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4 Elements 2 Nds 2 [HOT]

The ancient Greeks believed that there were four elements that everything was made up of: earth, water, air, and fire. This theory was suggested around 450 BC, and it was later supported and added to by Aristotle.

(Aristotle also suggested that there was a fifth element, aether, because it seemed strange that the stars would be made out of earthly elements. He would be surprised to learn that they are in fact made up of many elements found on earth, and are so hot they could be said to be on fire all the time!)

While we do know now that these previous theories are false, in a way the four elements do align with the four states of matter that modern science has agreed on: solid (earth), liquid (water), gas (air), and plasma (fire).

Although the Greeks believed that the four elements were unchanging in nature, everything was made up of different elements, which were held together or pushed apart by forces of attraction and repulsion, causing substances to appear to change. This is similar to what really happens with elements and all molecules at an atomic level.

Group 2A (or IIA) of the periodic table are the alkaline earth metals: beryllium (Be), magnesium (Mg), calcium (Ca), strontium (Sr), barium (Ba), and radium (Ra). They are harder and less reactive than the alkali metals of Group 1A. The name comes from the fact that the oxides of these metals produced basic solutions when dissolved in water, and they remained solids at the temperatures available to the ancient alchemists. Like the Group 1A elements, the alkaline earth metals are too reactive to be found in nature in their elemental form.

There are several types of Finite Elements. You can use beams/plates/solids depending on your model. With plates/solids, you can use easier to mesh triangular elements (TRI/TET), or more robust quadratic elements (QUAD/HEX). All elements can be linear or quadratic (the second computing longer but with nice perks in return).

With plate elements, you have of course the same thing. There are membrane elements, stuff that can be axisymmetric, etc. Such elements serve various purposes, and I assume you will know when to use them. There is however one thing that I guess is the biggest issue, and that is: should I use triangular or quadratic elements?

I'm usually reluctant to say that something is "better" all the time - after all if it would be so obvious who would ever bother to implement other types of elements? Although I admit that we often use QUAD4 elements. In my experience the computing time for similar accuracy of outcomes is better with those elements... but only for problems that we do (like shell design of pretty specific stuff). To be honest, I wouldn't even generalize this to "shells in general", although I like having a nice "small mesh" visually, so I'm clearly biased :)

Thank you for this amazing article! It has been a huge help in evaluating the mesh so far. I do have one question regarding the solid elements though. I see that you comment that it is a bad idea to use a single HEX8 element through the thickness of the part. Does this apply to TET10 as well?

I have a very complex geometry and it has been modeled as a solid part. There are, however, many areas where the part is quite thin. Due to the complexity of the part, I'm having trouble converting it to a shell model, so I am tempted to keep it as a solid part and use solid TET10 elements. The part is a sort of reel, and I will be looking into the stresses on the component during an emergency break of the rotational movement. There are no loads in the thickness direction of the part.

To be honest, it's very hard to give you a specific answer - it's case-dependent after all. And I do admit that while TET10 aren't bad, I don't use them myself, so I'm lacking the "feel" that would help me to answer you better. I think, that the best approach would be to make the mesh twice as small (so two elements across thickness) and check how much the outcomes differ. I can imagine that the difference might be quite high, so I don't have the courage to tell you that you don't have to do this, but I can be wrong here too... I just try to be wrong on the "safe side" when I advise people - I don't want to get you in trouble of course!

I'm afraid I will disappoint you here. This is more or less something I would attribute to "common knowledge". I've been using FEA software for quite some time, so I guess software manuals would be a reference. Also, I did some tests to see how various elements compute, which are better in the cases I was interested in, etc. So while I do believe in what I wrote I can easily imagine that there are FEA applications where other elements are better. In fact, TRI elements are often used in electromagnetic FEA as I recently learned from a friend.

Classical elements typically refer to earth, water, air, fire, and (later) aether which were proposed to explain the nature and complexity of all matter in terms of simpler substances.[1][2] Ancient cultures in Greece, Tibet, and India had similar lists which sometimes referred, in local languages, to "air" as "wind" and the fifth element as "void".

These different cultures and even individual philosophers had widely varying explanations concerning their attributes and how they related to observable phenomena as well as cosmology. Sometimes these theories overlapped with mythology and were personified in deities. Some of these interpretations included atomism (the idea of very small, indivisible portions of matter), but other interpretations considered the elements to be divisible into infinitely small pieces without changing their nature.

Modern science does not support the classical elements as the material basis of the physical world. Atomic theory classifies atoms into more than a hundred chemical elements such as oxygen, iron, and mercury. These elements form chemical compounds and mixtures, and under different temperatures and pressures, these substances can adopt different states of matter. The most commonly observed states of solid, liquid, gas, and plasma share many attributes with the classical elements of earth, water, air, and fire, respectively, but these states are due to similar behavior of different types of atoms at similar energy levels, and not due to containing a certain type of atom or substance.

According to Galen, these elements were used by Hippocrates in describing the human body with an association with the four humours: yellow bile (fire), black bile (earth), blood (air), and phlegm (water). Medical care was primarily about helping the patient stay in or return to their own personal natural balanced state.[11]

Aristotle added a fifth element, aether (αἰθήρ aither), as the quintessence, reasoning that whereas fire, earth, air, and water were earthly and corruptible, since no changes had been perceived in the heavenly regions, the stars cannot be made out of any of the four elements but must be made of a different, unchangeable, heavenly substance.[15] It had previously been believed by pre-Socratics such as Empedocles and Anaxagoras that aether, the name applied to the material of heavenly bodies, was a form of fire. Aristotle himself did not use the term aether for the fifth element, and strongly criticised the pre-Socratics for associating the term with fire. He preferred a number of other terms indicating eternal movement, thus emphasising the evidence for his discovery of a new element.[16] These five elements have been associated since Plato's Timaeus with the five platonic solids.

The Neoplatonic philosopher Proclus rejected Aristotle's theory relating the elements to the sensible qualities hot, cold, wet, and dry. He maintained that each of the elements has three properties. Fire is sharp, subtle, and mobile while its opposite, earth, is blunt, dense, and immobile; they are joined by the intermediate elements, air and water, in the following fashion:[17]

A text written in Egypt in Hellenistic or Roman times called the Kore Kosmou ("Virgin of the World") ascribed to Hermes Trismegistus (associated with the Egyptian god Thoth), names the four elements fire, water, air, and earth. As described in this book:

They further suggest that all of creation, including the human body, is made of these five essential elements and that upon death, the human body dissolves into these five elements of nature, thereby balancing the cycle of nature.[21]

In the Pali literature, the mahabhuta ("great elements") or catudhatu ("four elements") are earth, water, fire and air. In early Buddhism, the four elements are a basis for understanding suffering and for liberating oneself from suffering. The earliest Buddhist texts explain that the four primary material elements are solidity, fluidity, temperature, and mobility, characterized as earth, water, fire, and air, respectively.[25]

The Buddha's teaching regarding the four elements is to be understood as the base of all observation of real sensations rather than as a philosophy. The four properties are cohesion (water), solidity or inertia (earth), expansion or vibration (air) and heat or energy content (fire). He promulgated a categorization of mind and matter as composed of eight types of "kalapas" of which the four elements are primary and a secondary group of four are colour, smell, taste, and nutriment which are derivative from the four primaries.[26][a][27]

The elemental system used in medieval alchemy was developed primarily by the anonymous authors of the Arabic works attributed to Pseudo Apollonius of Tyana.[31] This system consisted of the four classical elements of air, earth, fire, and water, in addition to a new theory called the sulphur-mercury theory of metals, which was based on two elements: sulphur, characterizing the principle of combustibility, "the stone which burns"; and mercury, characterizing the principle of metallic properties. They were seen by early alchemists as idealized expressions of irreducible components of the universe[32] and are of larger consideration within philosophical alchemy. 2b1af7f3a8