What is Element: Definition and 880 Discussions

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. A

    How much does lumped element model effect our analysis?

    Previously I never noticed that we are making this abstraction - to abstract continuous systems into an idealized discrete element like resistor or capacitor. So since we have made this approximation, what kind of errors can occur in our calculations? Does this approximation ever fail so that...
  2. P

    Eliminating Elements in Commercial FEA Solvers

    I want to why actually elements are eliminated in commercial fea solvers. There is a criterion like stress or strain at which elements having acheived that state are eliminated. Wouldnt it lead to wrong results because, the material at eliminated elements place has become null.
  3. V

    A problem about surface element

    I really don't know how to do this question as it asks me to write the surface element of a hemisphere in xyz coordinates. I know how to answer if it is asked in spherical coordinates. I think this is a tricky question because it asks for the portion da near (0, A, 0) (in xyz) where A is the...
  4. D

    Efficient way to find which element of Z*n has largest order?

    Hey, I had two separate questions. (When I say Z*(n) I'm denoting the multiplicative group of integers mod n, namely, the units of Z(n)) First off, I know that if n is prime, that Z*(n) is cyclic. But this is not a biconditional statement. Is there any theorem which tells me conditions under...
  5. F

    In a linear space, 0 times an element of the space need not be 0?

    Homework Statement Hello, we are starting to get to Banach spaces and thus linear normed spaces in a functional analysis class and I am realizing that I don't have much experience or intuition with these spaces. So I was reading over the requirements for a linear space in my notes and was...
  6. T

    Electric Circuit Analysis: Calculating power absorbed/supplied by each element

    Once again, my textbook seems to do a poor job of explaining another concept just like I commented earlier here. Anyways, here is the relevant part of the textbook: http://www.mediafire.com/view/?cw5t2wr9vqqprnv To calculate p4 in example 1.7, voltage of 8V is multiplied by a current of -0.2I...
  7. E

    Finite Element Methods (global stiffness matrix)

    Homework Statement I have the following practice problem which is presented as follows: What is the size of the global stiffness matrix K (i.e., Kuu) for the 2-D problem? http://imgur.com/KZec3 (Unsolved) http://imgur.com/piv1J (Solved) Homework Equations The Attempt at a...
  8. B

    Can a Battery-Powered Heater Wire Prevent Freezing in Fridge Drainage Tubes?

    Hi there! I recently noticed that the little drainage tube in the back of my fridge keeps blocking up with ice. As a result massive condensation develops around the ice which eventually drips down the back causing the bottom of the fridge to fill with water the whole time. Apparently the...
  9. L

    How Does an Element of a Finite Group Relate to Cryptology Theorems?

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  10. K

    Please help me design a Li-Po powered nichrome heating element (400°F)

    Hello everybody, hopefully I am posting this in the right spot. What I am trying to do is design a heating element powered by a Li-Po battery (RC battery probably) to heat a heating element to a range of 360-420°F. I want the temp to be adjustable, probably on three settings, so one for 360...
  11. N

    Biot-Savart - Differential Length Element?

    Hi, I'm trying to work with the Biot-Savart law to look at the magnetic field strength along the center of an asymmetric solenoid I wrapped. I parameterized the coils with x = r cos 2(pi)t, y = r sin 2(pi)t, and z = D t where r is the radius of the coil layer, D is the diameter of the wire...
  12. H

    Converting binding energy of an element to joules

    Converting binding energy of an element to joules! The binding energy of Mg-24 is 198MeV. What is this value in Joules? Write your answer correct to three significant figures. MeV = megaelectron volt 1 megaelectron volt = 1.60217646 × 10-13 joules 198 megaelectron volts = 3.17230939 ×...
  13. S

    Algebra - Finding the Order of an Element from the Size if It's Conjugacy Class

    Sorry about the long title. I recently had a few homework problems which were similar to the title of the post. I struggled a bit with them so I'm trying to find additional problems to work on until I can master these ideas... Basically, if we have a group G s.t. |G|=n, and we know G has a...
  14. S

    Matlab and finite element

    Homework Statement The problem picture is attached(file 1),its a beam subjected to horizonatal ditributed load 2. Relevant examples the MATLAB solution for rectangular shape with vertical load on the upper right corner is like follow, i try to modify it according to the new picture...
  15. M

    Showing resultant stresses on a volume element

    Me again, (this is what happens when you make a designer do mechanics, and give her a lecturer she doesn't understand :P ). I'm stuck on a combined loadings question. This is the question: "The 60 mm diameter rod (fixed at end C on the wall) is subjected to the loads shown. 1) Transform...
  16. F

    Interpretation of finite element analysis results

    Hi, Recently started with FEA - loving it, at least the modelling / load application part. Interpreting the results is tricky - particularly around where loads are applied. Got a project (no pics sorry) which has a drilled hole in a plate, and have applied the load as a a pressure...
  17. L

    Spacetime line element to describe an expanding cube

    Hi, I have to write a spacetime line element for the shape of a cube of cosmological dimensions. This cube is expanding like this: i)With time, the cube becomes elongated along the z-axis, and the square x-y shape doesn't change. ii)The line element must be spatially homogeneus. (I don't...
  18. G

    Solving Neutron Problems with Commercial Finite Element Method Codes

    As I know, the method to solve neutron problem is divided into two steps now, neutron transport calculation for fuel assemblies and neutron diffusion calculation for whole reactor core, both using specified code such as CASMO and SIMULATE from STUSVIK. I want to know whether the commercial...
  19. M

    Preservation of the infinitesimal element of length

    My two questions are related to the title. The problematic is: "How can we connect the coordinates ... xα... for α = 0, 1, 2 and 3 to the coordinates of the same object in another frame, say ...yλ for λ = 0, 1, 2, 3 in preserving the quantity η(x)αβ. dxα.dxβ = η(y)λμ. dyλ. dyμ? Can someone...
  20. W

    Calculating Charge Entering an Element: Q=6.667 C

    Homework Statement The current flowing through an element is i = 2 A for 0<t<1 and i = 2t^2 A for t>1 Calculate the charge entering the element from t=0s to t=2s. Answer: 6.667 C. Homework Equations I used Q=t1∫t2 i dt The Attempt at a Solution I tried to solve using...
  21. H

    LC Circtuit finding Q across an element for given time

    Homework Statement A circuit is constructed with two capacitors and an inductor as shown. The values for the capacitors are: C1 = 513.0 μF and C2 = 68.0 μF. The inductance is L = 265.0 mH. At time t =0, the current through the inductor has its maximum value IL(0) = 106.0 mA and it has the...
  22. M

    How do we know the atomic number of an element?

    Here's what I know: Scientists used mass spectrometry to figure out the number of electrons in a neutral atom of the element. We know that if an atom has a neutral charge, the number of protons = the number of electrons - therefore, the atomic number = the number of electrons. Would anyone...
  23. Einj

    Π leptonic decay (current matrix element)

    I'm currently studying the pion leptonic decay and I'm getting a bit confused about some factors. Firstly, le correct lagrangian that describe the pion decay \pi^+\rightarrow l^+ + \nu_l is: $$L=\frac{4G_F}{\sqrt{2}}V_{ud}^* \bar{d}_L\gamma^\mu u_L \bar{\nu}_L \gamma_\mu l_L$$ We can't...
  24. M

    Assuming that the system (s,*) has an identity element ,prove that:

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  25. caffeinemachine

    MHB Number of p element subsets whose sum is divisible by p

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  26. K

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  27. soothsayer

    Transform of Line Element in Special Relativity

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  28. M

    Is PWM for control of Peltier Element logical?

    I'm making a circuit to control the temperature of a peltier element, and I'm trying to figure out the cheapest way that will actually work over the long term, and not burn out my components fast. At first I wanted to just use standard power regulation to control the power to the element and...
  29. R

    Finite element methods for Yield Line Analysis

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  30. C

    Findind Area element in Cylindrical Coordinate System

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  31. B

    Introduction to Finite Element Analysis

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  32. B

    Determining If An Element Is Part Of A Set

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  33. S

    Disproving Regularity with Transitivity of Sets

    Homework Statement Let A, B, and C be sets. Assume the standard ZFC axioms. Please see below for my updated question. Thanks.
  34. Y

    Engineering AC circuit with dependant current and voltage source and open circuit element

    I've been given the following problem (attached), not sure how to tackle this one, do I use mesh/node analysis and super node analysis, or can I find the v in the loop with the dependant voltage source then use that as the supply to the second and third loops? Not sure, any help would be...
  35. B

    Finite Element Analysis - Author J.N Reddy Book

    Folks, Is there anyone out there familiar with 'An introduction to the Finite Element Method' by J.N. Reddy? I am struggling to decipher what is happening on page 129 as shown in the attachment. If some-one is willing to help I will reply with a more specific query on that page. Thanks
  36. H

    How to get longitude from Two Line Element (TLE)

    Dear All I want to know the formula to extract the longitude of the satellite from the TLE below. I hope someone can help. Thanks 1 24652U 96063A 97251.85429118 .00000144 00000-0 00000-0 0 568 2 24652 0.0850 104.0202 0008355 303.2059 279.6585 1.00288964 3492
  37. M

    Finding the unknown atomic mass of element X

    Homework Statement Suppose a nameless element (X) was found to occur in three different substances (A, B and C). The relative molecular masses of A, B, and C were found to be 25.80, 43.70 and 83.50 respectively, compared to an assigned value of exactly 2.00 for H2. Subsequently, these...
  38. O

    Question about changing line element.

    Homework Statement Say we have a function such that x = uv , y = (u^2 - v^2) /2 Hence our line element in Cartesian coordinates is. ds^2 = dx^2 + dy^2 Now I have two questions. I like to work on math problems algebraically if possible so I thought to convert our line element I could take...
  39. H

    Proof about identity element of a group

    Homework Statement If G is a group, a is in G, and a*b=b for some b in G (* is a certain operation), prove that a is the identity element of G Homework Equations The Attempt at a Solution I feel like you should assume a is not the identity element and eventually show that a= the...
  40. L

    Lorentz invariance of four-volume element [itex] d^4x [/itex]

    I am slightly confused with the invariance of four-volume element. The orthodox way to show it is to prove that Jacobian is one, that I did, however in many textbooks I find a reasoning that because we have Lorentz contraction on one hand and time dilation on the other hand, the product is...
  41. M

    Power Supplied by the Leftmost element

    1. Determine the power supplied by the leftmost element in the circuit Homework Equations Power = Voltage ( Current) The Attempt at a Solution As power = voltage (current), that is the equation that will be used. The leftmost element shows a current of 2 AMPS entering through...
  42. S

    How to find gradient of a variable in 3D mapped finite element domain

    Hello, I know the value of a field variable in a 3d mapped finite element mesh. Can anyone suggest an effective method/methods to find its gradient throughout the mesh.
  43. H

    Resistor is a current limiting element.?

    In a simple circuit having battery (6v) connected to two resistors (1K each) in series, 3mA would flow through the entire circuit. 1) If resistor is a current limiting element, current following the first resistor should reduce its value (from 3mA to some other) before entering the another...
  44. P

    More than one identity element for absolute value?

    I was thinking about identities, and seem to have arrived at a contradiction. I'm sure I'm missing something. A(n) (two-sided) identity for a binary operation must be unique. I will reproduce the familiar proof: Proof: Suppose a is an arbitrary element of a set S, e and e' are both...
  45. A

    From matrix element to hadronic cross section

    Hello, currently I work on 2->3 scattering process. So there exist five external momenta and in my case 5 different Feynman diagrams, for which I have already calculated the full matrix element. The matrix element is a function of various scalar products of the four-momenta. This scattering...
  46. S

    Is Papapetrou line element the same as cylindrical coordinates?

    Hi all, Papapetrou line element describes an axial symmetric stationary spacetimes and the coordinates that appear in this metric are just similar to cylindrical coordinates; I mean they are labeled ρ, z and phi. I want to know if they are really the cylindrical coordinate or not; In other...
  47. X

    Finding valencies from a given element in 3 oxides

    Homework Statement The oxides of a certain element contain 27.28%, 42.86% and 52.94% oxygen. What is the ratio of valencies of the element in the 3 oxides? Homework Equations The Attempt at a Solution Following calculations were made: Molecular mass of the first oxide is 58.6...
  48. T

    Abaqus: write surface mesh element detail

    Hi, i need some help in writing the surface mesh in abaqus. i have a wing model, meshed using hexahedral mesh. now what i want is to write the surface element detail on a file, containing the element number and its neighbouring four nodes. for example 12, 2 3 5 6 here 12 is the element number...
  49. E

    Trace element analysis techniques

    I have a polymer sample and am interested in qualitatively determining the sulfur (sulfate group) content. Which analytical technique should I consider using? This polymer is not soluble in water but is soluble in THF and toluene. Thanks.
  50. P

    Surface flux through a single finite element

    Hi, I'm facing a real-life problem and I don't what specific mathematics topic it's related to. Homework Statement I know the value of the components of a vector field in three points of space and I have to find the flux of this vector field through the surface defined by those...
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