Looking for Reading Material on Theory about Design/MOI/Structural

[BreezyLeaf]

I've been thinking about the building-design simulation, and am hoping that someone can point me toward more complete treatises/references, than this hobbyist impression.

I'm trying to develop a mathematical outline of simulated deformation physics, with the hope of eventually creating a building-design cautions via simulation program and/or plugin (long-term hope).

(This is a re-posting since I mixed up torque and Moment-of-inertia...and I'm therefore not sure if I inadvertantly skipped between Force and Mass (F=ma). Please let me know.)

Here's what I've been thinking about:

If you know of nice references of this, please let me know. Thanks for you consideration.

 

[Mark44]

It's difficult for me to grasp what you're trying to do. In your initial summary, item 1 is Finite Element Analysis, but it doesn't seem to me that that discipline applies to what you're doing.

In your first example, you have a 1-unit force acting through a lever arm of 2 distance units, and a 4-unit force acting through a lever arm of 1 distance units. Therefore, there is a counterclockwise torque of 2 units and a clockwise torque of 4 units. These forces are not in balance and will cause the bar to turn clockwise (in fact, acclerate) about its pivot point. It's not clear to me that you understand that this will happen, even though it is elementary physics.

What is your purpose in dealing with the moment of inertia in a system that is so unbalanced?

 

[BreezyLeaf]

Torque is Inappropriate (too simple), Cylindrical Moment-of-Inertia?

In your first example, you have a 1-unit force acting through a lever arm of 2 distance units, and a 4-unit force acting through a lever arm of 1 distance units. Therefore, there is a counterclockwise torque of 2 units and a clockwise torque of 4 units. These forces are not in balance and will cause the bar to turn clockwise (in fact, acclerate) about its pivot point. It's not clear to me that you understand that this will happen, even though it is elementary physics.

What is your purpose in dealing with the moment of inertia in a system that is so unbalanced?

Torque is not always an appproriate unit.
What is 'unbalanced' with a torque-based analysis, in this case is balanced in terms of Moment of Inertia (Cylindrical MR^2 Rule).

Things don't balance in terms of torque, because Torque assumes linearity for effect of change of distance from fulcrum.
Moment of Inertia is a more-appropriate concept, since it assumes x^2 for the effect-of-change due to distance from fulcrum.

With twice of the distance from the fulcrum, torque would predict twice the effect, incorrect.
While Cylindrical Moment-of-Inertia (MR^2), predicts the intuitive quadrupling of the effect, with twice-length. (x^2)
I'm trying to find-in-research or develop, a more comprehensive rule for use with FEA. (Torque is too simple, I'm not sure how complex a mathematical-approach I need.)

Can we at least agree that Torque seems inappropriate to this analysis? (Compared with Moment of Inertia)
Thanks for the advice.

 

[BreezyLeaf]

This might help explain:

Thinking of this like a lever, I'm hoping someone can point me toward theory FEA-Theory that deals with the Cylindrical Moment of Inertia (mass * radius^2) concept in the FEA-Theory. Thanks for your consideration.

 

[Mark44]

Torque is not always an appproriate unit.

Torque is not a unit, nor is moment of inertia. When you apply a force at some distance from the pivot point of an object you are exerting a torque on that object. The units could be Newton-meters, of foot-pounds or some other unit that involves a force and a distance.

What is 'unbalanced' with a torque-based analysis, in this case is balanced in terms of Moment of Inertia (Cylindrical MR^2 Rule).

Things don't balance in terms of torque, because Torque assumes linearity for effect of change of distance from fulcrum.
Moment of Inertia is a more-appropriate concept, since it assumes x^2 for the effect-of-change due to distance from fulcrum.

With twice of the distance from the fulcrum, torque would predict twice the effect, incorrect.
While Cylindrical Moment-of-Inertia (MR^2), predicts the intuitive quadrupling of the effect, with twice-length. (x^2)

At the very least, what you wrote is confusing. You have used "the effect" in both sentences above, which implies that you are talking about the same thing in both sentences. Torque and moment of inertia are two entirely different concepts. If an object is rotating, it will have a angular momentum. You would need to apply a torque to change that angular momentum.

Also, neither torque nor moment of inertia "predicts" anything. A force applied at a distance from a pivot point produces a torque.

These are fairly simple concepts that are presented in introductory physics texts. I would advise you to spend some time at getting an understanding of these ideas.

I'm trying to find-in-research or develop, a more comprehensive rule for use with FEA. (Torque is too simple, I'm not sure how complex a mathematical-approach I need.)

How does what you're doing apply to finite-element analysis? In FEA you study a complex situation by partitioning the region using a mesh, and analyzing what happens at the nodes in the mesh, and interpolate for points that aren't mesh nodes. I took a class in FEA many years ago, and that's what I recall about this discipline.

Can we at least agree that Torque seems inappropriate to this analysis? (Compared with Moment of Inertia)
Thanks for the advice.

It's not clear to me what analysis you are trying to perform, so I can't say whether either of these attributes is applicable.

 

[Mark44]

Thinking of this like a lever, I'm hoping someone can point me toward theory FEA-Theory that deals with the Cylindrical Moment of Inertia (mass * radius^2) concept in the FEA-Theory. Thanks for your consideration.

Please do not ask questions in your figures. Just type them as text in the text input window.

In your first figure, the object is not a cylinder. It is effectively a thin (i.e., massless) rod with two masses attached, and fixed at a point one unit from left end, and two units from the right end. You are applying a force of 4 units on the left end, and another force of 1 unit on the right end. As I said before, the rod is not balanced, with a net torque of 2 units acting counterclockwise, which will cause the rod to accelerate in the direction.

What does moment of inertia have to do with this? How (and why) do you hope to tie finite element analysis to this? This is a system with essentially two bodies, so FEA seems like overkill to me.