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Four Leg support

Posted Dec 12, 2011, 4:36 p.m. EST Version 4.1, Version 4.2, Version 4.2a 3 Replies

Mohammed Bedier
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I am trying to model a four leg support for a parallel plate capacitor and calculate the spring constant of it.
the formula is k=4Ew(t/l)^3.
However I am confused about the boundary condition as I am trying to simulate the deflection using symmetry.
3 Replies Last Post Dec 13, 2011, 5:53 a.m. EST
Ivar KJELBERG COMSOL Multiphysics(r) fan, retired, former "Senior Expert" at CSEM SA (CH)
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Posted: 1 decade ago Dec 13, 2011, 1:29 a.m. EST
Hi

I do not see what is "wrong", but I can come with a few advises:

to get an easier handling of these thin MEMS geometries, try "Define right-click View" to define a second view and then select camera node and uncheck Preserve aspect ratio

with only 1) symmetry case you have a 2 leg device for me

you have only 1 mesh element per beam thickness, I would use at least 2 if not 4-8, you could use a structured layer as you have a stress gradient in thin layers in such a beam

try to avoid point loads, these make singularities, as rather domain or boundary loads eventually edge loads (as for point loads these are rather "poor practice")

--
Good luck
Ivar
Hi I do not see what is "wrong", but I can come with a few advises: to get an easier handling of these thin MEMS geometries, try "Define right-click View" to define a second view and then select camera node and uncheck Preserve aspect ratio with only 1) symmetry case you have a 2 leg device for me you have only 1 mesh element per beam thickness, I would use at least 2 if not 4-8, you could use a structured layer as you have a stress gradient in thin layers in such a beam try to avoid point loads, these make singularities, as rather domain or boundary loads eventually edge loads (as for point loads these are rather "poor practice") -- Good luck Ivar
Mohammed Bedier
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Posted: 1 decade ago Dec 13, 2011, 3:46 a.m. EST
Dear Ivar,
Thank alot for your quick reply.
The problem is that results does not match the caluclated one.
I calculate the stiffness by diving the force I apply (1uN) by total displacment in the z direction. However the results are also far from correct or at least must be multiplied by factor of 2 or 4!
My question is what do you mean by better handeling? What do you mean by using not just one mesh element?
Also could it be because of symmetry the total force is double? I mean should i be considering the force as double what I have defined in Comsol?
Thank you in advance, i have been into this for a month now.
Dear Ivar, Thank alot for your quick reply. The problem is that results does not match the caluclated one. I calculate the stiffness by diving the force I apply (1uN) by total displacment in the z direction. However the results are also far from correct or at least must be multiplied by factor of 2 or 4! My question is what do you mean by better handeling? What do you mean by using not just one mesh element? Also could it be because of symmetry the total force is double? I mean should i be considering the force as double what I have defined in Comsol? Thank you in advance, i have been into this for a month now.
Ivar KJELBERG COMSOL Multiphysics(r) fan, retired, former "Senior Expert" at CSEM SA (CH)
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Posted: 1 decade ago Dec 13, 2011, 5:53 a.m. EST
Hi

in case of symmetry, you must also adapt the forces, if you apply 2N on the left side with a symmetry case its as if you load with 4 N in total on the full model

to resolve correctly the stress in a thin beam, you need at lest 2, but better many more (8-10) mesh elements across the thickness, as the "solid" physics depend on the stress tensor and its gradients, and to resolve a gradient you need at lest 2 points. As a beam is mostly symmetric, neutral plane in the middle of the bending thickness,, you need at least 3 points on a curve to get a parabola and 3 points = 2 elements across. But with 3 points you do not really resolve the shape of a parabola, at best its an "abs()" type function approximation hence use more elements across the thickness.

Other alternative replace the solid by a "beam" with the related physics, then you need fewer elements

--
Good luck
Ivar
Hi in case of symmetry, you must also adapt the forces, if you apply 2N on the left side with a symmetry case its as if you load with 4 N in total on the full model to resolve correctly the stress in a thin beam, you need at lest 2, but better many more (8-10) mesh elements across the thickness, as the "solid" physics depend on the stress tensor and its gradients, and to resolve a gradient you need at lest 2 points. As a beam is mostly symmetric, neutral plane in the middle of the bending thickness,, you need at least 3 points on a curve to get a parabola and 3 points = 2 elements across. But with 3 points you do not really resolve the shape of a parabola, at best its an "abs()" type function approximation hence use more elements across the thickness. Other alternative replace the solid by a "beam" with the related physics, then you need fewer elements -- Good luck Ivar

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