- [Instructor] In this video, we're going to look at
various aspects of mass and stiffness modeling.
We look first at mass modeling
and we think of the element density.
We input the element density on the material property form.
Every element has a volume and times its density,
that gives us an element mass.
So that's the major contribution we find
to the mass within an FVA model.
As an alternative, if we look at the tray here,
the blue patch is where we want to apply a smeared
or non-structural mass on there.
At the input form over here,
you point towards that surface
and then you define the mass you want to smear
over that surface.
The remote or lumped mass, here, we define the part,
which is attached to the blue surface.
And SolidWorks calculates the CG and the mass
and the inertia terms of the part
and then connects the CG down to the surface,
so we're spidering off the surface to this CG of the part.
Mass and inertia terms are calculated.
The part is effectively replaced then
by this remote lumped mass and the spider.
This is the input form where we define the part
and then we define the surface we want to attach it to.
Now, mass versus weight can be an issue.
In the U.S., the system is pound, force, inch, seconds,
and we use weight, which is a pounds force
as a fundamental quantity.
Now, it's easier to understand
the weight of a body philosophically.
If we go down to the marketplace, we can see on a scale,
gravitational acceleration applied to the body
deflecting the spring, giving us the reading directly
of what the weight of the object is.
The resultant force is the body's weight.
Now, Newton's second law states
force equals mass times acceleration.
In our case, it's the acceleration due to gravity.
So therefore, we have mass equals force,
divided by acceleration,
but the acceleration is due to gravity,
so it becomes unit dependent.
If we're working in inches,
we have to use acceleration due to gravity in inches.
If we work in feet, then we have to use the value for feet.
Using inches, I define the pound mass
as being a pound weight
divided by 386.4.
Basically, anything associated with a pound weight
is divided by 386.4 to convert it to a pound mass.
Now, you need to be aware that SolidWorks
uses the mass density definition incorrectly
in other forms.
Here's one example which is that inputting the density.
This is described as the mass density.
But looking at the value .278 pounds per cubic inch,
that's actually a weight density,
so it is rather misleading.
The correct mass density is that value divided by 386.4.
It's a very small value indeed.
The units of density are pound per inch cubed,
which is a weight density, divided by acceleration,
which is inches per second squared,
so they become rather awkward units.
So pounds second squared per inch to the fourth.
Now, internally, this is resolved in SolidWorks Simulation,
so we don't actually need a correction.
But it's still slightly unnerving.
It's also continued through, for example,
many masses are defined as weights.
We convert it to mass internally.
Here's another example form
where again, we're talking about the distributive mass.
It's described as a mass.
The input is in pound units.
The conversion is done for you.
You just need to be aware of that.
The temptation is to divide by 386.4 again
and then we'll be effectively double-booking.
Now, in SI units, it's a lot simpler.
Units are kilogram, meter, second
and the mass, kilogram, is a fundamental quantity
in that system.
Mass is actually a direct measure of the amount
of material present in a component.
Again, force equals mass times acceleration,
Newton's second law.
As long as we balance the units using this law,
then we'll be okay.
So here, force is in Newtons, mass is in kilograms,
acceleration is in meters per second squared.
And that's a strict SI definition.
Now, we can vary that
if we want to use millimeters, for example.
Then the balance becomes force in Newtons,
mass in tonnes, which is 1000 kilograms,
then acceleration in meters per second squared.
It's a very popular variation on that.
So again, as long as we keep that set to units balanced,
multiplying kilograms by 1000, dividing meters by 1000
to get to millimeters, then we will be okay.
Now, some aspects of stiffness modeling.
First off, with the boundary conditions.
We need to use accurate stiffness terms.
If, for example, something is fully built-in,
then we use that approach.
If something is simply supported, then we use that approach.
Very often, though, if the boundary is somewhere in between,
then we need to get some estimate of the boundary stiffness,
then maybe we use boundary springs
to help that idealization.
With mesh density, the mesh density is controlled by
the highest order mode shape.
If we have inadequate mesh, then we could produce
inaccurate and possibly even infeasible mode shapes.
Now, there's an example here,
which is of this simple plate structure.
Mode one is a very simple shape.
There are plenty of elements in the mesh here
to describe that.
Mode 29 is getting a lot busier
and we just about have enough elements
to describe the mode shape.
I normally like to have five elements per half-wave
and this is just about on that limit there.
If we go to mode 49, then we really have insufficient
elements to describe each one of those little bulges
or those little pockets.
And again, we will be finding that we're getting
incorrect frequencies and possibly even producing
mode shapes which are not realizable in real life.
We're forcing the structure into particular shapes.
So in summary, we look at the highest frequency content
that we're interested in
and then we make we have sufficient mesh density
to capture that high frequency content.