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. Fredrik

    Divergence defined from volume element

    I need some help understanding a definition: This is supposed to be an explanation of what the author did on the page before. He had just described how to construct a (complex) Hilbert space from a (real) smooth manifold with a smooth nowhere vanishing volume element, and then moved on to...
  2. B

    What is the percent composition of CdSO4 in a 1.0 molal aqueous solution?

    What is the percent CdSO4 by mass in a 1.0 molal aqueous solution? My attempt: CdSO4 is 208.47g/mol 1.0 molal = 1 mol CdSO4/1kgH2O Converted mols to grams, and kg to g. 208.47g Cd/1000g H2O = .20847 .20847 x 100 to get % mass = 20.8% It is an old test question that I am going over...
  3. M

    Igma notation 2i-1 = 2n, for all n is an element of N

    prove or disprove n sigma notation 2i-1 = 2n, for all n is an element of N. i=1 N = natural numbers
  4. P

    Weight percent of element to give specific density for alloy

    Homework Statement Aluminium-Lithium alloys have been developed by the aircraft industry to reduce the weight and improve the performance of its aircraft. A commercial aircraft skin material having a density of 2.47 g/cm3 is desired. Compute the concentration of Li (in wt%) that is required...
  5. W

    Any implications of this diagonal element inequality?

    Given two definite positive definite matrices A and B of identical size with the following relationship of their diagonal elements: A_{ii} \geq B_{ii} (no summation) which also holds after any unitary change of coordinates \textbf{A}'=\textbf{U}^T\textbf{A}\textbf{U} where...
  6. P

    How many permutations leave an element unchanged?

    This seems like it should be easy, but my combinatorics is (are?) a little rusty. I want to know how many permutations of a given length leave at least one element unchanged, and how many leave exactly one unchanged. Started wondering about it when picking names out of a hat for a secret...
  7. S

    Order of an element in relation to the centre.

    If a is the only element of order 2 in a group, does it belong to the centre Z(G)?
  8. F

    How to Determine the Order of an Element in a Factor Group?

    I'm currently studying factor groups in abstract algebra and needed some help understanding how to determine the order of an element in a factor group Suppose I have Z (mod 12) / <4>. And I choose some random element from Z (mod 12) such as 5 or 7. How would I go about determining the order...
  9. N

    Which Element in Period 2 Has the Highest Density in Its Standard State?

    Homework Statement Which of the elements, from the second period, has the highest density in its standard state? Homework Equations Standard state is gas at 1 atm, concentration of 1 M for liquid, or pure substance at 25C and 1 atm. The Attempt at a Solution I thought that N, O, F...
  10. J

    How Is the Volume Element in Phase Space Determined for N Harmonic Oscillators?

    Hi all, I am solving a problem for N classic harmonic oscillators. I have the Hamiltonian H = sum(i=1,3N)(p_i^2/(2m) + m*o^2/2 *q_i^2 where p is momentum and q I presume is scaled coordinates. I am given the following hint that the volume in phase space can be written as V(E,N) =...
  11. B

    ANSYS command problem re element death/element table postprocessing

    I am a new to ANSYS command-language mode. I am having trouble animating the procedure described below. The procedure is meant to model melting over time through element death (based on example from U. Alberta at www.mece.uAlberta.ca/tutorials/ansys/AT/BirthDeath/BirthDeath.html). My...
  12. D

    How to Calculate Arc Length for Parametric Curves in 3D Space?

    Homework Statement x = \frac{u^{2} + v^{2}}{2} y = uv z = z Find the arc length given: u(t) = cos(t), v(t) = sin(t), z = \frac{2t^{\frac{3}{2}}}{3} Homework Equations ds^{2} = dx^{2} + dy^{2} + dz^{2} In curvilinear coordinates thhis becomes ds =...
  13. M

    Finding molar mass of unknown element

    Homework Statement element X reacts with oxygen to produce a pure sample of X2O3 . in an experiment, it is found that 1.0g of X produces 1.1596g of X2O3 . what is the molar mass of X? Homework Equations The Attempt at a Solution well we can write a equation for it 4X + 3O2 --->...
  14. N

    Magnetism Another Element to Manipulate?

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  15. J

    Find a set A (subset of R,set of real numbers) and an element a of R

    Find a set A (subset of R,set of real numbers) and an element a of R such that there is no bijecton from a+A(we add a to the set A)to A. I can't find a good example. Can someone help Are we done if we choose the empty set? (And is the empty set a subset of R?) Thank you
  16. F

    Proving Properties of a Group with Every Element of Order 2

    Homework Statement Let G be a group such that every x in G\{e} has order 2. (a) Let H<=G be a subgroup. Show that for every x in G the subset H U (xH) is also a subgroup. (b) Show that if G is finite, then |G|=2^n for some integer n. The Attempt at a Solution For (a), I know that since...
  17. F

    What are the identity elements in S_3 for x^2=e and y^3=e?

    Homework Statement In S_3, show that there are four elements satisfying x^2=e and three elements satisfying y^3=e. The Attempt at a Solution I don't understand what the question is asking at all...
  18. M

    Calculate the mass in grams of each element in the body of a 57kg person

    Homework Statement The natural abundaces of elements in the human body, expressed as a percent by mass, are oxygen (o) 65%; carbon (C), 18%; hydrogen (H), 10%; nitrogen (N), 3.0%; calcium (Ca), 1.6%; phosphorous(P), 1.2%; all other elements 1.2% Calculate the mass in gram of each element in...
  19. S

    Friedman equations from flat FRW universe line element

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  20. M

    Calculation of specific activity when element consists of two isotopes

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  21. R

    Transient conduction with finite element analysis

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  22. R

    Transient conductive heat flow using finite element method

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  23. A

    Form of line element of a torus.

    I noticed somewhere the line element of a two-dimensional torus is written in the form ds^2=r^2(d\theta^2_1+d\theta^2_2) The author only states that he assumes same radius parameter for simplicity and no further explanation is given. But I do not understand how that form is possible. I...
  24. L

    What is the Finite Element Method and How Can I Learn More About It?

    i need a full explanation on finite element method or better still a material i can read to help me understand better
  25. rohanprabhu

    Differential Area Element and surface integrals

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  26. K

    Suggest with reasons, to which group of the Periodic Table element X b

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  27. N

    What Is the Si to C Atom Ratio in Dust Grains Given Specific Depletions?

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  28. S

    First superheavy element found in nature

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  29. A

    Beam element vs. Finite element?

    Hello, am a bit confused when to use beam element and when to use Finite element? is the beam element a subset of Finite element?
  30. O

    Why Is the Schwarzschild Solution Considered Spatially Symmetric?

    I've read Schwarzschild paper and I don't understand his conditions "The solution is spatially symmetric with respect to the origin of the co-ordinate system in the sense that one finds again the same solution when x,y,z are subjected to an orthogonal transformation(rotation)" Could...
  31. J

    Finite element result in arbitrary point

    Hi all, I have to write a small program that reads the results from a finite element analysis and calculates some results in arbitrary points. The results could be either nodal or element based. What would be the best approach to do this? I've thought about using the shape functions to...
  32. X

    Radioactive Decay of Element 82-214

    Homework Statement An element of atomic number 82 and mass number 214 decays radioactively to an element of atomic number 82 and mass number 210. Which of the following emissions achieve this result? Check all that apply. a. four beta particles b. two beta particles and one alpha...
  33. B

    Mathematics for Finite Element Analysis

    Can anyone tell me what book is best to learn MATHEMATICS that used in Finite Element Analysis (FEA) algebraically and analytically?
  34. A

    MATLAB Finite Element Analysis in Matlab

    Hello folks :) I need to model a finite element model of a beam in bending in matlab i need directions and help thanks
  35. I

    Can Finite Element Analysis Programs Analyze Inflatable Vacuum Chambers?

    This summer i have an internship that expects me to write a program to analyze this inflatable vacuum chamber. The advisor wants to be able to put in a geometry and see if it will be stable. Would finite element analysis programs be able to do this? If so which one should I look into getting?
  36. M

    ANSYS Element for 2D Table Top Modeling w/ Z-Dir Load

    I am attempting to model a simple 2D surface in ANSYS that is subjected to a load in the 3rd dimension. My surface is a table top, in the X-Y plane. I have modeled it in 2D, and will give it a "simulated thickness". However, I am not sure which element type I can use to apply a force on the top...
  37. P

    Electronegativity and element identification

    As part of the exploration of one of the moons of Jupiter, a probe digs under the surface, where it finds a pocket of gas. It starts to do some on-board experimentation. The data stored in the probe's computer include the following table of Mulliken electronegativity values of gases. Element...
  38. M

    What elements can be represented by the letter R in organic chemical structures?

    Organic element symbol "R" I keep hearing different things about what exactly the letter R represents in organic chemical structures. Does the R always represent an alkyl group or can it represent groups with heteroatoms? For example...
  39. G

    How Many Subsets of 100 Elements Have More Than One Element?

    Homework Statement How many subsets of a set with 100 elements have more than one element? The thing throwing me off here is the zero-set, and whether it counts as an element or that. Can someone start me off?
  40. quasar987

    Exploring if 0 is a Prime Element in an Integral Domain

    [SOLVED] Is 0 a prime? Am I missing something or is 0 a prime element in an integral domain? In the definition of prime element p of an integral domain, we only ask that the ideal generated by p, be prime. Well (0) is obviously prime because if ab=0 in an integral domain, then it is that...
  41. T

    Deriving the line element in homogenous isotropic space

    If the Ricci-scalar R is constant for a given spatial hypersurface, then the curvature of that region should be homogenous and isotropic, right? A homogenous and isotropic hypersurface (disregarding time) has by definition the following line element (due to spherical symmetry): d\sigma^2 =...
  42. R

    Help me set up a PID temp controller w/ heating element

    I need to heat styrene to its forming temp of around 325 degrees F. I have a heating gun that operates at too many amps to use safely at home. So I found these temp controllers that don't use a lot of energy, but can get hotter then my blow dryer can, yet not as hot as the 700 degree heat gun I...
  43. R

    How do I find the line element on a torus?

    Hey folks, Does anyone know how to get the line element on a torus? The ds^2 term. I want to find the metric for toroidal geometry. Any help appreciated! Richard
  44. malawi_glenn

    Double bar matrix element

    Is wondering if anyone knows if the modulus square of the double matrix element that arises in Wigner-Eckart theorem obeys the same "rule" as the ordinary does, if the operator is hermitian: |<ajm|M|bj'm'>|^2 = |<bj'm'|M|ajm>|^2 if M is hermitian. Is then : |<aj||M||bj'>|^2 =...
  45. R

    FEMM - 2d finite element emag simulation

    Hi! Does anybody here have experience with the FEMM simulation software? Its pretty popular in the engg community. I basically use it for simulating magnetostatic problems. If you do (and if this is the right forum, it is EE after all), could somebody tell me how I can do transient...
  46. B

    How Do You Derive the Line Element on a 3-Sphere?

    Hello, I have been trying to figure out the line element on a 3-sphere for my GR class. Problem is that I am trying to go the traditional way of finding dx, dy, dz, and dw, then regroup and find the respective unit vectors and go from there. We are given that the answer as: ds^2 = a^2(d\chi^2...
  47. M

    Deriving Shear Stress on a Conical Bore Fluid Element

    I would like to derive a relation for shear stress on a conical bore shaped fluid element. Essentially, I have flow going through a converging nozzle. I know variables in this include length of the nozzle, inlet and outlet diameters and pressures and nozzle angle. I've done a force balance on...
  48. R

    Find Mass of Iron (Atomic Mass 56 g/mol)

    Homework Statement A part of one of my physics problems wants me to find the mass of iron. The atomic mass is 56 g/mol. How do you find the mass of iron?? Homework Equations Avagadros # = 6.022E23 The Attempt at a Solution I really am not sure how to solve, although it must...
  49. M

    Mathematica Access Matrix Element in Mathematica

    [SOLVED] Access Matrix Element in Mathematica Alright, so in Mathematica you define a matrix by saying A = {{a11,12,...},{21,a22,...}} for whatever matrix you are making. How do you access a particular element of that matrix? Argh, Matlab is so much better.
  50. B

    How do we Calculate Temperature & Time of Heating Element

    How do we 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)In order to Build Heating Element using the above wire for...
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