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. 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?
  2. K

    If I wanted a constant B field using an element

    Or some naturally occurring material what would I use. I'd like the strongest constant uniform magnetic field possible. Is there some sheet of material I can use?
  3. B

    Finding the inverse of an element in Q[√2,√3].

    Homework Statement I need to prove that Q[√2,√3] = \{a+b√2+c√3+d√6: a, b, c, d \in Q\} is a field. Homework Equations The Attempt at a Solution I proved all axioms except the existence of inverses for nonzero elements. My problem is that multiplication is quite hairy. I ended up...
  4. stripes

    The length element in cylindrical coordinates

    Homework Statement Show that in cylindrical coordinates x = \rho cos \theta y = \rho sin \theta z = z the length element ds is given by ds^{2} = dx^{2} + dy^{2} + dz^{2} = d \rho^{2} + \rho^{2} d \theta ^{2} + dz^{2} Homework Equations -- The Attempt at a Solution...
  5. P

    Finding the oxidized and reduced element

    1. I need to find the element being oxidized and reduced for: CO2 + C = 2CO I don't know how to do it for this one. 3. I know how to do it for ones like this: 2Al + 3Cl2 = 2Al(3+) 6Cl(-) it would be zero for elemental Al and Cl and the oxidation number for the...
  6. S

    Plane stress to a single element- help

    Dear All, I just have a single element, I need to apply a plane stress condition as in the attached image. For the boundary conditions; • I have constrained the nodes 1 and 2 in the horizontal (x) direction • I have constrained the nodes 1 and 3 in the vertical (Y) direction • I have...
  7. M

    Lightning compared to piezo electric element

    I'm building (or rather, debugging) a lightning detector that detects the electromagnetic charge emitted by a lightning bolt. I need a good way to generate a little lightning as a test signal and I'm currently using a the piezo electric part of an electric lighter which generates a small...
  8. B

    Why the off-diagonal elements of electric dipole element are zero?

    the two energy level atom, whose hamiltonian takes the form \hat{H_A}=E_g|g\rangle\langle g|+E_e|e\rangle\langle e|, where E_g as well as E_e represent the eigenvalues and |g\rangle as well as |e\rangle denote the ground state and excited state. There is an interaction between the atom...
  9. M

    Least k Such that a^k=1 in Finite Ring R

    Is there a term for the least k such that a^k = 1 in some ring R (if it exists, specifically in a finite ring)? Is there a way to get an upper bound in general? I know that it's hard to get even in say F_p, but I'm just looking for some conditions that would help me understand what it looks like.
  10. rrw4rusty

    RFC: The believability of a sci-fi concept: Gravity is an element of e

    Hello, I’m a sci-fi writer and I wish to gage the believability of (or lack of) the following which I’m using in a story. Concerning the extensions to cosmology and quantum physics, one of the cornerstones of my book’s sci-fi universe stems from a strange and intriguing fact that I’ve...
  11. C

    Problem in finite element method using direct stiffness method

    Hi, This is a sample problem from logan finite element method. I have attached the problem and solution given in the book. As per the problem i first derived the stiffness matrix and den putting the boundary conditions started solving for the forces. I am stuck as three forces are unknown but...
  12. M

    Understanding the Relative Element of a Vector: Definition and Applications

    Hello! I ve come across with something called ' relative element of a vector' Could you provide me a definition and how is it used? Thank you
  13. H

    Determination of Modal loss factor by Finite Element Software

    Dear all, Please tell me the steps are used to find Modal loss factor of composite constrained layer damped beam by using Finite Element software such as ANSYS etc.
  14. E

    Proof of Uniqueness of Non-Identity Commuting Element in D_2n

    Homework Statement If ##n = 2k## is even and ##n \ge 4##, show that ##z = r^k## is an element of order 2 which commutes with all elements of ##D_{2n}##. Show also that ##z## is the only nonidentity element of ##D_{2n}## which commutes with all elements of ##D_{2n}##. Homework Equations...
  15. P

    How do element normals impact FE mesh analysis results?

    Hi what is the importance of element normals in a FE mesh ? How does it matter if it is outward or inward in a FE solver ? I came across Visual Crash Pam software in which negative element ids would mean element normals in opposite direction. how would this affect the overall result of an...
  16. S

    Finite Element Meshing: Understanding Node Intersections

    Hello my question is basic but i would like to know this and get explanation I a have simple question, about meshing,I know from finite element the it is always better to have node on node of the mesh for two different parts.But if i have node of mesh of on part intersect with line of...
  17. B

    Family of sets without maximal element

    I have begun to learn about maximal elements from a linear algebraic perspective (maximal linearly independent subsets of vector spaces). I have a few questions of which I have been able to get few insights online: 1) Does every family of sets have a maximal element? How can I make a family...
  18. W

    Proving Element In Union of Two Infinite Sets Not Necessarily In Intersection

    Problem: Prove that if an element is in the union of two infinite sets then it is not necessarily in their intersection: Proof: Have I solved it correctly?
  19. S

    What are the Symmetry Constraints for a Quarter-Shape Concrete and Steel Box?

    Hello, Please help my question is really basic,but i need help I have concrete box and steel box and bolt as illustrated in picture one(quarter shape),so my questions are: the key points in symmetry for the quarter of the shape are: 1.prevent translation in the two plan...
  20. C

    Line element under coordinate transformation to get polar form

    Homework Statement Hello Guys, I am reading Hobson's General Relativity and I have come across an exercise problem, part of which frustrates me: 3.20 (P. 91) In the 2-space with line element ds^2=\frac{dr^{2}+r^{2}d\theta^{2}}{r^{2}-a^{2}}-\frac{r^{2}dr^{2}}{{(r^{2}-a^{2})}^{2}} and...
  21. P

    SSR vs SCR for heating element : what is the difference?

    Hello, I have Silicon Carbide heating elements which should be used with a Step Down Transformer or SCR as mentioned in the guide from manufacturer. I currently have a SSR available at hand, and was hoping it could be used instead. The Solid State Relay when connected to PID can...
  22. E

    Addition to a random matrix element

    Hi all! I have no application in mind for the following question but it find it curious to think about: Say that we have a square matrix where the sum of the elements in each row and each column is zero. Clearly such a matrix is singular. Suppose that no row or column of the matrix is the...
  23. J

    Inspect element in android browser

    I want to inspect element in my android browser. How do I do that. I have a stored password (yes it's mine, not someone else's) that I want to see. On my laptop, its easy using chrome. But how do I do that on the android browser? Is there any way to change the URL such that it affects the...
  24. P

    Can Scientists Synthesize Element 120?

    I've just been reading a little bit about attempts to create element 120 back in 2007. Do you guys think that it will be possible to create such an element?
  25. P

    How to subject the PR2 from a given equation?

    Homework Statement Subject the "PR2" from the following equationHomework Equations Tpwm = [(PR2) + 1] • 4 • TOSC • N • = multiply The Attempt at a Solution Actually I am not a student As well as I know how the equation after subject the "PR2"... PR2 = [Fosc / (Fpwm * 4 * N )] - 1 where(...
  26. A

    Calculate the valency of the element?

    1.The equivalent weight of an element is 4.It's chloride has a V.D.=59.25.Find out the valency of the element Homework Equations 3.Molecular wt=108.50 u.Then how to proceed?
  27. U

    X is an element of Y, such that 2/X is in Y. Is this allowed

    Hey guys, I was working on something today and I was trying to formalize what I was doing, and I tried to write out: M = { x | ( 2 / x ) \in M } Then I thought about it and wondered whether this is allowed in set theory. Its not clear that there is anything in M at all, and thus its not...
  28. C

    Interpretation and relevance of current matrix element

    In reading about the axial anomaly I stumbles across a matrix element on the form $$\langle p,k|j^{\mu 53}|0\rangle. $$ and I have seen similar matrix elements turn up other places. But when matrix elements (correlation functions) of the form $$ \langle 0 |T \phi(x) \phi(y)|0\rangle $$...
  29. C

    What element that can't pass through light?

    Hi guys. Just wondering. What element that can't pass through light? By the way I finished computer science so I don't know much about physics. Thanks in advanced.
  30. S

    Finite Element MATLAB Code for Solving Boundary Value Problems

    Homework Statement Consider the problem $$-u''\left(x\right) = 1, \;\; 0 < x < 3, \;\; u \left(0\right) = 0, \; -u' \left(3\right) = u\left(3\right)+1.$$ Formulate a MATLAB code to produce the solution and plot the solution from 0 to 3. Homework Equations The Attempt at a Solution Multiply by...
  31. H

    Uncovering the Unknown Circuit Element: An Exploration

    Hi, so I have a homework problem and I don't know how to approach. I am given a circuit, with an AC source, a resistor ( 2 Ω) and a unknown circuit element (that could be an inductor or a capacitor). I am also given a graph with the Voltage amplitud across the AC source (Which happens to be...
  32. E

    Zero as an element of an eigenvector

    Quick question on eigenvectors; Are there any general properties of a matrix that guarantee that a zero will or will not appear as an element in an eigenvector? Thank you!
  33. T

    Valid Basis Functions for Triangular 2D Elements: Solving for Coefficients

    Howdy, I am trying to formulate a proof to show that the shape function [N(x,y)] = [Ni(x,y) Nj(x,y) Nk(x,y)] and the the basis functions Ni(x,y) = (1/2A)(ai + bix + ciz) Nj(x,y) = (1/2A)(aj + bjx + cjy) Nk(x,y) = (1/2A)(ak + bkx + cky) are valid for triangular, 2 dimensional...
  34. A

    Understanding the Relationship between Line Element and Length in Four Vectors

    What is the difference between the line element and length of a four vector? They both seem to have the same definition just with slightly different notation, so is the line element just the length of a specfic vector. Also, if the magnitude of a four-vector is calculated to b -1 is this...
  35. F

    Finite Element analysis: Free body diagram help

    Homework Statement Hey guys, my problem is not really the end solution, but the preliminary step that I'm not too sure about. Given the following diagram: The image on the left is the given model, and the right image is my nodal element FBD, but somehow i don't believe that's correct. Can...
  36. X

    Archived Atomic Spectrum of an Unknown Element

    Homework Statement When an electron drops from the M shell (n = 3) to a vacancy in the K shell (n = 1), the measured wavelength of the emitted x-ray is found to be 0.0897 nm. Identify the element. Homework Equations E = 1240 / λ E = (-13.6 / n^2) * (Zeff^2) The Attempt at a...
  37. A

    Free Finite Element Analysis Software

    Anyone know of some good, free finite element analysis software? I used NASTRAN in college, but from what I can tell that costs at least several thousand.
  38. Bruce Wayne1

    MHB Prove a ring: showing an element has an additive inverse

    I'm working on showing that Z3 is a ring. The one portion I'd like to confirm is the additive inverse part. So here's what I'm thinking as my proof: Given [x]3 , suppose [3-x]3 is the additive inverse in the set Z3 . Thus: [3-x]3 = [3]3 + [-x]3 = [0]3 + [-x]3 = [0-x]3 = [-x]3 Then, it...
  39. B

    Is there an element that heats up when exposed to alpha/beta

    I am just curious Is there an element/alloy that heats up when exposed to a radioactive element
  40. G

    Nichrome Wire Heating Element for Tube Reactor

    Hey all, First post, thanks in advance for any help. I see there is a lot of discussion on this site and others about nichrome heating elements. I apologize if my question is very similar to others, but I have not exactly been able to figure out what I need to learn/lookup to answer my...
  41. C

    How to find the stiffness matrix for a beam element?

    I need to find the stiffness matrix of a beam element from the basic priciples. I am not allowed to use Lagrange's polynomial or other methods. Need to find the stiffness matrix from basic principles ie to find at each node k11 and so on.. I have attached a screenshot of the problem. When i...
  42. H

    R-L Circuit, Finding the current through a circuit element.

    Homework Statement So I am having a hard time trying figuring this out. The question asks for the current through the 20Ω resistor as well as the current through the battery AFTER THE SWITCH HAS BEEN CLOSE FOR ALONG TIME. Here is a picture of the circuit. http://i.imgur.com/VjoFSUd.jpg...
  43. B

    Polynomial to represent a linear rectangle element

    Folks, I have attached a picture illustrating the labelling of the linear reactangle element which can be represented by the following equation ##u(x,y)=c_1+c_2 x +c_3 y +c_4 xy## (1) ##u_1=u(0,0)=c_1## ##u_2=u(a,0)=c_1+c_2a## ##u_3=u(a,b)=c_1+c_2a+c_3b+c_4ab##...
  44. E

    A problem from finite element book

    ..though I figure it's sort of an analysis type problem. ∫wvdx=0 (int from 0 to 1) for all v in V. w is continuous on [0,1]. What it means to be in V: v in V satisfies being continuous on [0,1], v(0)=v(1)=0, and derivatives of v are piecewise continuous . Problem is: Show that w(x)=0 for x in...
  45. S

    Quick Matrix Element Question using Hermitian Operator

    Hi there, This should be very simple... If I have a state <1|AB|2> where A and B are Hermitian operators, can I rewrite this as <2|BA|1> ? That would be, taking the complex conjugate of the matrix element and saying that A*=A and B*=B. Thank you!
  46. Petrus

    MHB Calculating Element Count in Disjoint Volumes Using Venn Diagram

    Calculate the number of elements in A1 U A2 U A3 if there are 97 elements in A1, 997 elements in A2 and 10098 elements in A3 in each of the following situations: (a) The amounts are pairwise disjoint, i.e. , too . (b). (c) there are 10 elements in common for each pair of volumes and 4...
  47. A

    How much heat will be transfered ,from heating element to surrounding?

    I am using an heating element to heat the air in a closed container. Joule heating will give me the "heat generated at heating element." I want to know how much of it will be transferred to the surrounding air. Should I be using heat transfer due to all three modes ?
  48. N

    Magnitude of Fissile Element at the Order of a Neutron.

    Consider a fissile element whose magnitude is at the order of a neutron. In this situation, how can we derive the point kinetic equations? Thanks everyone.
  49. S

    How can I fix my program to properly delete elements from an array?

    Homework Statement Hey all. I have code that is supposed to delete the offset determined by the user and shift the elements after that offset to the left. My code works fine except for one problem: if the index is zero it terminates. I will post my code, and if anyone can see why it is giving...
  50. R

    Let G be a finite group in which every element has a square root

    Homework Statement Let G be a finite group in which every element has a square root. That is, for each x in G, there exists a y in G such that y^2=x. Prove every element in G has a unique square root. Homework Equations G being a group means it is a set with operation * satisfying...
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