An Adaptive Parallel-in-Time Method with Application to a Membrane Problem

2014 ◽  
pp. 707-717
Author(s):  
Noha Makhoul Karam ◽  
Nabil Nassif ◽  
Jocelyne Erhel
Keyword(s):  
Membrane Problem

Computer algebra takes on the vibrating-membrane problem

1999 ◽  
Vol 1 (2) ◽  
pp. 88-93 ◽  
Author(s):  
D. Frenkel ◽  
L. Golebiowski ◽  
R. Portugal
Keyword(s):  
Computer Algebra ◽  
Membrane Problem ◽  
Vibrating Membrane

scholarly journals A Revisit of the Boundary Value Problem for Föppl–Hencky Membranes: Improvement of Geometric Equations

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 631 ◽  
Author(s):  
Yong-Sheng Lian ◽  
Jun-Yi Sun ◽  
Zhi-Hang Zhao ◽  
Xiao-Ting He ◽  
Zhou-Lian Zheng
Keyword(s):  
Boundary Value Problem ◽  
Closed Form ◽  
Boundary Value ◽  
Closed Form Solution ◽  
Form Solution ◽  
Circular Membrane ◽  
Computational Accuracy ◽  
Power Series Method ◽  
Membrane Problem ◽  
Geometric Equation

In this paper, the well-known Föppl–Hencky membrane problem—that is, the problem of axisymmetric deformation of a transversely uniformly loaded and peripherally fixed circular membrane—was resolved, and a more refined closed-form solution of the problem was presented, where the so-called small rotation angle assumption of the membrane was given up. In particular, a more effective geometric equation was, for the first time, established to replace the classic one, and finally the resulting new boundary value problem due to the improvement of geometric equation was successfully solved by the power series method. The conducted numerical example indicates that the closed-form solution presented in this study has higher computational accuracy in comparison with the existing solutions of the well-known Föppl–Hencky membrane problem. In addition, some important issues were discussed, such as the difference between membrane problems and thin plate problems, reasonable approximation or assumption during establishing geometric equations, and the contribution of reducing approximations or relaxing assumptions to the improvement of the computational accuracy and applicability of a solution. Finally, some opinions on the follow-up work for the well-known Föppl–Hencky membrane were presented.

THE RANGE OF VALUES OF λ2/λ1 AND λ3/λ1 FOR THE FIXED MEMBRANE PROBLEM

1994 ◽  
Vol 06 (05a) ◽  
pp. 999-1009 ◽  
Author(s):  
MARK S. ASHBAUGH ◽  
RAFAEL D. BENGURIA
Keyword(s):  
Bounded Domain ◽  
The Other ◽  
Dirichlet Laplacian ◽  
Fixed Membrane ◽  
De Vries ◽  
Membrane Problem ◽  
Range Of Values

We investigate the region of the plane in which the point (λ2/λ1, λ3/λ1) can lie, where λ1, λ2, and λ3 are the first three eigenvalues of the Dirichlet Laplacian on an arbitrary bounded domain Ω ⊂ ℝ2. In particular, by making use of a technique introduced by de Vries we obtain the best bounds to date for the quantities λ3/λ1 and (λ2 + λ3)/λ1. These bounds are λ3/λ1 ≤ 3.90514+ and (λ2 + λ3)/λ1 ≤ 5.52485+ and give small improvements over previous bounds of Marcellini. Where Marcellini used a bound due to Brands in his argument we use a better version of this bound which we obtain by incorporating deVries' idea. The other bounds that yield the greatest information about the region where points (λ2/λ1, λ3/λ1) can (possibly) lie are those due to Marcellini, Hile and Protter, and us (of which there are several, with two of them being new with this paper).

scholarly journals A variational approach to a circular hyperelastic membrane problem

1993 ◽  
Vol 99 (1-4) ◽  
pp. 191-200 ◽  
Author(s):  
S. Liu ◽  
J. B. Haddow ◽  
S. Dost
Keyword(s):  
Variational Approach ◽  
Membrane Problem

scholarly journals On the two-phase membrane problem with coefficients below the Lipschitz threshold

2009 ◽  
Vol 26 (6) ◽  
pp. 2359-2372 ◽  
Author(s):  
Erik Lindgren ◽  
Henrik Shahgholian ◽  
Anders Edquist
Keyword(s):  
Two Phase ◽  
Membrane Problem

A multigrid method for the membrane problem

1988 ◽  
Vol 3 (5) ◽  
pp. 321-329 ◽  
Author(s):  
D. Braess
Keyword(s):  
Multigrid Method ◽  
Membrane Problem
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