Element Definition and 881 Threads

The finite element method (FEM) is a widely used method for numerically solving differential equations arising in engineering and mathematical modeling. Typical problem areas of interest include the traditional fields of structural analysis, heat transfer, fluid flow, mass transport, and electromagnetic potential.
The FEM is a general numerical method for solving partial differential equations in two or three space variables (i.e., some boundary value problems). To solve a problem, the FEM subdivides a large system into smaller, simpler parts that are called finite elements. This is achieved by a particular space discretization in the space dimensions, which is implemented by the construction of a mesh of the object: the numerical domain for the solution, which has a finite number of points.
The finite element method formulation of a boundary value problem finally results in a system of algebraic equations. The method approximates the unknown function over the domain.
The simple equations that model these finite elements are then assembled into a larger system of equations that models the entire problem. The FEM then uses variational methods from the calculus of variations to approximate a solution by minimizing an associated error function.
Studying or analyzing a phenomenon with FEM is often referred to as finite element analysis (FEA).

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  1. B

    How to Calculate Temperature & Time of Heating Element

    Heating Wire having the following Data : SWG 16(1.63mm) Specific Resistivity = 1.45 ohms-mm-3 Density = 7.1 gm-cm-3 Resistance = 0.685 ohms/Meter Weight = 15 Gram/Meter (a)Please help me in this Project to Build Heating Element using the above wire for Making 2.5 KiloWatt heating Element...
  2. M

    Conduction - Steady State Triangular Element

    Homework Statement Obtain the temperature distribution T(x,y) of the triangular cross section, assuming constant thermal conductivity, k. The triangle is a right-isosceles triangle with the right angle at (0,0). The triangle goes "up" to a, and to the right to a, then diagonally across...
  3. L

    Evaluating Element Mesh Conformance Criteria

    Homework Statement An element mesh is based on the following 3-node and 4-node elements (0,0) (0.5,0.5) (0,1) (1.5,0) (1.5,0.5). The approximation for the 4-node elements is T = a1 +a2x +a3y +a4xy, while the approximation for the 3-node element is T = b1 +b2x +b3y. Is the converegence...
  4. L

    Exploring the Reactivity of Element 18001: Is It More Powerful Than Cs and Rb?

    Element 18001 "reactium" Lets suppose that someone created element 18001 (although it would only last less than 1 microsecond), an alkaline metal. Noting that Cs reacts twice more vigorously than Rb and Rb twice more vigorously than K, would element 18001 be thousands of times more powerful as Cs?
  5. C

    Integrating with volume element (d^3)x

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  6. S

    Decreasing grain size with element addition

    Hello, I have found that in some processing cases that additional elements are added to metals which result in increased potential for smaller grain size. Does anyone know why this is so? Am I signiificantly misunderstanding the issue? Thanks, -scott
  7. M

    Chemical element and chemical property

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  8. M

    Elements 113 & 115: Uses & Benefits

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  9. S

    Calculating power of heating element

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  10. Mentz114

    Is this line element known to anyone ?

    This is based on the metric of the surface of a 3D sphere. A and B are constants with dimension (length)^2. Coordinates are x^0 = t, x^1 = \theta, x^2 = \phi ds^2 = -c^2AB^{-1}dt^2 + Bd\theta^2 + Bsin^2(\theta)d\phi^2 It satisfies the Einstein field equations with only one component of...
  11. N

    Motor run as a circuit element?

    Can you convert simple current in a wire to mechanical energy with a motor? What type of equipment would this require.
  12. K

    What is the field with one element ?

    What is the "field with one element"? From the definition of a field, it follows that such a thing does not exist. However a Google search reveals that apparently there is, or at least mathematicians think there ought to be, something that goes by that name. What is it? Is it called a "field"...
  13. F

    How can I express f*dA in terms of u and v for the given function?

    Homework Statement Let f(x,y,z)=x^2yz. Express f*dA in terms of u and v. The Attempt at a Solution We're given that x= u+v y= u-v z= u^2+v^2. The main problem I'm having is that I know I need to take partial derivatives in respect to u and v but I'm not sure how. I did an easier...
  14. G

    Making a Coiled Heating Element from Nichrome Wire

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  15. J

    Need to identify mysterious element

    Homework Statement An element X forms both a dicholride( XCl2) and tetrachloride(XCl4). Treatment of 10.0g of XCl2 with excess forms 12.55g of XCl4. Calculate Atomic Mass of X and Identify X Homework Equations no equation needed...but urgent The Attempt at a Solution i try...
  16. R

    "Proving Nilpotent Element in R has Unique Solution

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  17. K

    Best Introduction/Fundamentals of Finite Element Methods Texts

    Hi! Anyone know what would the best INTRODUCTION / FUNDAMENTALS of Finite Element Methods oriented text be? I had read O. C. Zienkiewicz’s The Finite Element Method: Its Basis and Fundamentals, 6E, Butterworth-Heinemann … No practice problems at all, un-systematic, etc. Any advice would be...
  18. U

    Target temperature of nichrome heating element

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  19. S

    Differences between natural element and built element?

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  20. D

    How to Tell if an element is radioactive

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  21. B

    Algorithm to find smallest element

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  22. C

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  23. P

    Is Hom(Lambda^k(V),Lambda^(k+1)(V)) and element of End(Lambda(V))?

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  24. R

    Moment of Inertia / Mass Element proof

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  25. B

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  26. P

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  27. A

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  28. I

    Cooling element optimizing -advanced help needed

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  29. I

    What Are the Zero and Unit Elements in R^2 for Proving Vector Space Axioms?

    Let R^2 be a set containing all possible rows: (a b) when using the 8 axioms to prove whether (a,b) is indeed a vector space, i have to show that there is a zero element and a unit element. Is the zero element 0? or is it in matrix form such that W = (0 0) and W is contained in R^2? Is...
  30. M

    Can a radioactive element decay by emitting more than 1 particles at once?

    Staight question : Can a radioactive element decay by emmitting more than 1 particles at once? ie. can a radioactive Uranium decay 2 beta and 1 alpha particles at the same time, or it must decay 1 particle (eg beta), itself becomes another elements and then decay further? thanks
  31. P

    CP violation and element forging

    Hi, I just saw the premier of "Birth of the Universe" on Naked Science (National Geographic) and had a couple of questions as a result, which I'm hoping somebody could answer. First, they said that the reason we have matter and no evidence of anti-matter is because when energy was converted...
  32. S

    General Orthogonal Coordinate System: Line Element Explained

    A general orthogonal coordinate system (u,v,w) will have a line elemet of the form: ds^2 = f^2 du^2 + g^2dv^2 + h^2dw^2 I have done a lot of vector calculus, but for some reason I can't figure out what this means! What is a line element? I know about the differential length element and its...
  33. F

    Dimensions of a probability amplitude (matrix element)?

    Greetings. I'm a little bit confused about the dimensions of a probability amplitude in a QFT calculation. My understanding a the squared, spin averaged\summed Feynman diagram should be dimensionless. However, if we consider a decay process, say pair creation from a photon or the decay of the...
  34. N

    Identifying an element from Emission Spectrum

    Using data collected from a spectrometer, with a diffraction grating of 100 lines/mm, I have collected a set of data. From this I have calculated wavelengths for the 1st and 2nd order lines of the three brightest visible colors, which were Blue/Violet, Green, and Orange. To complete my lab I...
  35. J

    How Can I Achieve 270 Degrees Celsius with a 12V 500mA Adapter and Wire?

    im trying to produce about 270degrees celcius and have a 12v 500ma adapter i plug into the wall, I've wound the wire from a toaster round a nail, imn not getting enough heat though. I've tryed 5 small lenghts in parallel a single long piece, a single short piece... so tell me, what...
  36. C

    Deriving stiffness of a node in finite element theory

    I want to derive the theory of finite element using my own understanding. With this derivation i want to understand the fea theory of rod element I call the nodes as "points" in a structure. This scenario is for a simple one dimensional displacement of points(that is the single degree of...
  37. J

    How does an atomic element jump the Quantum fence?

    I am at loss to understand (from a layman's point of view...with some math-stuff, too) how an element's electron(s) can jump the quantum fence. An element, any element, as shown on the periodic table, has certain characteristics within its 'earthly' domain, the 3-D world we live in. What causes...
  38. A

    Study Finite Element Methods: Books & Resources

    i start studying Finite element Methods any one who can help me on this subject, any good refrence book on this topic or other helping book.
  39. B

    What two measurements are made of an element using a mass

    what two measurements are made of an element using a mass spectrometer?
  40. P

    Which Metal Melts in Your Hand?

    There is one metallic element which is normally a solid, but which will melt if you hold it in your hand. Which element is it? Is it Francium?
  41. K

    Engineering Circuit Element Recommendations

    Could someone please recommend part values for the following components, or tell me if they do not exist: 1. differential op-amp that can source enough current to turn on a BJT and an LED, and also outputs a voltage near the +-5V inputs 2. a BJT that can withstand up to 2V across it 3. An LED...
  42. Astronuc

    Finite Element Analysis (FEA) Products and Developers

    These are the one with which I am most familiar. There are others, but these are the biggies. We use ABAQUS as well as our own proprietary methods, particularly for dynamic, large strain and nonlinear FEA. ABAQUS (HKS) - for nonlinear Finite Element Analysis (FEA) www.hks.com...
  43. R

    Highest element of the expression n^(1/n)

    how can I find the highest element of such set: A={\sqrt[n]{n}:n\in{N}} ?
  44. K

    Calculating Nuclear Density of Oxygen Element

    Calculate the nuclear density of Oxygen element.As I know the molar mass number is 15.9994 and the density is mass/volume how can I get the volume inorder to calculate the density?
  45. E

    Isotopes of an element differ in physical properties

    Im stuck on this question. Isotopes of an element differ in physical properties but not chemical properties. Explain this in terms of structure. I know isotopes have the same number of protons and diff neutrons, but don't know how to answer the question. Thanks!
  46. B

    Line element in spherical coordinates

    Hi, I was just reading up on some astrophysics and I saw the line element (general relativity stuff) written in spherical coordinates as: ds^2 = dr^2 + r^2(d\theta^2 + \sin\theta\d\phi) I don't get this. dr is the distance from origo to the given point, so why isn't ds^2 = dr^2 without...
  47. C

    Prove every even ordered group has an element of order 2

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  48. C

    Non linear finite element theory

    I wanted to get some thought in non linear fea. Let me say there is a spring of initial stiffness k. Let me say in a non linear analysis the load is divided into 20 steps of 1N each(Total load is 20N). 1.1st iteration.1N is applied and the displacement is arrived 2.2nd iteration 2N is...
  49. M

    What dictates the emergent properties of complex systems?

    We can say that the macro properties are emergent properties (non existent at the previous level of complexity, that of atoms) dependent also (apart the quantum laws) on the complex arrangements of the elements at the 'lower' structural level. In the case of many such emergent properties (such...
  50. B

    Atomic Structure Determines Element Properties

    What, in the atom, dictate elemental properties? I know that protons dictate different elements, but what part of an atom determines if it's a solid, gas, liquid, black, gold, or anything?
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