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SCORE! *Now with better graphs!* :D

Fenixgoon

Fenixgoon

Lifer
my brother helped me learn finite element method today and we used matlab to model a thin beam under the stress of its own weight.

finite element method is a way to break down a body into infinitely small (differential) blocks and solve for the material response to the environment (forces and torques, temperature variations, heat flow, etc.).

Fenixgoon's thin tungsten carbide beam

Better Looking Graphs!

as a note, the 3d graphs are only 100 elements since a 1000+ element graph is black (due to the black separation bars)

here are the resulting displacements and strains from a 5000 element model for a tungsten carbide beam with a surface area of 0.5m, length of 10m, density of 19.25 Mg/m^3, and assuming a linear young's modulus of 650GPa.

The left graph is displacement vs. element number. The bottom of the beam has a 0 displacement, while the top has a -0.01 (moves down by 1cm). The right graph is strain vs. element number. The bottom of the beam has the greatest amount of strain (relative to the differential element length) while the top has nearly 0. The strain makes intuitive sense, as the top of the beam has very little weight above it, while the bottom has all the weight above it.


This is so f'ing cool :beer:😀
 
Originally posted by: Fenixgoon
my brother helped me learn finite element method today and we used matlab to model a thin beam under the stress of its own weight.

finite element method is a way to break down a body into infinitely small (differential) blocks and solve for the material response to the environment (forces and torques, temperature variations, heat flow, etc.).

Fenixgoon's thin tungsten carbide beam

here are the resulting displacements and strains from a 5000 element model for a tungsten carbide beam with a surface area of 0.5m, length of 10m, density of 19.25 Mg/m^3, and assuming a linear young's modulus of 650GPa.

The left graph is displacement vs. element number. The bottom of the beam has a 0 displacement, while the top has a -0.01 (moves down by 1cm). The right graph is strain vs. element number. The bottom of the beam has the greatest amount of strain (relative to the differential element length) while the top has nearly 0. The strain makes intuitive sense, as the top of the beam has very little weight above it, while the bottom has all the weight above it.


This is so f'ing cool :beer:😀
Click to expand...

I used to be the future of America too y'know. :|

😛
 
Physics is cool. I try not to think about it too much and just let it happen.

Whoops, just dropped my lighter. Look at that.
 
I assume if your doing that then you already are in engineering school. If you are using MATLAB for fun then you should probably kill yourself now.
 
I do stuff like that for breakfast. And while I loved matlab, it pales in comparison to what Pro E can do with FEA
 
Originally posted by: BrownTown
I assume if your doing that then you already are in engineering school. If you are using MATLAB for fun then you should probably kill yourself now.
Click to expand...

I use matlab for fun. I've made a quantum computer simulator in matlab and probably more physics related stuff in my spare time.
 
Originally posted by: invidia
Originally posted by: BrownTown
I assume if your doing that then you already are in engineering school. If you are using MATLAB for fun then you should probably kill yourself now.
Click to expand...

I use matlab for fun. I've made a quantum computer simulator in matlab and probably more physics related stuff in my spare time.
Click to expand...

yes, materials engineering. from my understanding, abaqus is typically what we use at drexel for FEM. i have access to matlab at home though (on co-op right now). even so, programming alone in matlab will help give me a bit of an idea when i move to other math/modelling packages.

it was pretty cool to work on it. my next goal is doing heat transfer and (hopefully) expand that into the modelling of a heatsink at some point 🙂
 
Sweet.

I never used FEM, but I have written all sorts of solvers that used the finite difference method (Schroedinger 2D, 2D full vector waveguide, and 1D grating waveguide). For a while I wanted to try doing it with FEM because of its nonuniform meshing but I didn't have enough free time to do it.
 
Originally posted by: mfs378
Sweet.

I never used FEM, but I have written all sorts of solvers that used the finite difference method (Schroedinger 2D, 2D full vector waveguide, and 1D grating waveguide). For a while I wanted to try doing it with FEM because of its nonuniform meshing but I didn't have enough free time to do it.
Click to expand...

well this is a pretty basic FEM model, i think, and it only took an hour to code in matlab, and that includes my brother taking me through the math/coding 🙂
 
Maybe I'll give it another try then. 🙂

I was trying to do a full vector waveguide solver, which is (I think) more difficult because the system is actually described by two coupled equations rather than just a single equation. I know Matlab has a few built-in equation templates that you can fill in and it will solve for you, but unfortunately this equation doesn't fit into any of these templates.
 
Originally posted by: Fenixgoon
my brother helped me learn finite element method today and we used matlab to model a thin beam under the stress of its own weight.

finite element method is a way to break down a body into infinitely small (differential) blocks and solve for the material response to the environment (forces and torques, temperature variations, heat flow, etc.).
Click to expand...
That's not really what finite element analysis is. If that were the case, it would be called 'infinitesimal element analysis'. It's 'finite element analysis' because the elements are finite in size. The size of the elements needed to obtain the correct solution varies depending on the problem and the polynomial degree of the solution space. I highly recommend the book by Szabo and Babuska on how FEA should really be done. ABAQUS is crap because it uses h-extension (i.e. more and more elements) rather than p-extension (higher and higher polynomial degrees). StressCheck is the way to go for that reason. As the polynomial degree increases, exponential (or better) rates of convergence are achieved, whereas h-extension yields linear convergence at best. It's only marginally more difficult to code in the p-extension, but the solution will be achieved in much, much less time for almost any problem since so many fewer elements are required.
 
Originally posted by: CycloWizard
Originally posted by: Fenixgoon
my brother helped me learn finite element method today and we used matlab to model a thin beam under the stress of its own weight.

finite element method is a way to break down a body into infinitely small (differential) blocks and solve for the material response to the environment (forces and torques, temperature variations, heat flow, etc.).
Click to expand...
That's not really what finite element analysis is. If that were the case, it would be called 'infinitesimal element analysis'. It's 'finite element analysis' because the elements are finite in size. The size of the elements needed to obtain the correct solution varies depending on the problem and the polynomial degree of the solution space. I highly recommend the book by Szabo and Babuska on how FEA should really be done. ABAQUS is crap because it uses h-extension (i.e. more and more elements) rather than p-extension (higher and higher polynomial degrees). StressCheck is the way to go for that reason. As the polynomial degree increases, exponential (or better) rates of convergence are achieved, whereas h-extension yields linear convergence at best. It's only marginally more difficult to code in the p-extension, but the solution will be achieved in much, much less time for almost any problem since so many fewer elements are required.
Click to expand...

yes technically it's not infinitely small, but that's the idea behind it. just like numerical analysis - it's an approximation that often is infinitely close, but not really the "real" thing.
 
finite elements is cool. See if you can't get some time with a seat of Solidworks and Cosmosworks. That's where the real fun begins.

edit: your graphs suck. Very unclear.
 
Originally posted by: LordMorpheus
finite elements is cool. See if you can't get some time with a seat of Solidworks and Cosmosworks. That's where the real fun begins.

edit: your graphs suck. Very unclear.
Click to expand...

yeah, matlab's bar graph tool is a PITA to get what i actually want. i had to cheat in graphing it , so that's why it doesn't display how it actually *should* 🙁
 
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