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. I

    Can someone check pf: If y element reals and (y+1)/(y-2)=x, then x≠1

    Homework Statement If y element of Reals and (y+1)/y-2) = x, then x ≠ 1. Homework Equations The Attempt at a Solution Proof by contradiction. Assume x = 1. Then y + 1 = y -2 or 1 = -2. This is false. It contradicts (y+1)/(y-2)= x. Therefore, x ≠ 1.
  2. X

    Why Can't XRF & LIBS Distinguish Element Valences?

    Sorry, I had the typo in the topic, it should be"Why can't XRF and LIBS distinguish different valences of a certain element?" Dear all, I have two questions for you: 1: As in known, in the case for transition and rare Earth elements, different valences lead to totally different properties. It...
  3. X

    Detection of valences of a element using XRF and LIBS?

    Dear all, I have two questions for you: 1: As in known, in the case for transition and rare Earth elements, different valences lead to totally different properties. It is said that XRF can only detect the concentration of a certain element, but can not distinguish the valences of this element...
  4. A

    Find total Power absorbed or delivered to Element B .

    Find total Power absorbed or delivered to Element "B". I'm supposed to find how much power was absorbed or delivered by element "B". What is the thought process/solving technique for this type of problem? This was a quiz problem, it has already came and gone; if I see a problem like this...
  5. Y

    E and H pattern of 2 element antenna array.

    This is not a homework, too old for that! I just have a question that I create myself. All the books only show the pattern that is more obvious...they show either the E or the H pattern. I took an exercise that asked for the H pattern, in turn, using the pattern multiplication to try to find the...
  6. M

    Affordable Alternatives to Silver Solder for Heating Element Joining

    Right now I am using silver solder to combine heating elements on a copper pipe. This is becoming very expensive. Any other means/materials I could use that could get the similar results as the silver without the high cost!
  7. R

    Finite element method/crumple zones

    I'm looking for information regarding the use of the finite element method (FEM) for crash test analysis and crumple zones? Basically I'm wondering what part of FEM do I use to make crash test analysis possible. I'm also looking for books on the subject or software libraries that can be used for...
  8. M

    Comp Sci Java finding a specific element

    i am using dummy nodes for a doubly linked list and trying to get an object at the specified index. for whatever reason, when i test it, i am getting data but it is backwards. for example, when i have a list of integers from 0 to 21, and i attempt to call get(2), i get 19 which is at index 2...
  9. M

    Comp Sci Java Removing Element from List

    i am trying to remove an element from the back of the list (i.e. the node right before the tail). i am using a dummy head and tail node. the code compiles correctly, but when i try to test it, there is no execution. below is the segment of code that i am referring to: public Object...
  10. A

    Normalization problem; volume element to use?

    Hello! Homework Statement I'm revising my quantum mechanics course, but I don't get this normalizing-problem. \psi = N r cos \theta e^{-r/a_0} To begin with, this is how my teacher solves it in the solutions manual: 1=N^2\int_0^\infty r^2 e^{-r/a_0} r^2 dr \int_0^{\pi} \int_0^{2 \pi}...
  11. M

    Estimation of residual stress by finite element analysis

    I am trying to do a finite element analysis ofcold extrusion process of a tube wherein the steel tube is reduced from a larger outer diamter to a smaller one by extrusion process.The tube is held stationary and the die is pushed into the tube for a particular length and then retrieved.I am...
  12. S

    A group of order 6 that has no element of order 6 is isomorphic to S_3

    Homework Statement Suppose G contains an element of order 3, but none of order 6. Show G is isomorphic to S_3. Homework Equations I am not allowed to use Sylow's theorems, or quotient groups. The Attempt at a Solution I've established that G contains a subgroup H of order 3, and...
  13. A

    Instantaneous power at infinite distance from current element

    Hi all, Consider a 'current element' of length 'dl' carrying a current of I_{0} cos ({\omega}t). I understand the computation of the electric and magnetic fields due to this current element at any point (r, \theta, \phi), the computation of the Poynting vector at that point, and how the...
  14. A

    Fast Maximum Value Computation in CUDA C Arrays

    I was wondering if anyone knows a fast method of finding the maximum value in a Cuda C array. I can't get max_element to work, but not sure its very fast anyways. I know I could do a for loop, but for an array with 100,000+ elements (smallest cases) it takes a lot of time (plus it has to...
  15. T

    Infinitesimal volume element in different coordinate system

    I've already post this, but I've done it in the wrong section! So here I go again.. I've a doubt on the way the infinitesimal volume element transfoms when performing a coordinate transformation from x^j to x^{j'} It should change according to dx^1dx^2...dx^n=\frac{\partial...
  16. D

    Do H- annihilation spectra vary with element?

    Do \bar{H} annihilation spectra vary with element? If \bar{H} collides (slowly, at 10 Kelvin for example) with H, Beryllium, Lead, does it make a difference?
  17. T

    Volume element in different coordinate system

    Very simple question: Let x^0,x^1,...,x^n be some fixed coordinate system, so that the infinitesimal volume element is dV=dx^0dx^1...dx^n. Then any change to a new (primed) coordinate system x^{0'},x^{1'},...,x^{n'} transforms the volume to dV=\frac{\partial (x^0,x^1,...,x^n)}{\partial...
  18. M

    Counterexample to uniqueness of identity element?

    (Hopefully, this question falls under analysis. I was unable to match it well with any of the forums.) The proof that the identity element of a binary operation, f: X x X \rightarrow X, is unique is simple and quite convincing: for any e and e' belonging to X, e=f(e,e')=f(e',e)=e'. However...
  19. Rasalhague

    Fluid element, conceptual questions

    In chapter 4 of A First Course in General Relativity, Bernard Schutz introduces the idea of a fluid element, a different one assigned to each point in a fluid. When he talks, in section 4.5, about the 3-volume of a fluid element, is this 3-volume defined with respect to the MCRF (Momentarily...
  20. D

    Why Isn't Heat Transfer Occurring in My ANSYS Shell Element Contact Simulation?

    Hello All, I am facing some problem while defining contact between shell elements. My problem is as below. 1. Two thin layers (thickness of 10^-5 m each) of composite material are bonded to a solid material like foam. 2. A third layer of the same thickness comes in contact for a certain...
  21. Y

    Unique volume element in a vector space

    Given two orthonormal bases v_1,v_2,\cdots,v_n and u_1,u_2,\cdots,u_n for a vector space V, we know the following formula holds for an alternating tensor f: f(u_1,u_2,\cdots,u_n)=\det(A)f(v_1,v_2,\cdots,v_n) where A is the orthogonal matrix that changes one orthonormal basis to another...
  22. H

    Need A Finite Element Magnetics Code That Handles Dynamic Modeling

    To the EE Forum, I am a new guy on this Physics Forum and this is my first post. I have downloaded a free software code, Finite Element Method Magnetics (FEMM) solver (see http://www.femm.info/wiki/Download) but it doesn’t work because FEMM is limited to solving low frequency electromagnetic...
  23. V

    First fundamental form and squared arc length element

    First of all hello, I am new to this forum and I decided to join in order to exchange some information with other members that are more knowledgeable than me in the area of diff. geometry. My background is computer science but I am not a student. I am only now starting to learn about diff...
  24. K

    Group with exactly one element of order 2.

    Homework Statement Suppose G is a finite group containing precisely one element of order 2. Call this element f. Show that h= \prod_{g \in G} g is actually f. The Attempt at a Solution Since f has order 2, it must be in the center of G, and hence commutes with all other elements. It is...
  25. Z

    In which block does the element belong?

    Homework Statement In which block 106th element belongs? How do we solve such questions?
  26. R

    Is there an element that does not decay but can be identified from a

    Is there an element that does not decay but can be identified from a extremely far distance or an element with a multi-billion year half life
  27. N

    Learning the Finite Element Method: A Practical Guide for Engineers

    Hi guys I wish to self-study the Finite Element Method. I am mostly interested in learning how to understand and implement the method rather than to investigate if a solution exists, i.e. I wish to follow the "engineering-approach" rather than the "mathematician-approach". Do you have any...
  28. Q

    Finite Element Convergence Analysis

    Homework Statement I have a designed a Finite Element code for a Poisson problem using Bilinear Element. - \DeltaU= 2\pi^{2}Sin(\pi X)Sin(\pi Y) U = 0 The exact solution is given by : UEX = Sin(\pi X)Sin(\pi Y). 2. The attempt at a solution On convergence analysis:Theoretically, if...
  29. S

    How Does MATLAB Implement Finite Element Method for Modified Poisson's Equation?

    Homework Statement The MATLAB program below uses the finite element method to solve a Dirichlet problem for Poisson's equation. -a1u''(x) = 0, xl < x < xh u(xl) = 0, u(xh) = 1 Modify the problem to solve -u''(x) + u(x) = 1, xl < x < xh...
  30. E

    Every element of a finite field is a sum of 2 squares?

    Hi everyone, I have to prove that every element z of a finite field F is a sum of 2 squares. Really not sure how to go about proving this, though I've done some research and it is suggested to start with a function that maps F* to itself, defined by f(x) = x^{2} . I guess if I could show...
  31. A

    Finding the vectorial element and surface area dS

    Homework Statement The domain D is a tetrahedron bounded by the planes x = 0, y = 0, z = 0 and x + y + z = 1 Calculate (a). The volume of the domain. [10 marks] (b). The x-coordinate of the centre-of-mass of the domain, assuming constant density. [9 marks] (c). Find, in terms of x and y the...
  32. B

    Investigating Piezo Element Experiment: Seeking Advice

    Homework Statement Hello, I did the following measurement: A piezo element (mass approx. 50 gram) is fixed onto a vibration shaker The force exert on the piezo, 0,124 N (rms) is measured with an impedance head The vibration frequency (sinusoidal signal) is 142,4 Hz The acceleration is...
  33. J

    Is Mathematics a contingent element in the ad infinitum of legitimacy?

    Mathematics and ordinary language cannot show that a set of signs is not mathematical or semantic. For example x+2=2x-2. This set of signs is assumed to be a mathematical expression by working with it, mathematically, to assess it for truth or falsity. The conclusion, that the set of signs...
  34. M

    Kiln Building Q&A: Choosing the Right Element for 1500°C Heat

    Hello Everyone, I've been looking for an answer to problem I have and I'm getting nowhere so I thought asking the question in a place like this might be useful. I'm planning to build a kiln. I have refractory material that can sustain 1500 degrees celsius. I'm trying to choose an element...
  35. A

    Questions About Single Element Set X={0} in Euclidean Metric

    i have few doubt regarding a single element set. let X={0}, in euclidiean metric. my questions are: 1. does matric space even matters? or matric space is defined? 2. is this set open/closed/none of them? 3. for a discrete matric on [0,1], [0,1]= {0}+(0,1] = {0}+(0,1)+{1}, then {0},{1} are...
  36. D

    Trouble Understanding The Order of A Group Element

    My textbook (Abstract Algebra by W.E. Deskins) says that the order of an element of a group is equal to the integral power to which it must be raised to equal the identity element. It also says that the order of the generator of a cyclic group is equal to the order of the group it generates...
  37. M

    How Is the Volume of an Element in K-Space Determined?

    I've been trying to figure out the volume of an element in k-space (free electron gas in a crystal lattice). In deriving the density of states, dn/dE = dn/dk . dk/dE. My dn = 4pi(k^2).dk / V, where V is the volume of an element in k-space. I came across the spurious, Dk.Dx ~ 2pi (an...
  38. A

    Why does (dr)^2 equal 0 in the differential element equation?

    This is not a homework problem in itself. In my physics homework, I wanted to write the difference of two areas (thus yielding a differential disk) as: Pi*(r+dr)2-Pi*r2 It reduces to 2*Pi*r*dr+Pi*(dr)2 Now, I seem to recall from a prior class that a quick hand-waving made (dr)2 =...
  39. R

    How do you calculate the light cone for the following line element?

    Homework Statement Consider the two-dimensional spacetime spanned by coordinates (v,x) with the line element ds^2=-xdv^2 +2dvdx Calculate the light cone at a point (vx) The Attempt at a Solution I don't even know how the light cone for flat spacetime is calculated. So if that one's...
  40. M

    MATLAB Simple MATLAB- how to find indices of max element in matrix?

    Hi, Say I have a 10x10 matrix, is there a simple code to finding the indices of the maximum value? I'm trying to use max() but there doesn't appear to be any option of actually returning the index, rather than the value. I don't need the value, just the position. Thanks, Mike
  41. W

    A comprehensive book for finite element methods ?

    I am doing BE in mechanical engineering. I'm looking for a comprehensive book on finite element methods preferably with a lot of solved numericals . Suggestions, please?
  42. H

    How much energy is stored in borax element?

    One of my friends is insisting that a car can go 19000km with only 1kg of http://en.wikipedia.org/wiki/Borax" , and only one tea-spoon of borax can extract as much energy 100 tons of coal does. Is that true? Does borax contain this much of chemical energy?
  43. A

    Finding the atomic mass of a hypothetical element.

    Here is a problem I have. Not really sure where to start. I'm not looking for the answer, I just want someone to point me in the right direction. A hypothetical element X has three isotopes: 40X, 41X, and 42X. Their abundances are 72.00%, 9.00% and 19.0% respectively. What is the atomic mass of...
  44. U

    Invariant 4d volume-time element

    Homework Statement Prove that the element dt\ dx\ dy\ dz is invariant under Lorentz boost with velocity \beta along z axis. Homework Equations Convention c=1 Lorentz boost in z direction: L(z)=\left[ \begin{array}{cccc} \gamma & 0 & 0 & -\gamma\beta \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\...
  45. C

    Heating Element for Tree Grafting

    I need a solution for healing tree grafts. Fruit trees are often propagated in the spring by grafting (attaching) a piece of scion wood to rootstock. The graft must "heal" which means that the outer "cambium" layers of the two pieces join together. This process occurs around room temperature...
  46. A

    Differential cross section with invariant matrix element

    Homework Statement Calculate the differential cross section for A+B---> C+D with an invariant matrix element Homework Equations See attachment The Attempt at a Solution I have no idea how to even begin this problem. The course I am taking is an undergraduate course in intermediate modern...
  47. M

    |G|=p^k. Prove G has an element of order p.

    Let p be a prime, k a pos. int., and G a group with |G|=p^k. Prove that G has an element of order p.
  48. N

    Finite Element vs. Finite Volume

    Homework Statement Hi guys Is there a difference between finite element methods and finite volume methods? Or do they both rely on each other? Niles.
  49. D

    Finite element analysis software

    i am a 3rd year civil engineering student, currently taking a course in which i need to use finite element software for assignments. the course is 100% theory, and i need to learn how to use the software on my own, i am looking for FREE software with FE capabilities, and preferably one that...
  50. S

    Prove an element and its inverse have same order

    Homework Statement Prove that in any group, an element and its inverse have the same order. Homework Equations none The Attempt at a Solution I know that I need to show |g|=|g^-1|. This is how I approached it but I'm not sure I'm right, it seems like I'm missing something. Let...
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