iMechanica - source code - 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

MPM

Nguyen Chau Linh — Tue, 18 Mar 2008 23:33:17 -0400

Prof. Nain and his co-worker are research on Material Point Method, you can search on Google with keywords: Nairn, MPM, crack propagation...

Fun,

MPM + rockfall

pedroso — Tue, 18 Mar 2008 19:54:29 -0400

Hi, that's interesting. We, including Dr. Anna Giacomini, are also planning to run some simulations of rockfalls using the (Generalized)MPM.

MPM

Michael G. Sakellariou — Tue, 18 Mar 2008 07:19:00 -0400

We are developing a 3-D rockfall simulation in a GIS environment and we think the MPM could be very powerful method in simulating the impact phenomenon.

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