Relaxation method for mixed boundary conditions

1971 ◽  
Vol 7 (18) ◽  
pp. 525
Author(s):  
H. Niki ◽  
H. Kimura ◽  
M. Usui ◽  
Y. Akutu
Keyword(s):  
Boundary Conditions ◽  
Mixed Boundary ◽  
Mixed Boundary Conditions ◽  
Relaxation Method

Post-Buckling of Rectangular Plates with Various Boundary Conditions

1970 ◽  
Vol 21 (2) ◽  
pp. 163-181 ◽  
Author(s):  
K. R. Rushton
Keyword(s):  
Boundary Conditions ◽  
Mixed Boundary ◽  
Mixed Boundary Conditions ◽  
Relaxation Method ◽  
Rectangular Plates ◽  
Dynamic Relaxation ◽  
Various Boundary Conditions ◽  
Post Buckling ◽  
Dynamic Relaxation Method ◽  
Theoretical Results

SummaryThe Dynamic Relaxation method is used to analyse the post-buckling of flat rectangular plates. Extensive results are obtained for two types of problem in which the transverse edges are unloaded; in one case the transverse edges remain straight, in the other they are free to wave. Comparisons are made with alternative experimental and theoretical results. The potentiality of this approach to post-buckling problems is demonstrated by considering a variable thickness plate with mixed boundary conditions.

scholarly journals Relaxation methods applied to engineering problems - Biharmonic analysis as applied to the flexure and extension of flat elastic plates

1945 ◽  
Vol 239 (810) ◽  
pp. 419-460 ◽  
Keyword(s):  
Boundary Conditions ◽  
Elastic Plate ◽  
Mixed Boundary ◽  
Mixed Boundary Conditions ◽  
Relaxation Method ◽  
Elastic Plates ◽  
Relaxation Methods ◽  
Engineering Problems ◽  
Edge Conditions

By extension of technique described in earlier papers, biharmonic analysis and the solution of the equation V%> = W are brought within range of the relaxation method. Special attention is given to the problem of a fiat elastic plate which is either bent or stretched (the second case being that to which photo-elastic methods are commonly applied). In all, four cases are presented, since the edge conditions may specify either tractions or displacements both in the flexural and in the extensional problem: one example of each is treated. Mixed boundary conditions (tractions specified at some points, displacements at others) are not considered in this paper. It would seem that only slight modifications of method will be required to deal with acolo-tropic plates (which present much greater difficulties in an orthodox analysis).

scholarly journals General solutions in Chern-Simons gravity and $$ T\overline{T} $$-deformations

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Eva Llabrés
Keyword(s):  
Variational Principle ◽  
Boundary Conditions ◽  
Dirichlet Boundary ◽  
Mixed Boundary ◽  
Mixed Boundary Conditions ◽  
Dirichlet Boundary Conditions ◽  
Spin Connection ◽  
Departure Point ◽  
Boundary Stress ◽  
Chern Simons

Abstract We find the most general solution to Chern-Simons AdS3 gravity in Fefferman-Graham gauge. The connections are equivalent to geometries that have a non-trivial curved boundary, characterized by a 2-dimensional vielbein and a spin connection. We define a variational principle for Dirichlet boundary conditions and find the boundary stress tensor in the Chern-Simons formalism. Using this variational principle as the departure point, we show how to treat other choices of boundary conditions in this formalism, such as, including the mixed boundary conditions corresponding to a $$ T\overline{T} $$ T T ¯ -deformation.

scholarly journals Casimir effect for a massive scalar field under mixed boundary conditions

2003 ◽  
Vol 33 (4) ◽  
pp. 860-866 ◽  
Author(s):  
A.C. Aguiar Pinto ◽  
T.M. Britto ◽  
R. Bunchaft ◽  
F. Pascoal ◽  
F.S.S. da Rosa
Keyword(s):  
Scalar Field ◽  
Boundary Conditions ◽  
Mixed Boundary ◽  
Casimir Effect ◽  
Mixed Boundary Conditions ◽  
Massive Scalar ◽  
Massive Scalar Field
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