Numerical Errors in mldivide

4 次查看（过去 30 天）
Cameron Crook
Cameron Crook 2018-2-27
评论： Walter Roberson 2018-3-1
I wrote the following code to perform 2D heat transfer FEA with convection from the surface and quadrilateral elements. Currently it is a 2x2 element grid and heat is being generated in the first element. I would expect the result to be symmetric given the conduction in x and y is the same. However, the results are not symmetric. I believe I am assembling the K and F matrices correctly. Could the asymmetry be due to numerical errors with mldivide?
main file:
clc; clear all; close all;
eX = 2; %# X elements
eY = 2; %# Y elements
nodesPerElement = 4; %Quadrilateral element
kx = 10; %x conductivity
ky = 10; %y conductivity
L = 0.05; %length of element
W = 0.05; %width of element
h = 1; %convective heat transfer coefficient
z = 0.01; %thickness of board
Tinf = 25; %ambient temperature
graph = meshGrid(eX,eY);
numE = eX*eY; %# of elements
numN = (eX+1)*(eY+1); %# of nodes
Kglobal = zeros(numN,numN);
Fglobal = zeros(numN,1);
for e = 1:numE
if e == 1
qv = 1000;
else
qv = 0;
end
Kcx = kx*L/(6*W)*[-2 2 1 -1;
2 -2 -1 1;
1 -1 -2 2
-1 1 2 -2];
Kcy = ky*W/(6*L)*[-2 -1 1 2;
-1 -2 2 1
1 2 -2 -1
2 1 -1 -2];
Kh = -L*W*h/(36*z)*[4 2 1 2;
2 4 2 1;
1 2 4 2;
2 1 2 4];
K = Kcx + Kcy + Kh;
F = -(h/z*Tinf + qv)*L*W/4*[1; 1; 1; 1];
for n = 1:nodesPerElement
for m = 1:nodesPerElement
Kglobal( graph(e,n), graph(e,m)) = Kglobal( graph(e,n), graph(e,m)) + K(n,m);
end
Fglobal(graph(e,n)) = Fglobal(graph(e,n)) + F(1);
end
end
T = full(sparse(Kglobal)\sparse(Fglobal));
T = transpose(reshape(T, eX+1, eY+1));
x = linspace(0,eX*W,eX+1);
y = linspace(0,eY*L,eY+1);
[X,Y] = meshgrid(x,y);
surf(X,Y,T);
xlabel('x');
ylabel('y');
zlabel('Temperature (^oC)')
colorbar
axis equal
meshGrid.m:
function [map] = msehGrid(eX, eY)
numElements = eX*eY;
map = zeros(numElements, 4);
for n = 1:eY
for m = 1:eX
e = (n-1)*eX+m;
map(e,1) = m + (n-1)*(eX+1);
map(e,2) = m + 1 + (n-1)*(eX+1);
map(e,3) = m + (n)*(eX+1);
map(e,4) = m + (n)*(eX+1) + 1;
end
end
  1 个评论
Walter Roberson
Walter Roberson 2018-3-1
"Could the asymmetry be due to numerical errors with mldivide?"
Yes, if you count standard floating point round-off limitations as "numerical errors".

请先登录，再进行评论。

请先登录，再回答此问题。

回答（0 个）

类别

在 Help Center 和 File Exchange 中查找有关 Graphics Object Properties 的更多信息

标签

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Translated by