostatic problems. First the displacement and mixed problems are briefly described together with some numerical results. Next the displacements are eliminated by the use of Green's function, and a constrained minimum problem with respect to the normal and tangential tractions on the contact boundary is derived. Then the resulting approximation procedure is studied and certain convergence results are proved. Finally, some remarks on the Signorini problem with Coulomb friction are presented. Numerical results illustrate the theory.

Asymptotic Analysis of Frictional Contact Problem for Piezoelectric Shallow Shell

2019 ◽  
Vol 72 (4) ◽  
pp. 473-499 ◽  
Author(s):  
M E Mezabia ◽  
A Ghezal ◽  
D A Chacha
Keyword(s):  
Contact Problem ◽  
Asymptotic Analysis ◽  
Equilibrium State ◽  
Shallow Shell ◽  
Frictional Contact ◽  
Rigid Foundation ◽  
Two Dimensional ◽  
Signorini Problem ◽  
Dimensional Model ◽  
Two Dimensional Model

Summary The objective of this work is to study the asymptotic justification of a new two-dimensional model for the equilibrium state of a piezoelectric linear shallow shell in frictional contact with a rigid foundation. More precisely, we consider the Signorini problem with Tresca friction of a piezoelectric linear shallow shell in contact with a rigid foundation. Then, we establish the convergence of the mechanical displacement and the electric potential as the thickness of the shallow shell goes to zero.

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