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).
Question: Does the magnetic properties of an element, like Praseodymium, vary with radioactivity?
That is, in general, does radioactivity (perhaps beta decay or alpha decay) subtly or otherwise alter the electronic structure enough to alter magnetic properties? The case for beta decay may be...
We were taught that in cylindrical coodrinates, the position vector can be expressed as
And then we can write the line element by differentiating to get
.
We can then use this to do a line integral with a vector field along any path. And this seems to be what is done on all questions I've...
https://www.nasa.gov/image-feature/nasas-new-3d-printed-superalloy-can-take-the-heat
I searched for the composition, which I found in an open access Nature article
https://www.nature.com/articles/s41586-023-05893-0
Ni bal, 33 Co, 29 Cr, 3 W, 1.5 Re, 0.75 Nb, 0.25 Ti, 0.3 Al, 0.05 C; Nb and Ti...
Homework Statement: please, could you help me to know hoe I compute the Casimir element of lie algebra sl(2), I know the basis and their relations, but i could not find the book explain in details how we get the Casimir element.. I think it is related to killing form, but also I could not find...
Hey guys, i need insight on the highlighted part...the steps before this are quite clear:
where is the ##\dfrac{3}{4}M ## coming from? and how to show the argument does not work for ##n=-3##? i should be able to check on this ...later.
and why is the Norm of say;
##ϒ =a+c\sqrt b##
taken...
Why is the length element (vector ds) perpendicular to the current?
I though length element should be parallel to current.
Would anybody be kind enough to help.
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This is my HTML.
I've done CSS For all of them and generated this:
Now, I want the bat to move left and right when I press arrow keys...
I have solved many finite element problems using nodal based (rectangular element) for higher order. now i am trying to solve electromagnetic problem using vector element (Nedelec or Whitney). I know only triangular edge based element with first order only and not higher order. i am searching...
From Wikipedia article about Hyperbolic motion, I have the following coordinate equations of motion for Bob in his accelerated frame:
##t(T)=\frac{c}{g} \cdot \ln{(\sqrt{1+(\frac{g \cdot T}{c})^2}+\frac{g \cdot T}{c})} \quad (1)##
##x(T)=\frac{c^2}{g} \cdot (\sqrt{1+(\frac{g \cdot T}{c})^2}-1)...
I'm trying to understand the Schram plot, which is the graph of wiki here: https://en.wikipedia.org/wiki/Cosmological_lithium_problem
I do not understand why the yellow box (the observed light element abundance) for H3/H (red stripe) is absent? Is there any reason for this?
Hello
I wrote a Matlab code to form the 8 by 8 stiffness matrix of a single, 4-noded element, for a plane strain problem for an isotropic element.
I conduct an eigenvalue analysis on this matrix
Matlabe reports 5 non-zero eigenvalue modes, and 3 zero-eigenvalue modes (as expected)
Of the 3...
I know that if there is only one conductor providing the current density, then the current density can be used.
But if you apply Maxwell's equation when there are multiple current sources, I don't know which value to use.
This is not an analysis using a tool, but a problem when I develop the...
My child is learning the periodic table for science class, memorizing elements 1 - 20. Middle school.
While I assisted, I mused on the elements and on which are discussed most in physics classes.
Here is my ranking of the top three:
1. Z=1
2. Z=2
3. Z=92
Do you agree?
Consider the line element
$$dl^2=d\theta^2 + \sin^2\theta\, d\varphi^2$$
where ##\theta\in [0,\pi]##. The standard interpretation of this line element is to take ##\varphi\in [0,2\pi)##, in which case the line element represents the standard metric of the sphere ##S^2##. However, from the line...
I know how to apply boundary condition like Dirichlet, Neumann and Robin but i have been struggling to apply divergence free condition for Maxwells or Stokes equations in nodal finite element method. to overcome this difficulties a special element was developed called as edge element but i don't...
In a textbook I own a formula is given for the integration of natural coordinates over an element. In this case it is a 1 dimensional element (i.e. a line segment) with coordinates ##x_i## and ##x_j##. The coordinate ##x## over the element is written as:
$$
x = L_1(x) x_i + L_2(x) x_j
$$
with...
the simple rectangular isoparametric element (curved edges element) can be used to generate many complex shapes like..
square to circle
square to triangle
two square elements to annular.
and the results i calculated in python code (2D case) are very accurate, then i confused why to use complex...
Let ##\epsilon>0##. Choose ##N\in\mathbb{N}## s.t. for each integer ##n## s.t. ##n\geq N##,
$$|\sup\{|f-f_n|(x):x\in D\}|<\frac{\epsilon}{3}$$
where ##D## denotes the intersection of the domains of ##f## and ##f_n##.
Choose a partition ##P:=\{x_0,\ldots,x_m\}## with ##x_i<x_{i+1}## where...
I cannot figure how to do this. I looked through some old programming textbook and tried an online search and still cannot find. How can one element from an array be removed, and then the array put together but now with the one item less, and so the array is now one item smaller than it was...
program main
implicit none
real,dimension(3),target::x=[0,4,5]
real,pointer::y
call point_to_biggest(x,y)
!print *,y ! For testing purposes; to be unmuted only when y points to something
contains
subroutine point_to_biggest(array,ptr)
implicit none...
I have a problem in calculate a matrix element in a problem with hydrogen atom.
I have an hydrogen atom and Hamiltonian eigenstates ##|n,l,m>## where ##n## are energy quantum numbers, ##l## are ##L^2## quantum numbers and ##m## are ##L_z## quantum numbers, I have to calculate the matrix element...
I recall, about 30 years ago, seeing the eight mode shapes (and eigenvalues) of a single plane stress (or strain) finite element.
Also, years ago, I wrote a FORTRAN code to obtain them (using IMSL libraries)
I know there are eight (because the plane quad element had 8 degrees of freedom)
I...
##m##, ##n##, ##a##, and ##b## are in ##\mathbb{Z}##. The set of natural numbers is an abelian group, so ##\{ma+nb|m,n\in\mathbb{Z}\}## is a subset of ##\mathbb{Z}##.
##a ## and ##b## are either relatively prime or not relatively prime.
If ##a ## and ##b## are relatively prime, then there are...
Summary:: I need to loop through a number of strings replacing the numerals in them with an array element so that e.g.: flos1Field, flos2Field, flos3Field, etc. become flosAField, flosBField, flosCField. The array would be something like: const letters = ["A", "B", "C"];
I put the question in...
At the risk of waiting hours on simulations of a sensor, I was wondering if I could use infinite element domain on COMSOL to simplify it.
The first image consists of what I would like to simulate but found out that the simulation time is a huge factor as I have a lot to simulations to conduct...
I want to build a high performance computer optimized for FEA. If anyone has any suggestions or experience with this, please chime in.
I'm looking for suggestions on processors, RAM, video card, ALL of it!
Hello folks,
I want to simulate a 2D heat transfer process in the subsurface on a region which is infinite on the r-direction. So, as you know, the very basic way to model this is to draw a geometry that is very long in the r direction. I have done this, and the results that I obtain is correct...
The difference in energy between these two lines is that in the ultraviolet spectrum line, there is more energy because it has a shorter wavelength compared to the visible spectrum line as shown in figure 1.1 According to the Niels Bohr's model of the atom(figure 1.7) and figure 1.1, the least...
Is there any existing work focusing on analyzing finite element visualized results and how they differ from analytical solutions, rather than on the method?
I would like any tips about a Maple ''home made'' program that I received for a project but this program seems to stop before the very end of the code. I want to find de lift of an airfoil with Boundary finites elements method. I have this error at the very end :
Error, (in fprintf) number...
Assuming the line element ##ds^s=e^{2\alpha}dt^2-e^{2\beta}dr^2-r^2{d\Omega}^2 ##as usual into the form ##ds^s=e^{-2\alpha}dt^2-e^{-2\beta}dr^2-r^2{d\Omega}^2##, I found that the ##G_{tt}## tensor component of first expression do not reconcile with the second one though, it fits for ##G_{rr}...
i'm trying to find what sort of 2-d geometry this system is in, I've been given the line element
𝑑𝑠2=−sin𝜃cos𝜃sin𝜙cos𝜙[𝑑𝜃2+𝑑𝜙2]+(sin2𝜃sin2𝜙+cos2𝜃cos2𝜙)𝑑𝜃𝑑𝜙
where
0≤𝜙<2𝜋
and
0≤𝜃<𝜋/2
Im just not sure where to start. I've tried converting the coordinates to cartesian to see if it yields a...
If group ##(G,\cdot)## is defined with two generators ##a## and ##b##. And ##a^n=e##, ##b^{m}=e##. Is there any Theorem to tell us what is the largest group they can form?
Is there a general method to determine what geometry some line element is describing? I realize that you can tell whether a space is flat or not (by diagonalising the matrix, rescaling etc), but given some arbitrary line element, how does one determine the shape of the space?
Thanks
I write a Linear Search code,then ı decided ask to user "r" and "int arr".I mean,User decide their r and arr numbers.I tried scanf("%d",r); command but doesn't work
This code my first code before the decide Ask user :
#include <stdio.h>
int search(int arr[], int n, int r)
{
int i;
for...
I was reading a pdf on acoustic grating for my practicals when I saw that the grating element of an acoustic grating is equal to the wavelength of the sound wave. I also checked a few other sources and got the same.
I do not understand why. I know that for an acoustic wave, the standing wave...
Hello friends,
I have a problem with a exercise sheet. Given is the impulse response of a discret element. The task is to draw the block diagram. But I think that the solution in the sheet is wrong. Because based on the difference equation (Exercise.pdf) there should be 3 delay elements. I have...
Hello everyone, this is a thought experiment I made, it involves two ropes being pulled of a pulley similar to an atwood machine, and a block attached to the two pulleys at the other end. The ropes are being pulled at a constant velocity $ U$ from the end away from the block and the block rises...
Conversion: 9.65 kg = 9650 g
Mass Al = 26.98 g/mol
Molar Mass Al2O3 = (2 x 26.98) + ( 3 x 16.00) = 101.96 g/mol
Mol Al2O3 = 9650 g / 101.96 g/mol = 94.65 mol
Mol Al Required = 94.65 mol x 2 = 189.3 mol
Mass 100% Al required = 189.3 mol x 26.98 g/mol = 5.107x103 g
Mass 80% Al required =...
Summary:: How to load the plates with the Lead element in the spectrometer
I have a mass spectrometer with lead element which has an electronic configuration 1s^2 2s^2 2p^6 3s^2 3p^6 3d^10 4s^2 4p^6 4d^10 5s^2 5p^6 4f^14 5d^10 6s^2 6p^2. It has 2 free electron, so the ejected electrons go...
1 mole of K2CrO4 has formula mass of ((2 x K) + (1 x Cr) + (4 x O)) g
=> ((2 x 39.0983) + (1 x 51.9961) + (4 x 15.9994)) g = 194.1903 g
we have 2 moles of K in 1 mole of K2CrO4 = (2x 39.0983) g = 78.1966 g
so for 1 mole of substance we have 78.1966 g
So how many moles of the substance do we...
Hello engineer's community !
I got a problem. If i got a truss frame with 2 bars and an initial nodal displacement for the common node , then how can i calculate the velocity of the oscillation as function of time ? (the 2 bars have different length , same elasticity modulus , same density and...