Symmetry preserving algorithm for large displacement frictionless contact by the pre-discretization penalty method

2004 ◽  
Vol 61 (15) ◽  
pp. 2615-2638 ◽  
Author(s):  
D. Gabriel ◽  
J. Ple?ek ◽  
M. Ulbin
Keyword(s):  
Penalty Method ◽  
Large Displacement ◽  
Frictionless Contact

A nonsmooth static frictionless contact problem with locking materials

2018 ◽  
Vol 16 (06) ◽  
pp. 851-874 ◽  
Author(s):  
Mircea Sofonea
Keyword(s):  
Continuous Dependence ◽  
Penalty Method ◽  
Optimization Problem ◽  
Convergence Result ◽  
Normal Displacement ◽  
Unique Weak Solution ◽  
Unilateral Constraints ◽  
Weak Formulation ◽  
Frictionless Contact ◽  
Displacement Constraints

We study a new mathematical model which describes the equilibrium of a locking material in contact with a foundation. The contact is frictionless and is modeled with a nonsmooth multivalued interface law which involves unilateral constraints and subdifferential conditions. We describe the model and derive its weak formulation, which is in the form of an elliptic variational–hemivariational inequality for the displacement field. Then, we establish the existence of a unique weak solution to the problem. Next, we introduce a penalty method, for which we state and prove a convergence result. Finally, we consider a particular version of the model for which we prove the continuous dependence of the solution on the bounds which govern the locking and the normal displacement constraints, respectively. We apply this convergence result in the study of an optimization problem associated to the contact model.

Existence and regularity results for unilateral problems with degenerate coercivity

2019 ◽  
Vol 69 (6) ◽  
pp. 1351-1366 ◽  
Author(s):  
Hocine Ayadi ◽  
Rezak Souilah
Keyword(s):  
Penalty Method ◽  
Degenerate Coercivity ◽  
Unilateral Problems ◽  
Existence And Regularity Results ◽  
Regularity Results

Abstract In this paper we prove some existence and regularity results for nonlinear unilateral problems with degenerate coercivity via the penalty method.

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