How to plot temperature distribution T(X,Y) over a 2D rectangular plate in Matlab?

Hi all,

I recently attempted to code the FEM 2D triangular element method to solve for the temperature at each node of a rectangular plate with given temperature boundary conditions. I successfully assigned the (x,y) coordinates at each node and solved the corresponding temperature at each node. By the way, the temperature is a vector. Now I would like to know how to plot a temperature distribution for the reactangular plate in Matlab. I've attempted to use surfc(x,y,T); however, Matlab returned an error that states "T needs to have more than one row or column." I appreaciate for any help provided.

[Image Analyst]

How is T a vector? Let's take a look at the 100th element of T. How are we, or MATLAB, supposed to know what (row, column) or (y, x) element 100 is supposed to be at? Turn T into a 2-D array, then use imshow() to display it.

[Jin Au]

I'm sort of confused, why do I want to turn T into a 2D array when there's only one temperature at each node?

[Image Analyst]

Maybe you can show a diagram. I thought you had "a rectangular plate" and to me, that means a 2-D situation where for every (x,y) location you have a temperature. I'm not sure what your "nodes" are. I'm thinking that, for example a point 2 mm over and 4 mm down from the upper left corner should have a temperature. And likewise for every location in the rectangular plate. I thought you said that every node has an (x,y) coordinate. Apparently that's not what you are envisioning, so you'll have to explain better, like with diagrams or pictures of this rectangular plate with the where these one-D Temperatures are located on that rectangular plate.

[Jin Au]

I apologize for my unclear description. Here's the diagram of the problem.

Answer 1

[KSSV]

You said FEM....and triangular elements....so you have used unstructured grid. You should be having (x,y) points in the form of nX2 array and nodal connectivity data (say tri)in the form of nX3 array. So you have evaluated temperature T at each node; this is nX1 array, where n is the number of nodes. You can plot this using: trisurf

trisurf(tri,x,y,T)

doc triplot, trimesh , trisurf .

[Jin Au]

Hi, I've tried your suggestion, but it wasn;t particularly the figure I want. I believe that the answer I'm seeking is a display of the 2D temperature contour plot over the rectangular plate. Something similar to this picture. Thanks for the help.

[KSSV]

Attach the data you have....You said rectangular plate..but plate is circular here, with a hole at the center.

[Jin Au]

I'm so sorry for being unclear. I mean a 2D temperature contour plot of a rectangular plate without the hole.

[Jin Au]

Here's the figure that displays my nodal connectivity.

[Jin Au]

Also, here's the Matlab code if you are interested in taking a look.

[KSSV]

Try this file exchange: https://in.mathworks.com/matlabcentral/fileexchange/32029-plate-bending?focused=5205542&tab=function

It is easy,to achieve what you said. You are confused.

Answer 2

[Precise Simulation]

You can use the FEATool FEM toolbox and postprocessing function to plot unstructured FEM data on triangulated grids and meshes as described in the linked tutorial post.

Answer 3

[Sanjay Kumar]

send me answer, please