iMechanica - EFG Matlab Routines - Comments

EFG

Metsis Panagiotis — Wed, 10 Sep 2008 08:52:35 -0400

This was one of the first papers I red. From my last post, I solved some of the problems mentioned there and I am expanding my code... : )

Metsis Panagiotis

If we change the line as

Lance Shen — Sat, 30 Aug 2008 07:54:05 -0400

If we change the line as "ndivl = 48;ndivw = 24;", that means we set more nodals, so we also should set more GAUSS POINTS, we change the line:

"ndivlq = 10;ndivwq = 4;" as "ndivlq = 20;ndivwq = 8;", then the matrix m will not be singual.

I'm a graduate student come from China, JiangSu province. My subject is Topology Optimization of Continuum Structure Based on Meshless Method. Hope communicate with everyone. thanks!

my msn and email are all : lszab@163.com

THE LINE "if(x(1,j)==Lb)"

Lance Shen — Sat, 30 Aug 2008 07:28:25 -0400

THE LINE "if(x(1,j)==Lb)" CHANGE AS "if(x(1,j)==((Lb/ndivl)*ndivl))"

THEN ok!

RE: Nodal constraints

Alejandro A. Ortiz — Wed, 27 Aug 2008 02:39:33 -0400

have you looked at the original paper of EFG?

http://www.tam.northwestern.edu/tb/papers/94-02%20Element-Free%20Galerkin%20Methods.pdf

Alejandro A. Ortiz

Nodal constraints

Metsis Panagiotis — Wed, 27 Aug 2008 01:56:34 -0400

Thank you very much for your responses. The sparse matrix m (GG) I come up with, is propably due to the wrong implementation of the nodal constraints. I use the Langrange multiplier method but I can't find any analytical papers about that specific (nodal constraints) issue. Any ideas?

Thanks in advance,

Panagiotis

Re: Some further questions about EFG

Alejandro A. Ortiz — Tue, 26 Aug 2008 14:17:32 -0400

Dear Panagoitis,

For your sparse matrix try TAUCS. I have
successfully used it to manage large sparse matrices. It
is easy to use but has one problem. There are some OS that really
don't like TAUCS and so problems may arise. One of those systems is
Windows. But if you are familiar with UNIX/LINUX there shouldn't be
any problem. I use Red Hat Enterprise 9 and it runs pretty well.
TAUCS is open source code written in C. If you are using C++ you will
have to make a wrapper in order to compile it. If you use C, no wrap
is needed. Some of functions in Matlab and Mathematica were
implemented using TAUCS, so that should be a signal that TAUCS is not
a bad option.

Here is the link
to TAUCS:

http://www.tau.ac.il/~stoledo/taucs/

Best,

Alejandro A.
Ortiz

Dear Panagiotis,

abshaw — Tue, 26 Aug 2008 10:28:46 -0400

Dear Panagiotis,

let me try to answer few of your questions.

2) nodal integration technique does not require any background mesh. you may refer to this paper (A stabilized conforming nodal integration for Galerkin mesh-free methods, IJNME, 50, 435 - 466, 2001) and the references therein.

3) EFG also suffer shear locking unless explicitly treated.

4) if you do integration using background mesh then slight change in mesh may affect the solution. the background mesh is required to be chosen such that the support of the kernel and background cell are aligned perfectly. you may find some details in this paper (Numerical integration of the Galerkin weak form in meshfree methods, Computational Mechanics,23,219 -230,1999 ).

5) I find this (Cracking particles: a simplified meshfree method for arbitrary evolving cracks, IJNME< 61, 2316 - 2343, 2004) paper very promising.

1) i am not sure. you may try different solver which handles sparse matrix.

this response is not comprehensive but hope it helps.

Cheers!!!

Amit

Some further questions about EFG

Metsis Panagiotis — Mon, 25 Aug 2008 05:45:52 -0400

Dear Colleagues,

My name is Metsis Panagiotis and I am a doctoral candidate in the school of Civil Engineering of the National Technical University of Athens (Greece). I am trying to fully understand some of the meshless techniques and especially the Element Free Galerkin Method. For that reason I am developing a computer code (2D for now), trying to solve some simple (for the time being) problems. I was wondering if someone could answer (some of) my questions:

1) Incorporation of nodal constraints. When I am trying to solve a model with nodal constraints I come up with a very sparse G matrix (with the majority of the elements being zeros) that is problematic to invert (as part of the m matrix). Finally I acquire a solution, but with large errors (over the displacements field first of all). What should the overall approach be?

2) Background mesh. Are there any other integration methods for the EFG rather than constructing a background mesh of structured cells?

3) Shear locking. In specific models I have encountered something similar to shear locking phenomena. Is this a reality, or should I check my code again?

4) I acquire much different results with small change of variables (such as background cells or nodes). Is this true for the method?

5) My future goal is to simulate some fracture phenomena using the general pattern of meshless methods. Which of the existing meshless methods do you consider to be the most appropriate?

Thank you very much for your time.

Metsis Panagiotis

Civil Engineer, MSc

Doctoral Candidate

School of Civil Engineering

National Technical University of Athens

Greece

some questions !

longvan — Tue, 02 Oct 2007 11:20:45 -0400

Dear Prof.Dolbow

I have some questions about G matrix,qk and f vector.

1/.In order to form f vector in your program,we must loop on Gauss points on traction boundary.The results are values fx,fy at nodes on traction boundary.But I think because of DOI of Gauss points so there are some values fx,fy at nodes which are not on traction boundary in f vector.This contrast with FEM,just only nodes on traction have fx,fy and others are equal zeros.

2/.G matrix and qk vector in your program are formed by looping on 1 displacement boundary.If there are 2 or 3 boundaries which are not continuous,what should I do ? How could I treat nodes directly without looping on Gauss points ?

3/.In case essential BCs are nonlinear or general,is the discrete equations still hold ?

Please explain these things to me !

Regards !

Van

thanks Prof. Dolbow

vivek varshney — Sun, 23 Sep 2007 12:18:58 -0400

thanks a lot sir for your reply

vivek

re: point loads in EFG

John E. Dolbow — Sat, 22 Sep 2007 13:40:05 -0400

You need to find all active (i.e. non-zero) EFG shape functions at the location where the point load is applied. For the sake of argument, let's assume that there are five non-zero shape functions at the point in question, and their values are [0.1 0.2 0.4 0.2 0.1]. Then multiply the magnitude of the point load by the magnitude of each of the shape functions, so this gives a vector F*[0.1 0.2 0.4 0.2 0.1]. The entries to this vector then need to be placed in the appropriate slots in the global force vector.

dear prof. Dolbow

vivek varshney — Sat, 22 Sep 2007 03:02:16 -0400

i want to know how to treat point load on beam in EFG.earlier you have expained. but i could not get you. please explain

Dear Prof Dolbow ! I am

longvan — Mon, 27 Aug 2007 13:09:02 -0400

Dear Prof Dolbow !

I am using EFG for elasto plastic problems.I have a problem :

When i use Newton Raphson method for EFG i have equations

[K G;G' 0]*{du;dlamda}={f_ext - f_int ; q_ext - q_int} .

Is it right ? How could i get "f_int" and "q_int" ? Are they similar the process of "f" and "q" in your program ?

Regards !

Long Van

thanks

vivek varshney — Mon, 20 Aug 2007 10:06:03 -0400

thanks for your reply

re: EFG questions

John E. Dolbow — Mon, 20 Aug 2007 07:55:59 -0400

Vivek,

If you're seeking to modify the EFG Matlab routines to address your problem, I don't think it is a good idea. As I've mentioned here before, the code is not meant for research. It is designed for a very specific problem while being clear enough to allow people to learn the method.

Of course the formulation depends on the type of problem and governing equations you are solving. This is the case for any numerical method.

EFG for elasto-plasticity is really not any different than FEM for elasto-plasticity.

Your third question is very general and I'm not sure this forum is the best place to address it. It might be best for you to sit down with your advisor and work through these issues.

I'm not aware of any freely-available meshfree package that contains a soil model.

EFG Matlab Routines

John E. Dolbow — Tue, 12 Dec 2006 09:29:15 -0500

These used to be hosted at Northwestern, but the files were taken down some time ago. The original 1d and 2d Matlab routines for the element-free Galerkin method are now located at

http://www.duke.edu/~jdolbow/EFG/programs.html

These routines are described in detail in the paper

J. Dolbow and T. Belytschko (1998), "An Introduction to Programming the Meshless Element Free Galerkin Method," Archives of Computational Methods in Engineering, vol. 5, no. 3, pp. 207--242.

At the moment, the above page is a poor replica of the original, but at least the routines are there. I will add more when I find time.