scholarly journals Existence of an optimal domain for the buckling load of a clamped plate with prescribed volume

2021 ◽  
Author(s):  
Kathrin Stollenwerk
Keyword(s):  
Free Boundary ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Optimal Shape ◽  
Buckling Load ◽  
Volume Constraint ◽  
Free Boundary Value Problem ◽  
Optimal Domain ◽  
Clamped Plate

AbstractWe formulate the minimization of the buckling load of a clamped plate as a free boundary value problem with a penalization term for the volume constraint. As the penalization parameter becomes small, we show that the optimal shape problem with prescribed volume is solved. In addition, we discuss two different choices for the penalization term.

Singular perturbation of a nonlinear problem with multiple solutions

1985 ◽  
Vol 100 (3-4) ◽  
pp. 327-341
Author(s):  
Anne-Marie Lefevere
Keyword(s):  
Free Boundary ◽  
Boundary Value Problem ◽  
Multiple Solutions ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Critical Value ◽  
Free Boundary Value Problem ◽  
Singular Limits ◽  
Natural Extensions ◽  
Barrier Parameter

SynopsisA nonlinear boundary value problem (P) having positive parameters L and a is considered. We associate with it a family of perturbed problems () affected by the presence of a barrier parameter γ related to L and a. There is a critical value L*(a) of the parameter L such that for L >L*(a), (P) has no regular solution. Then some natural extensions of (P), solutions of a free boundary value problem, arise as singular limits of ().

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