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Jan
15
asked Heat convection differential equations from 1952 - Mathematica “fails to converge”
Dec
17
awarded  Good Question
Nov
26
awarded  Notable Question
Nov
13
comment Solution of Poisson equation with two regions
Can this be a case for "matched asymptotics" (perturbation methods)?.. or am I over-complicating the problem?
Oct
31
comment Shooting Method in Mathematica
I am curious to know what physics this is capturing. Looks like Falkner-Skan... boundary layer phenomenon? Have you tried NDSolve. I realize this isn't what you may have asked but as a lover of NDSolve... I just had to suggest that.
Oct
27
awarded  Popular Question
Oct
5
comment Time evolution/dynamics of circular plate with hole (Biharmonic equation and stiffness)
As mentioned, I am posting my comment about this answer and the question. The question itself, for those who are familiar with solid mechanics, is a fundamental problem in solid mechanics. The answer here allows me to juxtapose the time-evolution behavior of an annular plate with that obtained from menu/GUI driven commercial FEA solvers. It turns out that, yet again, for fundamental problems in mechanics (solid/fluid), Mathematica outdoes what other commercial solvers would do. The main problem I was trying to solve was the deflection of an orifice plate (4th order biharmonic eqn).
Sep
26
awarded  Benefactor
Sep
26
comment Time evolution/dynamics of circular plate with hole (Biharmonic equation and stiffness)
Thank you for both your detailed answers. I will post a detailed comment soon. I love the analytical solution, personally!
Sep
26
accepted Time evolution/dynamics of circular plate with hole (Biharmonic equation and stiffness)
Sep
24
comment FEM Solution desired for “Plate with orifice” deflection: Application of Boundary Conditions and use of Regions
Thank you! I never tried DSolve for this problem.
Sep
23
comment Time evolution/dynamics of circular plate with hole (Biharmonic equation and stiffness)
@bbgodfrey I am not sure. However, I am curious to know what the deflection (w) is at "long times". If for a negative time derivative, it is around the same value as the question this refers to, I would say, YES, the time derivative should be reversed. I hope that make sense? Thank you for pointing out that possible source of error.
Sep
23
comment Time evolution/dynamics of circular plate with hole (Biharmonic equation and stiffness)
@bbgodfrey They do exist for rectangular plates with rectangular and circular holes 1. Empirical solutions for circular plate with hole for deflections are readily available though. I did find a book entry by Timoshenko on elastic stability of circular plates with and without a hole 2. I do not have access to this paper.
Sep
22
comment Time evolution/dynamics of circular plate with hole (Biharmonic equation and stiffness)
@bbgodfrey 0.33 is a good standard value for nu.
Sep
22
comment Time evolution/dynamics of circular plate with hole (Biharmonic equation and stiffness)
@bbgodfrey yes it is supposed to be nu which is defined. It is poissons ratio . (can't type efficiently on phone right now...)
Sep
22
asked Using BSpline as initial condition in NDSolve
Sep
21
comment Nonlinear differential equation: numerical solution
I have generally found that for equations with singularities due to a 1/x type term, Method->"LSODA" has usually worked wonders. LSODA has generally been more time efficient than ExplicitRungeKutta and efficient in resolving stiffness.
Sep
20
awarded  Popular Question
Sep
19
comment ODE w/seasonal forcing term
Can you share what book you are using?
Sep
19
comment Time evolution/dynamics of circular plate with hole (Biharmonic equation and stiffness)
@xzczd It does return an interpolating function. However, this interpolating function gives a plot that shows a deflection and deflection "shape" that doesn't approach what was calculated here. I have made an edit to the question to reflect your comment.