Under the hood - part 01: Motivation
Analogies are always imprecise, but let’s risk one that equates a car with a numerical simulator, with their respective internal machinery “under the hood.”
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Step 1: Motivation
𝐃𝐫𝐢𝐯𝐢𝐧𝐠 𝐚𝐧𝐝 𝐓𝐞𝐜𝐡𝐧𝐢𝐜𝐚𝐥 𝐊𝐧𝐨𝐰𝐥𝐞𝐝𝐠𝐞
Many of us might think that it is possible to drive a car very well without knowing its internal machinery, delegating any technical analysis and decision to a specialist. Certainly, in many practical situations, we would be right!
𝐔𝐬𝐢𝐧𝐠 𝐍𝐮𝐦𝐞𝐫𝐢𝐜𝐚𝐥 𝐒𝐢𝐦𝐮𝐥𝐚𝐭𝐨𝐫𝐬
Similarly, we might think that to operate a numerical simulator, it is not necessary to know its internal formulation but only its usage procedure. Thus, we delegate important decisions by using the default options offered by its interface and symptom-treatment type tips, without a real notion of what is being done or why.
𝐓𝐡𝐞 𝐌𝐚𝐠𝐢𝐜 𝐈𝐬 𝐁𝐫𝐨𝐤𝐞𝐧
In both cases, the magic breaks at the slightest malfunction or unexpected result, as we only know “a simplified interface” that filters a lot of information we do not know how to manage as simple users. This is where someone with knowledge of computational or automotive mechanics steps in while the rest are stranded with their car or simulator!
𝐄𝐜𝐨𝐧𝐨𝐦𝐢𝐜 𝐈𝐧𝐭𝐞𝐫𝐞𝐬𝐭𝐬
Part of the blame lies with the economic interests behind the sale of cars and simulators. No car salesman will tell you what you don’t want to hear about the vehicle they offer, and no software salesman will tell you that you need to study computational mechanics to be a reliable user of the technology they offer!
𝐏𝐫𝐚𝐜𝐭𝐢𝐜𝐚𝐥 𝐄𝐱𝐚𝐦𝐩𝐥𝐞
You might find yourself in this precarious situation when using the Finite Element Method if you have no idea about weighted residual methods… nor do you relate this phrase to the errors of certain differential equations… and you never really understood what partial differential equations are or how they arise during the study of physical phenomena… and even less have you thought about the physical meaning of integrating those equations… nor the fact that such a thing leads to the creation of a linear or nonlinear algebraic system of which, by the way, you do not know the characteristics that make it easy or difficult to solve… nor do you find physical meaning in its eigenvalues and eigenvectors… and all the above, plus a long etc., still does not specifically delve into the Finite Element Method and its many specific theoretical-practical details!
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Step 2: Example of "zero Kelvin"
Did you know that many simulators don't know "zero Kelvin"?
For example, you can draw a simple bar in SolidWorks and do a very simple heat transfer study in SW-Simulation: impose two equal temperatures at its ends and remove heat from the inner points of the bar.
You might get a result like the following and, if you're not careful with your physics intuition, you might believe it!
𝘗𝘦𝘳𝘴𝘰𝘯𝘢𝘭𝘭𝘺, 𝘪𝘧 𝘐 𝘩𝘢𝘷𝘦 𝘵𝘰 𝘣𝘦𝘭𝘪𝘦𝘷𝘦 𝘴𝘰𝘮𝘦𝘰𝘯𝘦, 𝘐 𝘤𝘩𝘰𝘰𝘴𝘦 𝘓𝘰𝘳𝘥 𝘒𝘦𝘭𝘷𝘪𝘯 𝘢𝘯𝘥 𝘯𝘰𝘵 𝘵𝘩𝘦 𝘴𝘪𝘮𝘶𝘭𝘢𝘵𝘰𝘳, 𝘦𝘷𝘦𝘯 𝘪𝘧 𝘪𝘵 𝘤𝘰𝘴𝘵𝘴 𝘮𝘢𝘯𝘺 𝘵𝘩𝘰𝘶𝘴𝘢𝘯𝘥𝘴 𝘰𝘧 𝘥𝘰𝘭𝘭𝘢𝘳𝘴!
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Step 3: Example of "strange stretching"
If you think of a very simple, square, thin piece, for example, that has its bottom face recessed and its top face subjected to a tensile stress (constant throughout its length), your intuition would probably indicate that it will stretch in the direction of the stress, and that's fine!
But what would you think if the simulator tells you that the piece stretches vertically but also deflects horizontally?
If someone showed you the results of a simulation in which "I push the piece up (stimulus) but it goes to one side (response)" what would you think? Is something wrong?
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Step 4: Conclusion and suggestions
𝘚𝘰, 𝘸𝘩𝘢𝘵 𝘤𝘢𝘯 𝘸𝘦 𝘥𝘰 𝘪𝘧 𝘸𝘦 𝘢𝘳𝘦 𝘴𝘪𝘮𝘱𝘭𝘦 𝘶𝘴𝘦𝘳𝘴 𝘢𝘯𝘥 𝘸𝘢𝘯𝘵 𝘵𝘰 𝘢𝘤𝘩𝘪𝘦𝘷𝘦 𝘢 𝘥𝘦𝘦𝘱𝘦𝘳 𝘶𝘯𝘥𝘦𝘳𝘴𝘵𝘢𝘯𝘥𝘪𝘯𝘨? 𝘞𝘦𝘭𝘭, 𝘸𝘦 𝘤𝘢𝘯 𝘴𝘵𝘢𝘳𝘵 𝘣𝘺 𝘵𝘢𝘬𝘪𝘯𝘨 𝘴𝘰𝘮𝘦 𝘴𝘵𝘦𝘱𝘴, 𝘢𝘷𝘰𝘪𝘥𝘪𝘯𝘨 𝘰𝘷𝘦𝘳𝘸𝘩𝘦𝘭𝘮 𝘢𝘯𝘥 𝘦𝘹𝘤𝘦𝘴𝘴𝘪𝘷𝘦 𝘧𝘢𝘵𝘪𝘨𝘶𝘦. 𝘐𝘯 𝘵𝘩𝘪𝘴 𝘴𝘦𝘯𝘴𝘦, 𝘪𝘧 𝘵𝘩𝘪𝘴 𝘱𝘰𝘴𝘵 𝘢𝘳𝘰𝘶𝘴𝘦𝘴 𝘢𝘯𝘺 𝘪𝘯𝘵𝘦𝘳𝘦𝘴𝘵, 𝘐 𝘤𝘢𝘯 𝘰𝘧𝘧𝘦𝘳 𝘴𝘰𝘮𝘦 𝘩𝘦𝘭𝘱, 𝘥𝘪𝘥𝘢𝘤𝘵𝘪𝘤 𝘮𝘢𝘵𝘦𝘳𝘪𝘢𝘭 “𝘸𝘪𝘵𝘩𝘰𝘶𝘵 𝘮𝘢𝘵𝘩𝘦𝘮𝘢𝘵𝘪𝘤𝘢𝘭 𝘰𝘷𝘦𝘳𝘭𝘰𝘢𝘥” 𝘢𝘯𝘥 𝘵𝘢𝘭𝘬𝘴 𝘵𝘩𝘢𝘵 𝘩𝘦𝘭𝘱 𝘶𝘴 𝘪𝘮𝘱𝘳𝘰𝘷𝘦 𝘪𝘯 𝘵𝘩𝘪𝘴 𝘪𝘯𝘵𝘦𝘳𝘦𝘴𝘵𝘪𝘯𝘨 𝘧𝘪𝘦𝘭𝘥, 𝘸𝘪𝘵𝘩𝘰𝘶𝘵 𝘱𝘳𝘦𝘵𝘦𝘯𝘥𝘪𝘯𝘨 𝘵𝘰 𝘣𝘦𝘤𝘰𝘮𝘦 𝘴𝘱𝘦𝘤𝘪𝘢𝘭𝘪𝘴𝘵𝘴 𝘣𝘶𝘵, 𝘢𝘵 𝘭𝘦𝘢𝘴𝘵, 𝘳𝘦𝘴𝘱𝘰𝘯𝘴𝘪𝘣𝘭𝘦 𝘶𝘴𝘦𝘳𝘴!
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Step 5: Links
This tutorial comes from:
and continues in:
