Hello everyone, I hope you are doing well
I want to run a simulation on spinodal decomposition in 2 dimensions, and one of the governing equations is the Cahn-Hilliard equation which is basically a nonlinear 4th order PDE. I would like to solve it by using the Continuous Galerkin method. is there any handbook that I can use? or is there any other numerical method for this particular type of problem that you would recommend?
Many thanks!
P.S. I am experienced in using the CG method for 2nd order nonlinear PDEs
Hello everyone,
I am currently planning my masters courses and might need to decide between these two courses. I was wondering what structural engineers find to be more useful and maybe help me decide which course would be better to take if needed.
Thank you
Thinking about taking ENVE3003 but I'm not sure if its too much, I already took both complimentary studies electives but should I keep it 5 or 6? trying to figure out if its worth it or not or if i should just wait and take it as a 4th year engineering elective.
https://preview.redd.it/my3kxgq0fh371.png?width=1628&format=png&auto=webp&s=af1c49b29b75d6d4e5f392a72f34ff6ac4fc16b2
Last semester I took Intro to FEA. I am starting my masters in ME and this upcoming semester I will be taking computational mechanics. Is this practically the same thing but a sub discipline? I’ve been trying to find the difference but having trouble finding it.
As the title indicates, I will applying to graduate programs this fall. I hope to study applied math; particularly, partial differential equations and their numerical solutions. I can more details on the type of graduate coursework and research I'd like to do, but are there any suggestions for FEM vs Optimization when it comes to numerical PDE?
(FEM seems like to obvious choice, explicitly dealing with numerical PDE, but Optimization might provide a stronger analysis background.)
Looking for R. W. LEWIS Fundamentals of the Finite Element Method for Heat and Fluid Flow Solutions Manual
Hey guys,
i'm doing a fem analysis of one of the raptor thrust hinges, seen in those pictures, for an university project [BocaChicaGal].
I approximated the geometry with some help from online models and my own impressions.
Now with each of those hinges taking half the thrust of the raptor [1.100kN] at an angle of 15° gimble angle (reduced gimble to one axis for simplicity) i can't really figure out which material they use to bear those high loads. From the looks of it i choose graphite cast iron (GJS-800) as a material which should be fitted well but it can't reach the high strains which are being put onto it, even with higher strength GJS.
Does anyone here have a guess which material they might be using. It needs to be able to withstand around 1000 MPa of strain. You can also give feedback if i'm off with the geometry or am doing something wrong in general. :) I can't imagine them having to use some very secret sauce in such a relatively simple part.
All I can say about that class is...damn.
Hi,
I have stumbled upon this subreddit and I have really enjoyed reading some of the posts here. Occasionally some high-level stuff that really keeps the mind going. I hope to get some insights on some of the questions I have. Mind you, they are spread all over the map of the finite element method.
I have been using FEA for a while and decided to go back to the roots and see if I could get a better grasp on everything and maybe try to python/matlab a couple of things to prove my understanding without the pressure on passing an exam (lol).There are a ton of videos/bloggs and material of sorts all over the web but then again there are also people that might be willing to discuss some of these things.
So here we go:
Quote with modification describing FEM.
“Going from continuum mechanics converting functions with the properties of being in an infinite dimensional function space to a finite dimensional space and then simpler vector math. This is how we might interpet when describing a problem with a weak formulation approximating a strong one. “
The description is very informative, but there is a ton of stuff going on looking into the details.
While using principal of virtual work, we can create this weak formulation and solve a problem, am I then correct to say that the Galerkin and Collocation methods essentially are Principal of virtual work since they yield the same outcome?
Looking into the procedures of Galerkin, it is most often solved with a “Educated guess” function which apparently comes from the L.^2 Hillbert space. How do you assume an approximation before-hand that is hopefully close to the accurate solution in order to solve the problem? And further, does anyone have recommendations on literature on Hillbert-spaces made for simpler engineers?Seems like a rabbit hole of abstract math, but It would not hurt to look at it, I think lol.
More questions, are base-functions and shape-functions the name for the same thing in regards of discretization (meshing).
Looking at how problems are solved there are explicit and implicit methods of solving certain problems and it is well documented regarding methods as selection when looking on dynamic/static- problems with reference to the time it takes to solve it (A lot more to this than this example ofc). I get that. However, different types of solvers are mentioned all the time, namely Newton-Raphson (Full/modified/etc), Backwards differentiation, generalized alpha, runge-kutta and more.
On what gr
... keep reading on reddit ➡Hi, everyone,
I was excited about the possibility of using Julia's metaprogramming capabilities to build a generic and versatile finite element method tool with the language, so I made this:
https://github.com/pedrosecchi67/SymFinel.jl
It's a package that uses algorithmic differentiation and metaprogramming to integrate weighed residuals over finite elements in spaces with an arbitrary number of dimensions, with variables and weights interpolated by user-defined expressions at run-time.
Metaprogramming allows the code to adapt itself to any interpolation function, element order or domain geometry with very few changes for the user, thus reducing the necessary programming effort to make alterations to your model's mathematical formulation.
I'm posting about it here in case anyone out there has some interest in the project, or some form of constructive criticism to offer. In either case, thanks in advance!!
Hello, I am looking for expert advice from someone who's an expert in chemical kinetics (primarily focusing on rates of the reactions). My expertise is in Continuum Mechanics and the Finite Element Method. I wanted to expand my horizons a bit and after taking a course on engines that talked about a bit rates of chemical reactions, I got curious about the subject. After picking up a book on Chemical Kinetics (the one by Paul L Houston), I saw that early on the techniques to solve simpler problems was just to consider either steady state solutions or do some equation manipulation to make it work. I couldn't really find papers that directly tackled the differential equations besides a few from the 90s and those were primarily from industry not universities that used some cooked up version of the Finite Element method requiring multiple assumptions and simplifications.
Any links, advice or conversation is appreciated.
I am following the development of PINNs (Physics Informed Neural Networks) as a mesh-free method to solve PDEs. PINNs use the expressivity of neural networks to approximate a solution and the PDE (i.e the Physics) is part of the loss function which provides feedback to the optimizer. Although the method is currently in its nascent stages of development and no concrete theory for this method exists, it shows great promise as a method to solve PDEs.
I am looking for insights/views about the extent to which PINNs can replace FEM as a method to solve PDEs. More precisely will PINNs make FEM obsolete?
Some related papers:
1.Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations (Proposes PINN)
(Provides a good review of the developments)
(Transfer Learning applied to PINNs)
(Improves PINN convergence by introducing a new scalable hyperparameter in the activation function)
5.On the Convergence and generalization of Physics Informed Neural Networks
(Establishes mathematical foundation of the PINN methodology)
I just completed high school and I want to learn Ansys and FEM. Are there any good resources that could help? How do I proceed? Also, what is prerequisite for learning this?
I am just starting to learn Finite Element Procedures and taking reference from the book of K.J. Bathe.
I am getting very confused about seeing different methods and also not finding the different literature to be consistent. Why are different methods like Galerkin, Weighted Residual, and Ritz-Rayleigh are confusing?
Why is it that different literature calls the different method by the same names?
If you are a visual learner: FEM Series
If you are more of a visual & auditory learner: The Finite-Element Method - A Beginner's Guide
Just shooting this out there for anyone in the area who might know this subject well and be open to tutoring.
Hello everyone, I hope you are doing well
I want to run a simulation on spinodal decomposition in 2 dimensions, and one of the governing equations is the Cahn-Hilliard equation which is basically a nonlinear 4th order PDE. I would like to solve it by using the Continuous Galerkin method. is there any handbook that I can use? or is there any other numerical method for this particular type of problem that you would recommend?
Many thanks!
P.S. I am experienced in using the CG method for 2nd order nonlinear PDEs
Hi, everyone,
I was excited about the possibility of using Julia's metaprogramming capabilities to build a generic and versatile finite element method tool with the language, so I made this:
https://github.com/pedrosecchi67/SymFinel.jl
It's a package that uses algorithmic differentiation and metaprogramming to integrate weighed residuals over finite elements in spaces with an arbitrary number of dimensions, with variables and weights interpolated by user-defined expressions at run-time.
Metaprogramming allows the code to adapt itself to any interpolation function, element order or domain geometry with very few changes for the user, thus reducing the necessary programming effort to make alterations to your model's mathematical formulation.
I'm posting about it here in case anyone out there has some interest in the project, or some form of constructive criticism to offer. In either case, thanks in advance!!
If you are a visual learner: FEM Series
If you are more of a visual & auditory learner: The Finite-Element Method - A Beginner's Guide
If you are a visual learner: FEM Series
If you are more of a visual & auditory learner: The Finite-Element Method - A Beginner's Guide
