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. J

    Proving Equality of Sets in Algebra

    Homework Statement Prove A \times (B \cap C) = (A \times B) \cap (A \times C) The Attempt at a Solution Let x \in A and y \in B \cap C \rightarrow y \in B \wedge y \in C now \exists (x,y) \in A \times (B \cap C) so (x,y) \in A \times B \wedge (x,y) \in A \times C thus...
  2. S

    What is the best book to start learning Finite Element Analysis?

    Hi guys, :smile: I am a mechanical engineer, and want to learn finite element analysis. I want to know what is the best book to start with. Assume I have no prior knowledge of the subject. :redface: Thanks, Sety.
  3. M

    The invers of fixed Levi-Civita symbol's element

    Homework Statement Hi every one, I am really confused on how to calculate the inverse of this Levi Civita symbole's element \epsilon^{tabc}, I tried to used this equation...
  4. H

    Stiffness Matrix for Linear Tetrahedral Element

    Dear all, I am writing my finite element code for linear elasticity analysis with linear tetrahedral elements. I am not new to the finite element method and my code already works well with element types of triangles, quadrangles in 2D and hexahedrons in 3D but I don't get the correct result...
  5. Salvador

    Pressure-Induced Solidification: Materials That Defy Conventional Phase Changes

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  6. N

    Transformer powering Heating Element

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  7. C

    Why do we need postulate 4 in Euclid's element (P14)?

    http://aleph0.clarku.edu/~djoyce/java/elements/bookI/propI14.html Hi, I was reading proposition 14 of Euclid's elements and there is only one thing which I find weird : why do we need postulate 4 to conclude that " the sum of the angles CBA and ABE equals the sum of the angles CBA and ABD."...
  8. kq6up

    Not the element of the set?

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  9. T

    Water heater with element in the top section - bad?

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  10. S

    Volume element for null hypersurface

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  11. Sorthal

    With all news of element 117 being a step closer to the Island of stab

  12. O

    MHB Proof that Ha=Hb: Element y in Hb Proven True for Ha

    i was given that if y is an element in Hb then it is an element in Ha. that is Ha=Hb proof I said: since y in Hb then then y= h(1)b for h(1) in H to show that Ha=Hb let x be an elt in Ha hence x=h(2)a for some h(2) in H. now i am stuck
  13. B

    Bondi's Radiating Line Element: Solve the Mystery!

    Hello, Some knows how to Bondi deduce his radiating line element? I read some papers and there isn't any hint about hit. Best regards
  14. B

    Cylindrically symmetric line element canonical form

    Hello, What is the most general cylindrically symmetric line element in the canonical form? Best regards.
  15. J

    Small mass element for laminar (moment of inertia)

    Hi, I was just going over the moment of inertia for a 2D lamina, I've been happy with writing the small mass element dM as dM = ρdxdy where ρ is the area density, but for some reason decided on doing it like this, M(x,y) = ρxy so dM = \frac{∂M}{∂x}dx + \frac{∂M}{∂y}dy = ρ(ydx +...
  16. M

    Commutative rings and unity element proof

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  17. S

    Deformation of a continuum element

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  18. M

    Discrete Element Method(SEM) suggestion

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  19. S

    Why is there a flux depression in CANDU fuel and how is it addressed in design?

    let say there is an bundle of fuel with 4 rings. Where ring 1 is center most ring and ring 4 is outer most ring. 1st ring contains: 1 fuel element 2nd ring contains : 6 fuel elements 3rd ring contains: 12 fuel element 4th ring contains : 18 fuel elements The general distribution of...
  20. J

    HTML element with multiple classes

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  21. binbagsss

    Spherical surface area element

    See image attached. (I've had a google but can't find anything). I am trying to understand the expression : Rdθ.2∏Rsinθ Here are my thoughts so far: Rdθ is the width of a strip, θ being the variable changing/to integrate over, giving arise to the elements. 2∏Rsinθ must then...
  22. G

    Find number of elements combinations covered by a given set of element

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  23. F

    Finite element method and applied element method

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  24. Sudharaka

    MHB Annihilator of an Element in a R-Module

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  25. S

    Matrix element for direct reactions

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  26. J

    Area element, volume element and matrix

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  27. hilbert2

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  28. M

    What is a Standard State or Reference State of an element?

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  29. pellman

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  30. M

    MHB Finite element method for the construction of the approximation of the solution

    Hey! :o Given the following two-point problem: $$-y''(x)+(by)'(x)=f(x), \forall x \in [0,1]$$ $$y(0)=0, y'(1)=my(1)$$ where $ b \in C^1([0,1];R), f \in C([0,1];R)$ and $ m \in R$ a constant. Give a finite element method for the construction of the approximation of the solution $y$ of the...
  31. P

    Meaning of line element vector on work formula

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  32. J

    Using SPICE with FEMM (Finite Element Method Magnetics)

    Hello All, Some of you may have heard of the freeware FEA program called FEMM written by David Meeker. It is used to simulate 2D electromagnetic geometries and also has an integrated LUA scripting host which allows script files to be written to automate the process. I'm currently using...
  33. B

    Area element vector for parametric surface integrals

    When doing surface integrals of surfaces described parametrically, we use the area element dA = ndS = (rv x rw)dvdw Where dS is the surface area element and v and w are the parameters. I'm fine with the derivation of this (I think) but I don't understand why it's necessary to have n and dS...
  34. S

    Commutator of two element in GL(2,5)

    Homework Statement This is more about checking a solution I've been given is correct, because either my professor is consistently getting this wrong or I am.The Attempt at a Solution My professor's answers say [ \left( \begin{array}{ccc} 1 & 0 \\ 0 & 4 \end{array} \right), \left(...
  35. H

    Why does each element only react with certain elements?

    I want to know what causes this specificity of reactions in between elements. Why does carbon only react with X elements? What are the factors that come into play to cause this specificity? From what I understand every element has the potential to bond with every other element but a lot of...
  36. C

    Finite element procedures book - Bathe

    Hi, I have been stuck on a problem for a while now (3.24 part c). My attempt is as follows: Internal virtual work = external virtual work T/2 ∫0->L (∂u/dx)(∂v/dx)dx + ∫0->L (∂^2u/∂t^2)vdx = ∫0->L (Pv)dx Stationarity is already invoked on this functional as it's the principle of...
  37. M

    Help with finite element program I developed for Diff Eqns

    I developed finite element program (MFEM) in java for BVP &IVP to compute partial differential equation. I am facing one problem and description is as follows my problem is on generalized eigenvalue problem generated in wave propagation through rectangular wave guide in TE mode. (Differential...
  38. S

    Taking small element for integration purpose in SOLID sphere?

    Homework Statement The Question originally is to find the m of a solid uniformly charged solid sphere which is rotating uniformly with ω Now Homework Equations Now my question to you is how to take the small element? The Attempt at a Solution i take a small disc with...
  39. Y

    MHB Finding element of inverse matrix

    Hello all, I have this matrix A \[A=\begin{pmatrix} 1 &2 &3 &4 \\ 9 &8 &2 &0 \\ 17 &2 &0 &0 \\ 1 &0 &0 &0 \end{pmatrix}\] B is defined as the inverse of A. I need to find the element in the first row and fourth column of B, without using determinants, so without using adjoint. How should I...
  40. A

    Inflation and Element Formation: Irreconcialble?

    I write this in the hope that somebody reading this can explain to me, a laymen, in non-mathematical, plain English terms, why my thinking is wrong regarding the calculation of the age of the observable Universe and the formation of the elements in the Periodic Table given the (short) age of...
  41. Superposed_Cat

    Could element 137 electrons become superluminal in a retrocausal atom?

    I found the equation for the speed of an electron today. atomic number*fine-structure constant*speed of light. rearranging we get z= v/σc. if you set v to c then you find that at element 137 the electrons become superluminal. This can be possible right? a retrocausal atom! Could someone please...
  42. C

    Is a Finite Element Method Course Right for Me?

    I am thinking about taking a finite element method course. I know what FEM is and how it solves boundary value problems and stuff but I'm wondering how widespread it is used... Is it a useful numerical technique? What industries/research use it? I am interested in research in continuum...
  43. V

    What is the difference between sets and classes in set theory?

    Question 2 (a) how is it possible? B is a set (since A is a set), how can a set be an element of another set? Rather than saying: B is an element of C I thought it would be better to say: B is a subset of C. Also, can someone explain question 2 (d) to me? thanks
  44. A

    Solve Grad Shafranov Equation using Finite element method?

    I want to compute the flux surfaces using FEM but i haven't found any good source to read. any help will be appreciated. Thank you
  45. S

    MHB Proving span of a Set with Scalar attached to First Element

    hi Guys, i Needed your help to prove out the following, thanks in advance; Let u1,u2,...,ut be vectors in $\Re^n$ and $k\in\Re ,k\neq0.$ Prove that $Span\{u_1,u_2,...,u_t\}=Span\{ku_1,u_2,...,u_t\}$
  46. C

    Oxygen forms ions with element X

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  47. skate_nerd

    MHB Proving that not every non-empty set of integers has a least element

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  48. Math Amateur

    MHB Field Theory - Element u transcendental of F

    Field Theory - Element u transcendental over F In Section 10.2 Algebraic Extensions in Papantonopoulou: Algebra - Pure and Applied, Proposition 10.2.2 on page 309 (see attachment) reads as follows...
  49. D

    Proof of a linear operator acting on an inverse of a group element

    Hey guys! Basically, I was wondering how to prove the following statement. I've seen it in the Hamermesh textbook without proof, so I wanted to know how you go about doing it. Let's say you have a group element g_{1}, which has a corresponding inverse g_{1}^{-1}. Let's also define a linear...
  50. M

    Are the polarities of the wires connected to the circuit element incorrect?

    I highlighted a portion in the paint document. Is that a mistake? How am I supposed to compare the polarity of the wire connected to the left to the polarity of the wire connected to the right?
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