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define delta force
Posted 2010/03/31 3:22 JST 10 Replies
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Hi,
I am trying to model a plate vibration problem where the plate will be excited by an impact applied at 1 point. I want to do a transient analysis. Hence I need to define a force function of the form delta(x,y)*delta(t). How can I do that?
I am trying to model a plate vibration problem where the plate will be excited by an impact applied at 1 point. I want to do a transient analysis. Hence I need to define a force function of the form delta(x,y)*delta(t). How can I do that?
10 Replies Last Post 2010/04/04 18:28 JST
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Posted:
1 decade ago
wellI think it is time for you to learn the weak form.
a good starting point will be the poisson equation with a point source [a delta function] Once you understand it generalisation to deta(x,y) is obvious.
For delta(t) I will suggest to approximate it with a gaussian.
if you are not familiar with it, a book on distribution theory will explain or maybe
en.wikipedia.org/wiki/Dirac_delta_function
will be enough .
and also you should shift your time origin as well so that the time of impact is t0>0 .
. the scaling coefficient for the gaussian need to be chosen carefully ,
You need to figure out what are the frequencies you want to resolve in your system and pick the sacling factor small enough accordingly but not too small
you need to compromise between computational time and accuracy and meaningful result.
have done plenty of these calculations myself [ with delta] and works like a charm in comsol.
it might also be possible to use a dweak term for the delta( t) BUT I have not tried it not even thought about it,
and I will not go that way myself even if it was possible I wil rpefer the gaussin approach for you have more control on what you really resolve.
JF
a good starting point will be the poisson equation with a point source [a delta function] Once you understand it generalisation to deta(x,y) is obvious.
For delta(t) I will suggest to approximate it with a gaussian.
if you are not familiar with it, a book on distribution theory will explain or maybe
en.wikipedia.org/wiki/Dirac_delta_function
will be enough .
and also you should shift your time origin as well so that the time of impact is t0>0 .
. the scaling coefficient for the gaussian need to be chosen carefully ,
You need to figure out what are the frequencies you want to resolve in your system and pick the sacling factor small enough accordingly but not too small
you need to compromise between computational time and accuracy and meaningful result.
have done plenty of these calculations myself [ with delta] and works like a charm in comsol.
it might also be possible to use a dweak term for the delta( t) BUT I have not tried it not even thought about it,
and I will not go that way myself even if it was possible I wil rpefer the gaussin approach for you have more control on what you really resolve.
JF
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Posted:
1 decade ago
Hi
Jean-François' reply is certainly the cleanest one,
but by "brute force" you can define a point on your surface for the impact point and put a transient à la
"F_impact[N]*(flch2(t[1/s]-Dt_wait,dt_rise)- flch2(t[1/s]-(Dt_wait+dt-duration),dt_fall))" Heaviside smoothed time dependent pulse type.
but be avare that point loads are singularities with their limitations
Good luck
Ivar
Jean-François' reply is certainly the cleanest one,
but by "brute force" you can define a point on your surface for the impact point and put a transient à la
"F_impact[N]*(flch2(t[1/s]-Dt_wait,dt_rise)- flch2(t[1/s]-(Dt_wait+dt-duration),dt_fall))" Heaviside smoothed time dependent pulse type.
but be avare that point loads are singularities with their limitations
Good luck
Ivar
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Posted:
1 decade ago
Ivar,
the complexity with your approach is that if you want to approximate a true delta, the approximating function must be normalized such that its integral is 1. The problem with flchs in that context is that you need to calculate the integral everytime when you want to play with the scaling factors. This is why using standard gaussian already normalized is I believe much more practical and I will say "standard accepted practice" too
For in the end you need to do parametric studies with mesh size vs "quality of the approximating function... ti understand the quality of your computed solution.
[ in fact the fist time i tried to use flchs approximately along the line you suggest and switched toward gaussian because of that very issue.
jf
the complexity with your approach is that if you want to approximate a true delta, the approximating function must be normalized such that its integral is 1. The problem with flchs in that context is that you need to calculate the integral everytime when you want to play with the scaling factors. This is why using standard gaussian already normalized is I believe much more practical and I will say "standard accepted practice" too
For in the end you need to do parametric studies with mesh size vs "quality of the approximating function... ti understand the quality of your computed solution.
[ in fact the fist time i tried to use flchs approximately along the line you suggest and switched toward gaussian because of that very issue.
jf
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Posted:
1 decade ago
Hi Jean-François
I fully agree with you, it all depends on the time and precision you will set in.
It's always better to do it "correct" (in that sens I do not consider point constraints as "correct"), but the first time it takes often somewhat longer and you must get it validated, especially so that you can reuse it easily and quicker a second time ...
So if you have a good example, do not hesitate to put it on the model exchange :)
Ivar
I fully agree with you, it all depends on the time and precision you will set in.
It's always better to do it "correct" (in that sens I do not consider point constraints as "correct"), but the first time it takes often somewhat longer and you must get it validated, especially so that you can reuse it easily and quicker a second time ...
So if you have a good example, do not hesitate to put it on the model exchange :)
Ivar
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Posted:
1 decade ago
Ivar,
Unfortunately the models I build using these features are a part of my paid job, so I am not at liberty to publish them ...but if I ever feel the need to build a pedagogical model [ that is a model I build for myself in order to understand a feature] I will definitively publish it, even if given my low level of proficiency in using comsol I am sure it wont be something to rely upon blindly ;-)
JF
Unfortunately the models I build using these features are a part of my paid job, so I am not at liberty to publish them ...but if I ever feel the need to build a pedagogical model [ that is a model I build for myself in order to understand a feature] I will definitively publish it, even if given my low level of proficiency in using comsol I am sure it wont be something to rely upon blindly ;-)
JF
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Posted:
1 decade ago
Hi
I'm rather in the same situation, apart that I use quite (too much?) an amount of private time learning & playing with COMSOL
Ivar
I'm rather in the same situation, apart that I use quite (too much?) an amount of private time learning & playing with COMSOL
Ivar
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Posted:
1 decade ago
Hi there,
Here is my simple approach to such problems. I will only address the implementation of forcing on a point (spatially); the temporal part is already very well explained by the previous responders.
I suggest you split your computational domain in a way that you have a discrete, small boundary face where you want to apply the "point" forcing, then instead of applying a point force use an equivalent surface loading on that face. As area of the face --> 0 you approach a situation equivalent to applying a point force. Of course don't forget to adjust the loading (Pressure) relative to the area so your force, P*A, gives you the force you wanted.
This should be acceptable for most engineering calculations; besides a true point force is non-physical so your point forcing in a real situation is really always applied over a small area. The resultant solution "sufficiently" far away from the forcing face ( ~ point) should be insensitive to details of exactly how small your forcing area was, thus your overall global solution should be accurate except at and near the point forcing singularity.
Hope this helps
Ozgur
Here is my simple approach to such problems. I will only address the implementation of forcing on a point (spatially); the temporal part is already very well explained by the previous responders.
I suggest you split your computational domain in a way that you have a discrete, small boundary face where you want to apply the "point" forcing, then instead of applying a point force use an equivalent surface loading on that face. As area of the face --> 0 you approach a situation equivalent to applying a point force. Of course don't forget to adjust the loading (Pressure) relative to the area so your force, P*A, gives you the force you wanted.
This should be acceptable for most engineering calculations; besides a true point force is non-physical so your point forcing in a real situation is really always applied over a small area. The resultant solution "sufficiently" far away from the forcing face ( ~ point) should be insensitive to details of exactly how small your forcing area was, thus your overall global solution should be accurate except at and near the point forcing singularity.
Hope this helps
Ozgur
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Posted:
1 decade ago
Hello again JF
I wanted to add why I do not like Gaussian functions for impacts or pulses even if they are infinetly derivable, because they "never" end nor start.
I prefer 1-cos() type functions as these also have a cleaner modal contribution, they are also, as you point out, easy to normalise, an inportant feature indeed. But you could use COMSOL to integrate the function too ;)
And as Ozgur Yildirim is pointing out, using a finite area over which to apply the load, reduces the trouble of the singularity, and is cleaner than a bolean function that is not necessarily linked to the local mesh density
Have fun Comsoling
Ivar
I wanted to add why I do not like Gaussian functions for impacts or pulses even if they are infinetly derivable, because they "never" end nor start.
I prefer 1-cos() type functions as these also have a cleaner modal contribution, they are also, as you point out, easy to normalise, an inportant feature indeed. But you could use COMSOL to integrate the function too ;)
And as Ozgur Yildirim is pointing out, using a finite area over which to apply the load, reduces the trouble of the singularity, and is cleaner than a bolean function that is not necessarily linked to the local mesh density
Have fun Comsoling
Ivar
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Posted:
1 decade ago
Ivar,
for delta approximating functions, there are plenty of them of course [ but depending on the kind of problem (1-cos) can be a bad choice becasue of the derivative at cutoff point, but I guess you know that
my opinion is that the best choice is to use always the same function to build a practial experience... short of that whatever works for you...
for the spatialdelta I understand and agree with what has been said by Ozgur and You
.. my only comments is that the weak form exist in Comsol for a reason :-)
and is recommended AND demonstrated by Comsol for that very kind of problem
my guess is that it does ultimately what you suggest, but in an optimized and self consistent way that does not force us, the user, to define a special subdomain with a special mesh and so forth...
so is there a good reason NOT TO USE a weak term at point of impact when once want to model a delta...?
jf
for delta approximating functions, there are plenty of them of course [ but depending on the kind of problem (1-cos) can be a bad choice becasue of the derivative at cutoff point, but I guess you know that
my opinion is that the best choice is to use always the same function to build a practial experience... short of that whatever works for you...
for the spatialdelta I understand and agree with what has been said by Ozgur and You
.. my only comments is that the weak form exist in Comsol for a reason :-)
and is recommended AND demonstrated by Comsol for that very kind of problem
my guess is that it does ultimately what you suggest, but in an optimized and self consistent way that does not force us, the user, to define a special subdomain with a special mesh and so forth...
so is there a good reason NOT TO USE a weak term at point of impact when once want to model a delta...?
jf
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Posted:
1 decade ago
Hi
No, I agree with you, I believe too that the "weak" form is the best solution, but you must feel 100% comfortable with it, for all cases, and I havent managed yet, even after a few years comsoling, luckily there are "many ways to Rome".
We should put out more examples on the model exchange treating different approaches for the same "simple" cases:
- special constraint & constraint forces,
- weak boundaries and dweak,
- weak form PDE's,
- ...
More moonlight projects in view ...
I'm currently fighting how to correctly reduce large structural models by simplifying large chunks as point masses and distributed loads (other programmes do that automatically for you, when the full 3D CAD is already there). It is easy to forget some cross couplings: such as moments, inertias, rotations ... when you are in full 3D, and you have the eigenmode representation as well as the static and transient cases to consider ;)
Ivar
No, I agree with you, I believe too that the "weak" form is the best solution, but you must feel 100% comfortable with it, for all cases, and I havent managed yet, even after a few years comsoling, luckily there are "many ways to Rome".
We should put out more examples on the model exchange treating different approaches for the same "simple" cases:
- special constraint & constraint forces,
- weak boundaries and dweak,
- weak form PDE's,
- ...
More moonlight projects in view ...
I'm currently fighting how to correctly reduce large structural models by simplifying large chunks as point masses and distributed loads (other programmes do that automatically for you, when the full 3D CAD is already there). It is easy to forget some cross couplings: such as moments, inertias, rotations ... when you are in full 3D, and you have the eigenmode representation as well as the static and transient cases to consider ;)
Ivar