scholarly journals A three-field augmented Lagrangian formulation of unilateral contact problems with cohesive forces

2010 ◽  
Vol 44 (2) ◽  
pp. 323-346 ◽  
Author(s):  
David Doyen ◽  
Alexandre Ern ◽  
Serge Piperno
Keyword(s):  
Augmented Lagrangian ◽  
Contact Problems ◽  
Unilateral Contact ◽  
Lagrangian Formulation ◽  
Cohesive Forces ◽  
Unilateral Contact Problems ◽  
Augmented Lagrangian Formulation

scholarly journals Shape derivatives for an augmented Lagrangian formulation of elastic contact problems

2020 ◽  
Author(s):  
Bastien Chaudet-Dumas ◽  
Jean Deteix
Keyword(s):  
Augmented Lagrangian ◽  
Sufficient Conditions ◽  
Contact Problems ◽  
Lagrangian Formulation ◽  
Directional Derivatives ◽  
Practical Reasons ◽  
Process Conditions ◽  
Shape Derivatives ◽  
Derivatives Of ◽  
Augmented Lagrangian Formulation

This work deals with shape optimization of an elastic body in sliding contact (Signorini) with a rigid foundation. The mechanical problem is written under its augmented Lagrangian formulation, then solved using a classical iterative approach. For practical reasons we are interested in applying the optimization process with respect to an intermediate solution produced by the iterative method. Due to the projection operator involved at each iteration, the iterate solution is not classically shape differentiable. However, using an approach based on directional derivatives, we are able to prove that it is conically differentiable with respect to the shape, and express sufficient conditions for shape differentiability. Finally, from the analysis of the sequence of conical shape derivatives of the iterative process, conditions are established for the convergence to the conical derivative of the original contact problem.

scholarly journals Nitsche’s method for unilateral contact problems

2019 ◽  
Vol 75 (3) ◽  
pp. 189-204
Author(s):  
Tom Gustafsson ◽  
Rolf Stenberg ◽  
Juha Videman
Keyword(s):  
Contact Problems ◽  
Unilateral Contact ◽  
Nitsche’S Method ◽  
Nitsche's Method ◽  
Unilateral Contact Problems
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