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. K

    Color in matrix element calculation

    Hello! I am trying to calculate the matrix element of the process where an incoming upp quark and gluon interact via an upquark and emit a photon and an upquark. ---u(p1)->--~~gamma(p3)~~ | | u(q) |...
  2. 0

    ANSYS Element Type for Stress Analysis of Protection Windows

    Hello, I have to do stress analysis on a protection window at work but I am getting errors when meshing in ANSYS because of the element type I am choosing. The window is of course is a solid and is a wide, thin sheet. What Element Type should I use? Also, do I need to create nodes or not...
  3. W

    Heat element, atomization, portable, melt tank

    Hello, Can anyone help me? I want to pay a material/chemical enigneer to create a portable, commercial ( less industrial than what is on the market today), hot melt spray system. I know it sounds weird but I really need some advice on which company to call that will either tell me...
  4. F

    Field extensions, proving an element is in a field

    I can do all the question apart from the 'Conclude rt(2) in an element of Q(rt(2) + rt(3))' That's all I need help on. I tried rt(2) = a + b(rt(2) + rt(3)) squaring it and equating you get 2 = a2 + 5b2 + (some other terms of rt(2) rt(3) rt(5)) but this cannot be true for a, b...
  5. S

    Is a Transistor Considered a Fundamental Circuit Element?

    How do you define what is a fundamental circuit element? I am not really sure, why isn't a transistor a fundamental circuit element. Can u consider a switch a fundamental circuit element or is it a resistor with infinite resistance.
  6. G

    Determine if sqrt(-3) is an element in a splitting field

    Homework Statement L is the splitting field generated by x^2+x+1 (over \mathbb{Q}) a) Is \sqrt{-3} an element of L? b) Is sqrt(-3) an element of \mathbb{Q}(a), where a is a complex root of x^3+x+1? Homework Equations The Attempt at a Solution Really no idea.
  7. G

    How do you formally show subsequent element in a series is larger?

    As an example, for the sequence: s_{1} =2 s_{n+1}=\frac{s^{2}_{n}+1}{2} We see: When s_{n} >1 then, s_{n+1}=\frac{s^{2}_{n}+1}{2}>s_{n} But how do I formally show that this last inequality is true? This example is fine or just one similar to it. Thanks! EDIT: Many of those...
  8. B

    So, very amateur question regarding element combinations

    Firstly, sorry if this is in the wrong place. I'm new here. Seems to be an awesome site! :) Homework Statement Well, I've got to learn all these formulae (regarding the periodic table) and was wandering if there's any specific way to be able to understand when something is and Oxide or...
  9. G

    What does the oxidation states of each element in a compound mean?

    If I have SO42-, I can figure out that the oxidation state of each O ion is 2- and the sulfur ion must then be 6+. What does this number mean? What does it tell you about the electrons in that molecule?
  10. K

    Closed subset of R^n has an element of minimal norm

    Homework Statement a) Let V be a normed vector space. Then show that (by the triangle inequality) the function f(x)=||x|| is a Lipschitz function from V into [0,∞). In particular, f is uniformly continuous on V. b) Show that a closed subset F of contains an element of minimal norm, that...
  11. R

    Creating an Air Flow Meter Using an Iron Heating Element

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  12. K

    Ansys Element Type: Hi Friends - Why & What to Use?

    Hi Friends I am new to ansys. I designed a beam in Pro.E and save it in igs format and then open it in ansys now what element type i should use for this and why?
  13. S

    Synthesizing Element 117: Practical Applications of a Potential Element 126

    Element 117 has been synthesized: http://www.nytimes.com/2010/04/07/science/07element.html If the Island of Stability exists, and significant quantities of a stable element 126 could be synthesized, then what would be the practical applications of such a material? Could it be used for...
  14. rhody

    Discover Magazine: the element that could change the world: Vanadium

    This story is over a year old, and a quick search on PF did not turn up any hits, and to me at least I think is worth a look: http://www.energydigital.com/Uranium-Star-Corp-Unearthing-new-power-source_31962" . I realize this is a marketing and sales pitch over the virtues of this strategic...
  15. T

    Proving or Disproving |a^2|=|b^2| when |a|=|b| in Group Z20

    Homework Statement If |a^2|=|b^2|, prove or disprove that |a|=|b|. Homework Equations |x| means the order of the element x. The Attempt at a Solution Let consider the group Z20. |a^2|=|b^2| when a = 2 and b = 4 (since the order of 4 and 8 are both 5 in z20). But |2| does not equal...
  16. N

    What Is the Chemical Sign of Antimony?

    what is the chemical sign of antimony
  17. O

    MATLAB Apply if/else if to each element in array in MATLAB

    Hi! I have an array that is 1 column by many rows, of which each element represents a time. I want to find variable f at each time, where f is defined as follows: if t < tp f=(sin((pi*t)/(2*tp)))^2; if tp < t < ts f=(cos((pi*(t-tp))/(2*(ts-tp))))^2; otherwise f=0 I've tried...
  18. M

    Resistance & Diameter of heating element

    Design of heating element: Supply Voltage: 220V/3Ph/60HZ, Power: 9KW Resistance= VXV/P= 220X220/9000= 5.4 Ohms, But when physically when measure the resistance of wire using multimeter it is showing 17 ohms. Can you explain why there is differnece in practical and theortical value...
  19. R

    Understanding the Relationship Between the RW Line Element and Universe Density

    Hello! :-) I've been thinking about the RW line element (c^2 d tau^2), and I understand that there is a term which describes the geometry of the Universe (d sigma^2) and then a term corresponding to the cosmic time (c^2 dt^2). The resulting (c^2 d tau^2 ) term would be the line measured by...
  20. R

    No Poisson Ratio for Link Element in FEA

    in finite element analysis there is no poisson ratio for LINK ELEMENT (truss structure) just explain ?
  21. M

    Order of an element in a group

    Hey guys! I'm having some trouble trying to solve this question.. Any advice/help is appreciated! Homework Statement Suppose that a and b belong to a group such that: |a| = 4, |b| = 2, and suppose a3b=ba Find the order of ab. Homework Equations The Attempt at a Solution So...
  22. maverick280857

    MATLAB 2D surface integral in MATLAB for Finite Element Calculation

    Hi everyone, As part of a project, I am required to numerically compute the expression b_{i}^{e} &=& \frac{E_{0}^{i}k_0^2(\epsilon_r-1/\mu_r)}{2\Delta^e}\left[\iint\limits_{\Omega^e}(a_i^e + b_i^e x + c_i^e y)e^{-jk_0 x} dx dy\right] \nonumber\\&&- \frac{jk_0 E_0^i r'}{2\Delta^e...
  23. T

    Modeling a simple heating element

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  24. O

    Surface element meniscus - free body diagram

    Consider the free body diagram of a surface element of a water - glass meniscus in a vacuum. Along the line normal to the surface, the water pressure acts towards the vacuum, and the direction of the surface tension 'curvature force' depends on whether the surface curves like a 'u' or like an...
  25. S

    Heating project (powering a silcone heating element)

    Hello new to the site and i usually don't post questions but after a few days searching I answered a few and found many more I'm hoping someone here can help. Background for project: Looking to preheat my RC (remote control) nitro motors to 200-220'F prior to starting the break-in process.i...
  26. N

    Sakurai 3.5.37: Formula for Matrix Element <j m | S^2_+ |j m >

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  27. P

    Locate maximum occuring element array in perl

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  28. A

    Finite Element Analysis of Collision Impact in MD Patran/Nastran

    I am trying to run a finite element analysis for a collision impact. The program I am using is MD Patran/Nastran. My model consists of moving object colliding with a stationary object. I have created the mesh, applied the appropriate material, applied the boundary conditions (fixed for the...
  29. T

    If a is an element of R can you assume -a is an element of R?

    Homework Statement Simply like the title says, "If a is an element of R can you assume -a is an element of R?" R={All Real Numbers} Homework Equations N/AThe Attempt at a Solution I concluded that if a is a real number so must -a. Can that be assumed in a proof? Should a simple "If a \epsilon...
  30. L

    Calculating Power Dissipation on Cylinder Surface

    Homework Statement I am trying to calculate power dissipated over a cylindrical surface using poynting vector - \oint ExH ds I know ds for a sphere is r^2 sin \theta d\theta d\phi But now sure what ds is for a cylinder? Homework Equations The Attempt at a Solution
  31. K

    Difference between least, minimal element

    Can you guys explain to me what is the difference between least element and minimal element? I keep struggling to understand the difference between them but till now i still cannot resolved it. right now, i am trying to learn set theory, do you have any reference(book, link,whatever) that i...
  32. T

    Can I calculate the (multiplicative) inverse of any element in a cyclic group?

    Homework Statement The original problem has to do with telling messages encrypted with a version of the ElGamal public key crypto system apart. It relies on exponentiation in an arbitrary cyclic group G of prime order p with generator g. The public key is y = g^x where x is the private key...
  33. B

    Show isomorphism for element g in group G

    Homework Statement let G be a group and let g be one fixed element of G. Show that the map ig, such that ig(x) = gxg' for x in G, is an isomorphism of G with itself.Homework Equations The Attempt at a Solution not even really understanding the question. can someone break it down for me, and...
  34. F

    QFT: calculating decay rates from invariant matrix element M

    Hi! I am currently taking a first course in QFT with Peskin & Schroeder's book. I've got stuck with the equation that relates the differential decay rate of a particle A at rest into a set of final particles with the invariant matrix element M of the process. M can be found from the Feynman...
  35. L

    How Do You Write an Isotope Compared to an Element on the Periodic Table?

    Homework Statement Like, if you are writing out one of the blocks on the table of elements chart, you would write out the letter of the element, and then you would write the atomic average (or atamoic mass it is also known as,) on the bottom left , and the atmomic mass on the top to the...
  36. P

    Energy from combustion of element

    So I was reading about lightbulbs... and if I broke the bulb so that oxygen came onto the heated filament, I understand that the tungsten would combust. But how would I figure out how much energy would be given off? Would this cause a fire? I have no chemistry training so be gentle!
  37. D

    Finite Element Analysis Program

    I am on a research project where I am finding the heat capacitance and thermal conductance of a material and would like to simulate it on a larger scale as material for heated flooring. Is there a program where I can do a looping heating pipe at a set temperature and show the conductance of the...
  38. R

    Battery Powered Nichrome Heating Element (80 Degrees)

    Hi there, I have been doing research on a lil private project of my own, and am looking for some help. Would it make sense to use nichrome wire to build a heating element that will heat to 80-100 degrees? It seems that nichrome is great for heating way way past that temperature. I want to...
  39. S

    Find out the charge is delivered to the element and power and energy?

    Homework Statement Current flowing through an element is i(t)= 2e^(-t) and voltage across that conductor is v(t)= 2 (di/dt). Find out the charge is delivered to the element and power and energy consumed by the element in between 0 to 3 seconds. Homework Equations i(t) = dq/dt power =...
  40. M

    Prove that the additive inverse -v of an element v in a vector space is unique.

    Homework Statement Prove that the additive inverse -v of an element v in a vector space is unique. Homework Equations Additive Inverse in V For each v in V, there is an element -v in V such that v + (-v) = 0. The Attempt at a Solution Assume that the additive inverse is not...
  41. Ƒ

    Buy a rare earth element Thorium

    I've been searching around on Google for a place to buy a rare Earth element, specifically Thorium (.5 to 1 kilograms), and have been unsuccessful. Are there any sites that I can go to that would sell it, or has this type of commodity become unavailable to the average person due to possible...
  42. N

    How can the properties of the same element differ

    Hi friends, Can you help me to seeing the meaning of the following pat from Gottfried's book on qm?to illustrate the failure of classical physics before the invention of quantum physics,he says--- "classical physics cannot explain why the properties of a sample of an element are identical to...
  43. E

    Seeking Heating Element: 5 cm x 5 cm, 293-373 K

    Hi I need a heating element, 5 cm x 5 cm, to heat up a chip. Temperature range 293 - 373 Kelvin Anyone know what to go for?
  44. H

    Show there exist an element of order 2 in this group

    Homework Statement If G is a finite groups whose order is even, then there exists an element a in G whose order is 2. Homework Equations The Attempt at a Solution does this mean that a^2 is the identity? how can i prove this? Also, would't this make G cyclic?
  45. H

    Is α a Primitive Element Modulo p Given α^q ≡ -1 mod p?

    Suppose that p and q are odd primes and p=2q+1. Suppose that α∈ Z_p^*,α≢±1 mod p. Prove that α is primitive element modulo p if and only if α^q≡-1 mod q.
  46. C

    Is there a notation for the last element in a set?

    Say set p = \left\{p_1, p_2,\ldots,p_n\right\}, how to notate p_n without saying p_n, since I'm not explicitly writing out p like that for a variety of reasons? Like max(p) has the maximal element, what about last(p) or something? Is that recognized?
  47. S

    What Compounds Form When Every Element Is Combined in a Box?

    If you were to put 1 atom every element in its elemental form in a box, what would be the resulting compounds? 1.) I know it's probably impossible. 2.) I don't mean highly radioactive elements (transuranium metals, francium, radon, astatine, etc.) 3.) I'm really only talking about some of...
  48. J

    Area Element of Elliptic Cylinder Coordinates

    Homework Statement Compute the area element for elliptic cylinder coordinates Homework Equations The coordinates are defined as follows: x=a*cosh(u)*cos(v) y=a*sinh(u)*sin(v) The Attempt at a Solution Starting from the assumption that the area element dA=dx*dy, I found dx and dy...
  49. T

    Can you calculate energy required to maintain heating element?

    Regarding a 12v source, is there a way to calculate how much energy is required to maintain a certain temperature through an element? Meaning if you want to maintain an element temperature of 35 F how much energy will it consume using 12v? How will the ambient temperature affect this equation...
  50. G

    How to Prove Uniqueness in Ritz-Galerkin Approximations?

    Hi there I'm having a trouble with the following proof.I have the exam soon and he has asked this question every year so I have no doubt that he will ask it again.I have no idea how to do it?If you can help me I would be greatly appreciative. Question: Consider the 2-point boundary value...
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