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. J

    Single shear element in stress tensor: Finding Von Mises

    When finding the Von Mises of given a stress tensor who's only element is a single shear component (τ): \begin{bmatrix} 0 & τ & 0\\ τ & 0 & 0\\ 0 & 0 & 0 \end{bmatrix} the result is simply √3×τ. Is the Von Mises criterion not valid when considering a single component as in this example? I...
  2. Ben Wilson

    MATLAB Replace NaN with next element in Multidimensional Array

    I have a a multidimensional array (49x49x49) which has NaN values scattered randomly. For each NaN, I want to replace the value with the previous non NaN value. e.g. if i had a 3 x 3 matrix 4 7 9 2 7 NaN 1 2 NaN should become 4 7 9 2 7 7 1 2 2 I have 3 dimensions [i,j,k], but...
  3. S

    Uniqueness of identity element of addition

    Homework Statement Here, V is a vector space. a) Show that identity element of addition is unique. b) If v, w and 0 belong to V and v + w = 0, then w = -v Homework EquationsThe Attempt at a Solution a) If u, 0', 0* belong to V, then u + 0' = u u + 0* = u Adding the additive inverse on both...
  4. G

    MHB How to Determine the Order of \( g^8 \) in a Group?

    Say an element $g$ in a group has order $28$. How do I find the order of say $g^8$?
  5. O

    What Material Can Quickly Absorb and Release Heat for Thermal Projects?

    Hello all and thanks from advance, 1.I'm looking for a certain kind of material for a project of mine that can quickly absorb heat and in the same time quickly realesing (I guess that's the right term) heat. Of course it's all based on diffrent parameters, but I'm sure there is a better...
  6. Anithadhruvbud

    How to say whether an element is more electronegative?

    Amoung phosphorous and nitrogen which one is more electronegative? My book says it is nitrogen because it is small in size but shouldn't it be phosphorous since it has higher valency than nitrogen? When we compare two elements based on their electronegativity, should we not look at it's...
  7. A

    Nonuniform finite element method

    I am solving some 2nd order differential equations using the finite element method. Doing so I represent the second order derivative at a given point as: ∂2ψi/∂x2 = 1/(Δx)2 (ψi-1+ψi+1-2ψi) And solve the differential equation by setting up a matrix of N entries and solving for the eigenvectors...
  8. Alain De Vos

    Line element and derivation of lagrange equation

    With coordinates q en basis e ,textbooks use as line element : ds=∑ ei*dqi But ei is a function of place, as one can see in deriving formulas for covariant derivative. Why don't they use as line element the correct: ds=∑ (ei*dqi+dei*qi) Same question in deriving covariant derivative,
  9. FrancescoS

    S-matrix element for forward scattering and amputed green fu

    I'm studying dispersion relations applied as alternative method to perturbation theory from Weinberg's book (Vol.1) Let's consider the forward scattering in the lab frame of a massless boson of any spin on an arbitrary target ##\alpha## of mass ##m_\alpha>0## and ##\vec{p}_\alpha = 0##...
  10. Stephanus

    Understanding ORP in Water with NaCl

    Dear PF Forum, I would like to thank this forum for providing me invaluable helps lately. I'd like to understand ORP in water. I'm aware that PF discourages member for not doing research first. I've (been) reading redox, antioxidant, pH, covalent, including...
  11. I

    Area of Ring Element: Puzzling Out dA

    The circumference of the shaded ring is 2πρ however I am struggling to understand how the area, dA, of the ring is equal to (2πρ)dρ? I mean the circumference varies depending on the value of ρ so surely we can't multiply by dρ to yield the entire area of the shaded ring? If we decided to go by...
  12. M

    Finite element method for frames/beams

    I would like to know how to implement internal hinges in a program I'm developing. A hinge is created by changing the stiffness matrix of the beam. The problem is when two interconnected beams have a hinge at the same location, so basically we have a hinged joint, in this scenario I will obtain...
  13. A

    Low rpm motor and heating element in 250 W

    i wanted to know if it's possible to run a heating coil which reaches some 300 C and a dc motor of low rpm of some 10 or so...and all this under 250 W??
  14. Creaver

    Eurosciences junior chemical element question

    Hello, Imagine a chemical element of the periodic classification with 2046 as atomic number. The highest physicists will tell you that such an element is totally unstable. It prevents not at all the rule of Klechkowski from applying to the atom of this element.. Would you know how to give me...
  15. S

    Decoherence in the long time limit of density matrix element

    For a state |\Psi(t)\rangle = \sum_{k}c_k e^{-iE_kt/\hbar}|E_k\rangle , the density matrix elements in the energy basis are \rho_{ab}(t) = c_a c^*_be^{-it(E_a -E_b)/\hbar} How is it that in the long time limit, this reduces to \rho_{ab}(t) \approx |c_a|^2 \delta_{ab} ? Is there some...
  16. Lagraaaange

    Assumptions of Kinetic Theory: How big should a cubical element be?

    Homework Statement Assuming uniform distribution. What must be the size of a cubical element of volume in the container so that the number of particles in each volume element may vary by 0.1% when the gas is as standard conditions. Probable deviation is given by N^(1/2) where N is the number of...
  17. M

    Surface element in cylindrical coordinates

    Homework Statement \vec J_b = 3s \hat z \int \vec J_b \, d\vec a I need to solve this integral in cylindrical coordinates. It's the bound current of an infinite cylinder, with everything done in cylindrical coordinates and s is the radius of the cylinder. The answer should end up with a phi...
  18. ognik

    MHB Inertia matrix from orbital angular momentum of the ith element (please check)

    Starting with the orbital angular momentum of the ith element of mass, $ \vec{L}_I = \vec{r}_I \times \vec{p}_I = m_i \vec{r}_i \times \left( \omega \times \vec{r}_i\right) $, derive the inertia matrix such that $\vec{L} =I\omega, |\vec{L} \rangle = I |\vec{\omega} \rangle $ I used a X b X c...
  19. Paradox101

    Notation of mass number of an element

    In a lot of books I have seen the mass number of an element being written on left superscript of its chemical symbol,while my professor and other teachers write it in right superscript.However, it is written at the bottom of the symbol in the periodic table.Which is/are correct, or are all...
  20. M

    Different FEA results of the same element

    Hello. Consider the model shown below. The problem is to be solved by FEA. The plane element is constrained from moving at the red line. A concentrated load P is applied at the red point and pointing downward. We solve the problem using the following meshes. Same elements are being used and...
  21. H

    Calculating the line element after a change of coordinates

    Homework Statement [/B] Consider ##\mathbb{R}^3## in standard Cartesian co-ordinates, and the surface ##S^2## embedded within it defined by ##(x^2+y^2+z^2)|_{S^2}=1##. A particular set of co-ords on ##S^2## are defined by ##\zeta = \frac{x}{z-1}##, ##\eta = \frac{y}{z-1}##. Express...
  22. R

    Plasma Cooling: Liquid or Reformed Element?

    Hello all, quick question: When Plasma cools what state does it return to? Is it a liquid or the state it was in before at room temperature? Do the atoms rearrange into what it was like before i.e. the same element or something completely different? Thank you
  23. J

    Mini heat element Construction

    Hello to all, glad to be here. I have a sort of general question about the construction of a small, rod shaped, battery powered (2 9volts), heating element, that will keep approximately 4 ounces of fluid at a steady temperature between 95 and 100 degrees Farentheit. The heating rod will need to...
  24. ElegantSir

    Calculating Energy from Mass Using E=mc²

    Homework Statement I have the question with a diagram posted in the thumbnail to make things easier. Homework Equations E = mc² The Attempt at a Solution The homework only had a single example for a question like this so I am not 100% sure how to get the answer. So far I've added the 2...
  25. Mewniew

    Element of a vector group (subset?)

    EDIT: I think i screwed up and posted in the wrong section. Sorry. Should i make a new one to the correct place? Can this one be moved? Hello. I have a couple of problems here, that i will have to translate from another language, so I am not 100% sure if I am using the correct terms. (1) Let...
  26. B

    Is There a Solution to the Inconvenient Expression for Area and Element of Area?

    If A = x y (if the area of the paralelepid A is equal to edge x multiplied by edge y), so, dA is equal dx y + x dy. See: But this is so much incovenient! The convenient would be dA = dx dy. Let's see now d²A... d²A = d dA = d²x y + dx dy + dx dy + x d²y Now dx dy appears! But, is not a...
  27. mariem.makh

    Fortran FORTRAN Code for Control Volume Finite Element Method Fluid Flow Problems

    where i can found an example A FORTRAN control volume finite element method code FOR FLUID FLOW PROBLEMS thanks for help
  28. Eli137

    Is the tetraneutron a real element without any protons?

    I have heard of the tetraneutron, but is it real? Could it have electrons? If so, how unstable would it be? Could fermions not typically in an atom balance this instability?
  29. W

    Charge moves through a circuit element and loses energy

    Homework Statement If +6 (C) charge moves through a circuit element, and in so doing the charge loses 12 (J) of energy, then what is the magnitude of the voltage across this circuit element? A)2(V) B)6(V) C)12(V) D)72(V) For the same circuit element and situation described in question 1, is...
  30. F

    How much resistance for a heating resistive element?

    Hello Forum, Most devices that are supposed to generate heat via resistance are connected to a constant voltage source. That means that the amount of power dissipated as heat is given by P= V^2/R = I^2*R This implies that the smaller the resistance the larger the current through the heating...
  31. Ogi

    Properties of X Element for Sci-Fi Story Writing

    Hi, in the sci-fi story I'm writing there is a planet rich of carbon-like element(let's name it X element), that must posses this characteristics: 1 - X element common form is stable(non-radioactive) and it's like graphite - soft and with dark metallic shine. while it's hardest allotropic form...
  32. CaptCoonoor

    Is There Research on Using Hydrogen and Isotopes to Prepare Other Elements?

    Hydrogen is the only element and all the other elemnts can be prepared thru hydrogen and isotopes of hydrogen, is there any research paper on this?
  33. C

    Can You Help With Finite Element Analysis in Cylindrical Coordinates?

    I am trying to numerically calculate the electric potential inside a truncated cone using the finite element method (FEM). The cone is embedded in cylindrical coordinates (r,phi,z). I am assuming phi-independence on the potential, therefore the problem is essentially 2D; I am working only with...
  34. B

    Evaluate the partial derivative of a matrix element

    Homework Statement A determinant a is defined in the following manner ar * Ak = Σns=1 ars Aks = δkr a , where a=det(aij), ar , Ak , are rows of the coefficient matrix and cofactor matrix respectively. The second term in the equation is the expansion over the columns of both matrices, δkr is...
  35. S

    Finite Element Symmetry Problem

    Hi, I am running a finite element on a cylinder with that converges at the bottom for a opening, which is symmetrical in both directions so i modeled one quarter but the problem is my stresses are the same with when i compare with a full model that i also done but the deflections are different...
  36. J

    Find the next element in the list

    The problem https://i.gyazo.com/66f03e2caa6ee751adc02e3535287e74.png Find the next element in the list List 1: 2, 4, 8, 16, 32 List 2: 1, 4, 9, 16, 25 List 3: 1, 4, 7, 10 List 4: J, F, M, A, M, J List 5: Symbols, see photo My approaches List 1: This one seemed obvious. Any given element is...
  37. phinds

    What is the heaviest element yet known to man and what are its properties?

    The NEWEST ELEMENT. Scientists have discovered the heaviest element yet known to man. It is called governmentium (Gv). It has 1 neutron, 25 assistant neutrons, 88 deputy neutrons and 198 assistant deputy neutrons, giving it an atomic mass of 312. Since governmentium has no electrons or...
  38. Luca_Mantani

    Doubt regarding volume element in Spherical Coordinate

    Homework Statement Hi everyone. Here's my problem. I know that the volume element in spherical coordinate is ##dV=r^2\sin{\theta}drd\theta d\phi##. The problem is that when i have to compute an integral, sometimes is useful to write it like this: $$r^2d(-\cos{\theta})dr d\phi$$ because...
  39. nilesh_pat

    Result of Bombarding Electron to any element

    What happen if we bombard Electron, Proton and neutron to any element in vaccume tube ? Will it change that eleement to another element obsorbing electron, proton and neutron or what will happen > With regards Nilesh
  40. F

    Finite Element Analysis: PE of an element

    Homework Statement The potential energy of an element in terms of local displacements q1 and q2 is given by the expression: Π = 3(q1^2) - 6q1q2 + 9(q2^2) + 9q1 Write down the expressions for element stiffness matrix k and element force f. I am at a complete loss as to what...
  41. Tony Stark

    Metric Tensor of a line element

    When we define line element of Minkowski space, we also define the metric tensor of the equation. What actually is the function of the tensor with the line element.
  42. Mr Davis 97

    Why does an element in a circuit cause a "voltage drop"

    I have seen this topic in other threads before, but I have not found an answer that eliminates my confusion. I know that electric potential is defined so that only the position of a charge with respect to a field determines the quantity of the electric potential (voltage). This allows us to...
  43. Tony Stark

    Line element in Euclidean Space

    The line element is defined as How is dx2+dy2+dz2 be written as gijdqidqj. Is some sort of notation used??
  44. avito009

    Same distance of electrons from the nucleus for same element

    Why distance of electrons from the nucleus is the same for same element?
  45. Tony Stark

    Calculating Area and Volume of a sphere through line element

    Homework Statement Flat space-time in polar coordinate is considered. The line element is ds2= -dt2+dr2+r2(dθ2+sin2θdΦ2) The actual answers are given below, but I can't come up to them. Need urgent help. Homework Equations dA = √g11g22 dx1 dx2 dV = √g11g22g33 dx1 dx2dx3 The Attempt at a...
  46. K

    Memristor is really fourth circuit element or not?

    Hello friends and genius, I have heard about the missing circuit element which is called memristor. I want to know is it real or the whole world accept that creation of memristor as a fourth circuit element? I was confused about that because in my opinion...
  47. Saracen Rue

    Finding element X in an unknown compound

    Homework Statement An unknown compound weighs 1.023 kg. It is known that element X composes 28.3% of the compound. Given that the molar mass is 240.5 g/mol, find element X. Homework Equations mole = mass / atomic weight (n = m / Ar) mole = mass / molecular weight (n = m / Mr) mole = number...
  48. M

    What happens when an element is heated?

    Let's say we have a bar of 100% pure iron. We know that on a 'human' level- that which we can see with the naked eye, Iron (Fe) will "grow" when heated. But on an atomic level, Is this due to exansion of the atomic particles, or due to a growth of the atom itself, or due to an expansion in the...
  49. R

    A heating element in a container with low pressure gas?

    This is just a qualitative question but feel free to show an equation if possible. Basically if you have a container with a heating element, let's say 500 W with a temperature of 2500 Kelvins and inside this box is a low pressure ideal gas, something like 1/100 of an atmosphere. Also imagine...
  50. S

    Type Godel Metric Line Element - Get Help Here!

    Can someone please type out the line element for the Godel metric (including any and all c terms and any other terms that one might omit if they were using natural units to set terms like c = 1)? I ask this because different sources on line have it written out in different ways which look...
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