FEM VS beso

I apologize in advance for my English, it's not my main language. Do you want to code this exact problem in MATLAB? If you need this specific problem just write the global matrix and global force vector. If you want to implement a full program for heat transfer is not hard either. You must create single element matrices and vectors. Then, using a for loop you can create the global matrix just adding small matrices. Border conditions are very important. You can create a matrix of border conditions. The first column is the node in which the border condition is applied and the second column is the border condition value. You can create both essential, natural and convective border condition matrices. In the computational implementation it is not very useful to remove rows and columns of the global matrix. The reason is that your solution vector size will be different to the number of degree of freedom. That makes the process harder (and slower) (source Reddy's book). There are several methods to assign the border conditions. For example, you can extract the column with the same number of the border condition degree of freedom. Then multiply the whole column by the border condition value and subtract it to the force global vector. Last is to modify the column and row of the global matrix to 0 except the diagonal value which have to be changed to 1. The row of the force vector with the same degree of freedom has to be the border condition value. When you solve the equation system you end with the node solution. You can create graphs with these values or create better graphs using the shape functions. You can create a heat flux graph using shape functions too!! I made a Python FEM package, it has a heat transfer option. It's not Matlab, but maybe you can find it useful. Link https://github.com/ZibraMax/FEM

Does this help: https://github.com/calculix/beso

Just wanted to share my thoughts on the macro created by https://github.com/calculix/beso . I must say that I would like to thank the creators they did a very good job first off. The main thing that I wished was that someone made a video tutorial showing how to overall set everything up and view the results/ and create a design based of of these result. ( I know there is written instructions but I may make a tutorial on youtube to make it easier to understand). Was just wondering if anyone else had any thoughts on this macro or if outher people would be interested in a tutorial? Because I feel this is a very useful feature that every cad program should have.

And this FreeCAD forum thread about the beso topology optimizer, which might do you what you want out of the box, or give you a good jumping-off point for your code.

Yeah it's really complicated. So far I have only found references to "topological optimization" and specifically this python module called beso and some discusion in the forums.