Existence of solutions of dynamic contact problems for elastic von Kármán-Donnell shells

2013 ◽  
pp. 65-68
Author(s):  
I Bock ◽  
J Jarušek
Keyword(s):  
Existence Of Solutions ◽  
Contact Problems ◽  
Dynamic Contact ◽  
Von Karman ◽  
Von Kármán

On the Existence of Solutions to the Generalized Marguerre-von Kármán Equations

2006 ◽  
Vol 11 (1) ◽  
pp. 83-100 ◽  
Author(s):  
Philippe G. Ciarlet ◽  
Liliana Gratie
Keyword(s):  
Operator Equation ◽  
Shallow Shell ◽  
Existence Of Solutions ◽  
Vertical Displacement ◽  
Existence Of A Solution ◽  
Von Karman ◽  
Von Kármán Equations ◽  
Nonlinearly Elastic Plate ◽  
Von Kármán ◽  
Nonlinearly Elastic

Using techniques from asymptotic analysis, the second author has recently identified equations that generalize the classical Marguerre-von Kármán equations for a nonlinearly elastic shallow shell by allowing more realistic boundary conditions, which may change their type along the lateral face of the shell. We first reduce these more general equations to a single “cubic” operator equation, whose sole unknown is the vertical displacement of the shell. This equation generalizes a cubic operator equation introduced by M. S. Berger and P. Fife for analyzing the von Kármán equations for a nonlinearly elastic plate. We then establish the existence of a solution to this operator equation by means of a compactness method due to J. L. Lions.

scholarly journals BILINEAR OPTIMAL CONTROL OF THE VELOCITY TERM IN A VON KÁRMÁN PLATE EQUATION

2013 ◽  
Vol 54 (4) ◽  
pp. 291-305
Author(s):  
JONG YEOUL PARK ◽  
SUN HYE PARK ◽  
YONG HAN KANG
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Existence Of Solutions ◽  
Plate Equation ◽  
Spatial Variables ◽  
Von Karman ◽  
Von Kármán Plate ◽  
Von Kármán ◽  
Objective Functional

AbstractWe consider a bilinear optimal control problem for a von Kármán plate equation. The control is a function of the spatial variables and acts as a multiplier of the velocity term. We first state the existence of solutions for the von Kármán equation and then derive optimality conditions for a given objective functional. Finally, we show the uniqueness of the optimal control.

DYNAMIC CONTACT PROBLEMS WITH SMALL COULOMB FRICTION FOR VISCOELASTIC BODIES: EXISTENCE OF SOLUTIONS

1999 ◽  
Vol 09 (01) ◽  
pp. 11-34 ◽  
Author(s):  
J. JARUŠEK ◽  
C. ECK
Keyword(s):  
Contact Problem ◽  
Coulomb Friction ◽  
Existence Of Solutions ◽  
Contact Problems ◽  
Dynamic Contact ◽  
Contact Condition ◽  
Regularization Methods ◽  
Dynamic Contact Problem ◽  
The Coefficient Of Friction ◽  
Viscoelastic Bodies

The existence of solutions to the dynamic contact problem with Coulomb friction for viscoelastic bodies is proved with the use of penalization and regularization methods. The contact condition, which describes the nonpenetrability of mass, is formulated in velocities. The coefficient of friction may depend on the solution but is assumed to be bounded by a certain constant.

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