Cause and Effect from an Engineering Perspective

[Q_Goest]

I'd like to better define cause and effect in engineering terms so I thought what better place to start than finite element analysis (FEA)… ok, strange you may say. But here's the idea.

In FEA, one might say that each element is acted upon by some kind of 'causal action' which affects the element depending on its material properties. The book, "What Every Engineer Should Know About Finite Element Analysis", edited by John Brauer, separates FEA into the following types:
1. Structural Analysis
2. Thermal Analysis
3. Electromagnetic Analysis
4. Fluid Analysis

In each case, Brauer examines a field and says, "each field has a different influence on device performance." and then points out the field for each "potential". Note that in the list below, each first term is a field and each second term is a potential and is written "Field" / "Potential" such that Heat Flux is a field and Temperature is a potential. From Table 2.1 in this book:
Heat Flux / Temperature
Mechanical Stress / Displacement
Electric Field / Voltage
Magnetic Field / Magnetic vector potential
Fluid Velocity / Fluid Potential

The concept of a field and a potential operating at any point within the model gives us a starting point in defining a causal action. Each field is in a sense a "causal action". Heat flux is the flow of thermal energy and Brauer is suggesting it is 'driven' by a potential. Of course, the potential AT ANY SINGLE POINT is what is driving this heat flux, so we might also recognize that temperature potential is a local causal effect in the sense that heat flux is driven by the local temperature differential, not by a temperature differential some distance away. Here, the causal action might be considered to be the heat flux with the effect being an affect on the temperature at some point. How the temperature at some point is affected is of course dependant on the material property. In this case the properties include thermal conductivity and heat capacity among other properties.

Similarly, mechanical stress can be thought of as causal action with the effect being the displacement each element experiences.

In each case, it seems to me the "field" is what causes a change, and the effect is what is being called the potential which exists across the entire model and is dependant on material properties. To me, this makes more sense than reversing the two and suggesting the potential is the cause and the field is the affect. Regardless, what do you think is a cause and which is an effect, or perhaps you don't think it matters?

 

[chroot]

What you're describing is normally referred to as the "potential and flow" formalism.

- Warren

 

[Q_Goest]

Thanks. Any references?

 

[NoTime]

A potential is the cause of a field.
Seems to me you are confusing "causal action" which is probably better stated as "change in potential" or more simply "work" with cause.

 

[Q_Goest]

NoTime. Thanks for the responce.

Consider a beam in bending. From the perspective of some small finite element within the material, what are the cause and effect relationships on it?

 

[NoTime]

Much the same as moving a rock to the top of a hill.
You have done work to displace it.
It now has a potential to do work.
In the case of the rock the field is spacetime curvature, gravity or mechanical stress as you prefer.
In the case of the point beam particle the field is mechanical stress.
It might help if you thought of a field as the potential energy storage mechanisim.

 

[Q_Goest]

Yes, it's certainly valid to consider that work can create potential energy, kinetic energy, increase temperature, etc... that's all perfectly valid. Unfortunately it says nothing to the concept of cause and effect. If there is such a thing as cause and effect, then you've not been able to describe it using terms of potential energy or fields.

On the other hand, if you said the rock was pushed up the hill and the cause of the displaced rock was due to a force, and the effect was an increase in the potential or kinetic energy of the rock, then you've now put potential energy and work into terms of cause and effect.

How about the structural finite element being acted upon at each side? Consider that there are normal and shear stresses acting on it which cause it to deform. Is there no way to consider cause and effect on such an element?

 

[NoTime]

On the other hand, if you said the rock was pushed up the hill and the cause of the displaced rock was due to a force, and the effect was an increase in the potential or kinetic energy of the rock, then you've now put potential energy and work into terms of cause and effect.

Seems to me you answered your own question.

In the the case of any finite point in the beam the hill will look different, the displacement will be different, you will need vector sums for the force, but the same laws apply.

 

[Q_Goest]

I'm trying to better understand various philosophical concepts in engineering which is the impetus for this thread. I'd welcome any and all comments.

I think there's a conceptual difference between the concept of fields and potentials as used in FEA, and the concept of cause and effect. The concept of fields and potentials suggests one must examine what happens at some point in a field as if all points within the field are intimately dependant on each other. FEA suggests we must find some equilibrium between all elements in the field in order to resolve the state of any given element. We are forced into a philosophy of there being some kind of overall state which is used to define the states of each element.

On the other hand, we could look at each element and suggest there are only causal affects on each one, and it is these causal affects that create an influence over some local neighboring element.. The concept of cause and effect suggests only local affects act at any interface. This in fact, is the philosophy of a "control volume" as used in thermo and fluid dynamics, which tells us to draw a control surface around any given volume and find the energy flux and mass flux into and out of the volume.

The concept of fields and potentials is used in FEA. The concept of cause and effect is used in control volume analysis. I believe the end result is the same, as I've tried to show above. The difference however is not trivial, each philosophy leads to a slightly different perspective of nature.