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. S

    Finite element method (proof question)

    Homework Statement this is part of a theorem for the error estimate for the model problem for finite element method. i have to prove the following inequality: \left|u'(x)-\tilde{u}'_h(x)\right|\leq max_{0\leq(y)\leq1}\left|u''(y)\right| Homework Equations \tilde{u_h} is the...
  2. J

    Every element in R/Q has order 1 or ∞

    Homework Statement Let R and Q be the groups of real and rational numbers under addition, and R/Q be a quotient group (or factor group). Part a) If a + Q = b + Q for a,b ∈ R, what can you deduce about a and b? Part b) Prove that every element in R/Q has order 1 or ∞. Homework...
  3. G

    In a finite group G, the inverse of each element is a power of itself.

    Homework Statement If G is a finite group and g is in G, then there exists a positive integer r with g^r=e. and in general, prove that, in any finite group G, the inverse of each element is a power of itself. Homework Equations The Attempt at a Solution I know if a group is...
  4. P

    Calculating Principal Stress in Combined Loading of a Beam

    Consider a beam under combined loading. Axial force, bending moment and torsion. I'm interested in determining the principle stress in any stress element on surface of beam. Well as per rule I've to show my attempt so: normal stress=axial load/beam crosssection shear...
  5. P

    Implicit vs explicit finite element solvers

    Hello, I was just reading about implicit vs explicit finite element solvers and have a question about the difference between them. I understand that the implicit solver has a linear approximation step that is used to force equilibrium. My question is does that make the explicit solver...
  6. M

    How Do Trigonometric Identities Derive the Area Element in Polar Coordinates?

    Homework Statement using only trigonometric identities, derive the differential area element in polar coordinates? any help with this problem or at least a start? Homework Equations i found this so far dA=(dr)(rd θ) The Attempt at a Solution i have tried to figure this one out...
  7. W

    Engineering Electron flow through basic circuit element

    Homework Statement Given that the current flow is due to electron flow, state whether electrons are entering or leaving terminal 2. i _____ --> | | - -----|1 | v | | + -----|2 | |___| Situation A: V=40V, i=-10A Situation B: V=-60V, i=-10A Homework...
  8. L

    Solving Elasticity Problems with Finite Element Method

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  9. R

    How do I determine the stresses on an I-Beam element?

    http://users.on.net/~rohanlal/MOHR.JPG For this I-Beam which has a depth of 50mm I need to determine the Principal and maximum shear stresses acting on an element mid way between the Neutral Axis and the top of the flange (12.5mm from the top of the flange). I don't know how to determine...
  10. G

    Is there a unique identity element for matrices?

    For a set S, there is an identity element e with respect to operation * such that for an element a in S: a*e = e*a = a. For a matrix B that is m x n, the identity element for matrix multiplication e = I should satisfy IB = BI = B. But for IB, I is m x m, whereas for BI, I is n x n. Doesn't...
  11. P

    Can we predict element decay using Quantum mechanics?

    Is it possible create a quantum mechanics simulation to predict what the half life of an element will be, say C-14? I know one way to figure an element's half life is to get a bunch of atoms(a really big number of them), wait for some time to pass, and count how many atoms decayed, thus the...
  12. W

    Finding the value of the element dq

    Homework Statement Hi guys, i need a bit of help with the following question. Ok the question states the following, explain why the element of charge, dq, located within an infinitesimally thin spherical shell or radius r is equal to rho(r)*4*pi*(r)^2dr, where dr is the thickness of the...
  13. W

    Finding the value of the element dq

    Homework Statement Ok the question states the following, explain why the element of charge, dq, located within an infinitesimally thin spherical shell or radius r is equal to rho(r)4\pi(r)^2dr, where dr is the thickness of the shellHomework Equations The Attempt at a Solution ok i know that...
  14. Astronuc

    What is the proposed name for Element 112 and why was it chosen?

    According to Webelements.com, http://www.webelements.com/nexus/node/1419 I bet people will call it Copernicum, just like we say aluminum in the US as opposed to aluminium (UK, Australia, NZ, etc).
  15. maverick280857

    How to make contour plots for 2D Finite Element problems

    To the moderator: Please shift this to the appropriate forum if this isn't the place for it. EDIT -- It seems this (https://www.physicsforums.com/forumdisplay.php?f=189) is the right place for it? Sorry I overlooked this forum. ----- Hi everyone, I am solving some 2D boundary value problems in...
  16. S

    Finding center of a group with one element of order 2

    I need to prove that if a group contains exactly one element with order 2, then that element is the center of the group. Here is how I formulated the problem: Let A be a group with an element c such that c^2 = 1 (i.e. c = c^-1), and b^2 = 1 implies b=c. Want either: ac = ca, for all a in...
  17. G

    Element abundance on earth's crust

    May anyone help me on how to define the units used to define the abundance of elements on Earth's crust "It's written ppb(parts per billion by weight)" I really fail to define that!
  18. G

    A group of order 2n conatins an element of order 2

    Homework Statement Let G be a group of order 2n. Show that G contains an element of order 2. If n is odd and G is abelian, then there is only one element of order 2 Homework Equations Theorem (Lagrange): If H is a subgroup of a group G, then |G|=[G:H]|H|. In particular, if G is finite...
  19. O

    Optical Instruments I: Optical Element

    Homework Statement In the 7 diagrams below, the solid arrow represents the object and the dashed arrow the image. The rectangle shows the position of an SINGLE OPTICAL ELEMENT. Match each diagram with the appropriate optical element. 1)http://img190.imageshack.us/img190/5176/92585723.gif...
  20. M

    Only one isotope of element X occurs in nature

    only one isotope of element X occurs in nature. One atom of this isotope has a mass of 9.123x10-23g. What is the molar of the element X?
  21. P

    Supernova explosions element detection.

    Hey ppl i wanted to know that wat is the name of the method with which astrosphysicists are able to detect the elements present in supernovae.for eg they say type 2 suprnva is mainly hydrogen containing. Is it by spectroscopy if yes which one? pleasez temme soon
  22. daniel_i_l

    Can Two Sets Be Checked for Equality in Less Than O(nlogn) Time?

    Let's say I have an unsorted array of integers. Is it possible to determine if there exists a number in the array that appears only once with a time complexity of less than O(nlogn)? Sorting the array takes nlogn time so I'm wondering if it's possible without sorting. I don't need to return...
  23. mnb96

    Semigroup partitions and Identity element

    If I have a semigroup S, is it possible to partition the set of element S into two semigroups S_1 and S_2 (with S_1 \cap S_2 = 0), in such a way that S_1 has an identity element but S_2 has none?
  24. G

    Is my landing gear design suitable for the cyclone airplane?

    Hello I have an assignemt to analysis a landing gear for the cyclone earoplane, an initial design being supplied, I have being askedto check for the suitability of the part, the conditions are: Aircraft mass with fuel: 43000 lbs Landing speed: 65 Knots Maximum deceleration: 3g Each part...
  25. R

    Set A: Element of Itself? Meaning Explained

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  26. K

    Off diagonal element of density matrix

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  27. E

    Stokes' Theorem: Finding the Flux of a Vector Field on a Surface

    Homework Statement Let \vec{F} = xy\vec{i} + yz\vec{j} + xz\vec{k} and C is the boundary of S, the surface z = 9 - x2 for 0 ≤ x ≤ 3 and -6 ≤ y ≤ 6, oriented upward. Use Stokes' Theorem to find [tex] \int\limits_c \vec{F} \cdot d\vec{r}. Homework Equations The Attempt at a Solution well...
  28. E

    Given properties of nucleus, find its atomic number, mass, and element symbol.

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  29. M

    Oxide Measurement of a fuel element.

    Everyone, I am a Mechanical Engineer working on a design modification (or existing product recommendation) for an Idaho National Laboratory project. What follows is the situation description. At the end is the question. You can skip down to the bottom of the post (which details the...
  30. O

    3-Dimensions Finite Element Programming

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  31. C

    Oxidation numbers for each element

    Homework Statement 3Ag2 S + 2Al --> 6Ag + Al2 S3 consider the equation for silver tarnishing. a) state the oxidation number for each element in the reaction. b)identify the the oxidized reactant and the reduced reactant. The Attempt at a Solution Ag2=2 S= -2 Al=0 --->...
  32. S

    What is the heaviest element that a supernova can produce?

    As I understand it, Uranium is the heaviest "natural" element that is still observable on Earth because of it's stability, but what is the heaviest element that may have ever been produced by a supernova regardless of stability?
  33. J

    Question about Circuit element in pencil sharpener

    Hey guys I'm dissecting this pencil sharpener to see how it works. I understand every component except one. The sharpener is battery operated, running on 4 AA's and once the current leaves the battery you can trace the wire to a small platform containing two elements connected. The first element...
  34. M

    What is the percentage of heavy element of the sun?

    what is the percentage of heavy element (heavier than helium) of the sun? (not the photospheric composition)
  35. S

    How the radioactive decay depends on total mass of the element?

    how the decay depends on total mass of the radioactive element? is it necessary that all the atoms of the element keep contact among them, for the above case?
  36. X

    Resistance and Power if an element is removed from parallel circuit

    Homework Statement A heater consists of heating elements connected in parallel across a power supply. A wire in one of the heating elements breaks. What happens to the total resistance of the heater? And the power output of the heater? The Attempt at a Solution Will the resistance...
  37. A

    4D angular coordinate system and corresponding hypervolume element

    I am looking for a 4D angular coordinate system (radius and three angles) and its corresponding "hypervolume element". 2D: polar coordinates - dA = r dr dtheta 3D: spherical coordinates - dV = r^2 sin(phi) dphi dtheta dr 4D: ?
  38. A

    Question on order of an element

    Hello, I was thinking about how to predict the order of an element a*b if the orders of a and b are known where a and b are elements of some group. One textbook I have gives the result (without proof) that if a and b commute and their orders are relatively prime, then order(a*b) =...
  39. E

    MATLAB Truncating a vector from an addressed element in MatLab

    hi, in MatLab, if you have x and y vectors and want to address an element in vector x, let's say i>=3 from which to construct a new vector x that starts from the addressed element until the last element and at the same time construct a new y vector corresponding to the new x vector? x=[1 2 3...
  40. M

    Why is the volume element a scalar density of weight -1?

    In Ray d'Inverno's book on general relativity, he defines the volume element in a way which makes it a scalar density of weight -1, meaning it transforms with the inverse of the Jacobian. Every other source I have looked at seems to say it should transform with the Jacobian, making it a scalar...
  41. K

    Identity element for group theory

    Homework Statement Show that (S, *) is a group where S is the set of all real numbers except for -1. Define * on S by a*b=a+b+ab The Attempt at a Solution Well I know that i have to follow the axioms to prove this. So I started with G1 which is associativity. This one I got to...
  42. H

    Discover the Mass Number of Element X

    how would you set this up to solve this problem A newly discovered element occurs naturally as the two isotopes: 108X and 114X. In nature 65.8 % of is the isotope 108X and the remaining percentage is 114X. What is the mass number for element X.
  43. TheFerruccio

    MATLAB MATLAB: 100 element vector between A and B

    Is there a quick way to define a vector with 100 elements going between two different values? I know of just using division and using that as a step size, but it would be nice if there was something quicker.
  44. K

    Finding the percent weight an element in an Alloy

    Homework Statement Determine the wt% of lithium required to obtain an Al-Li alloy with a density of 2.55 g/cm^3. Homework Equations The Attempt at a Solution I am so lost in this problem, any hints of how to start this problem with GREATLY appreciated!
  45. W

    Atomic Decay: Charged Element After Alpha Helium Release?

    In atomic decay, when an atom decays and releases the (Alpha) Helium nucleus, the atom left behind changes to the element 2 Proton Numbers prior. So is this new element charged? because the electrons stay behind, or do they go? and if so, where to and how?
  46. fluidistic

    Proof that there exist such an element in Q

    Homework Statement I'm asked to say whether the set Q,+,. is a field. To be a field it must respect 8 conditions. And one of them is that there exists a unique element -x in Q such that x+(-x)=0 for all x in Q. I realize I have to prove the existence of -x but also its uniqueness. For the...
  47. G

    Finding finite element soluton for a PDE

    Find the Finite element solution for a equation: (∂^2 u)/〖∂x〗^(2 ) +(∂^2 u)/〖∂y〗^2 +λu-c=0 using linear triangular finite elememts. In the above equation u is scalar,λ is a constant and is a body force term(constant). The boundary conditons are in terms of prescribed values of the function...
  48. U

    How to design rupture disc leak detection sensor element?

    I am to design a sensor element that can detect a leakage through a thin metal disc (rupture disc) in a pipeline. Ideally, the metal disc closes the pipeline at the upstreaming side with certain pressure. Its downstream can be either open to atmosphere or close. When a higher pressure occurs...
  49. S

    Momentum eq for cylindrical element

    Help! I trying to improve momentum eq for cylindrical element coordinate by using vector method or may other methods Please give me response v.ergent . Thanks! =)
  50. 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...
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