iMechanica - Comments

Lianhua, Thank you for

Xuanhe Zhao — Sat, 04 Jul 2009 16:56:00 -0400

Lianhua,

Thank you for your interests in our work. We implemented the method via ABAQUS UMAT. The same principle has also been implemented with UHYPER by O’Brien et al in a very neat way. I think their paper will answer your question clearly.

Xuanhe

modelling of concrete in ansys

omaromar — Fri, 03 Jul 2009 07:58:26 -0400

hiii all

i make FEA for my master research, i simulate a prestressed concrete beam with two precast units connected by contact element (CONTA.52). i used solid 65 for concrete modelling and link 8 for for prestressing steel with initial strain, i entered the stress strain curve for the concrete with linear isotropic, concrete and multilinear isotropic in five points as below:strain=0.0004 stress = 12 MpaStrain = 0.001 stress = 30 MpaStrain = 0.0015 stress=37.5 Mpastrain =0.002 stress = 40 Mpastrain = 0.0003 stress = 40 MPai applied the load up to failure, then, i found that at the contact area, the strain =0.003 but the stress = 34 Mpa, however from the stress strain curve which i entered it must be = 40 Mpa.i tried to change the stress strain curve to be the fc'=60 Mpa instead of 40 Mpa(just as a trial). and i applied the same load, i found that the strain at that load = 0.0016 but the stress still = 34 Mpa at the same node i hope if someone helps me, i do not know how i can pass this problem

In this case, you should

Yixiang Gan — Fri, 03 Jul 2009 07:40:17 -0400

In this case, you should first add a reference node, e.g. called RefNode, and using the following.

*Equation
3
R17, 2, 1., L17, 2, -1., ReNode, 1, 1.0
2
R17, 2, 1., L17, 2, -1.

2
R17, 3, 1., L17, 3, -1.

Here, RefNode represents the relative U1 displacement of your left and right boundaries.

Missing vibration modes

Jayadeep U. B. — Fri, 03 Jul 2009 03:25:37 -0400

Hi,

If you specify start and end frequencies in this manner, you might be missing many vibration modes of significance. I would suggest you to extract more natural frequencies in your first analysis, look at the mode shapes, and make the decisions on correctness etc. As far as I understand, the start and end frequencies are given for checking the possibility of resonance etc., if you have a critical range of frequencies (may be due to the presence of time varying forces).

Regards,

Jayadeep

Re: Stability

Alejandro A. Ortiz — Thu, 02 Jul 2009 17:02:17 -0400

Dear Mike,

First I have to say that I wanted to say that you need at least three nodes to reproduce a linear field in 2D. I guess you are thinking in Guass points instead. Second, I am not familiar with MLPG but I have read something and still there is some similarities, for example, with EFG. So, most of the problems of Galerkin-based methods should remain in MLPG (which is not strictly Galerkin-based).

I think your problem might be when gap are present. I could be completely wrong with what I am going to say (maybe other experienced user should clarify). If you have gaps in the local domains used for the test functions, you will not cover all the domain of analysis. This way, I am not sure that equilibrium equations along with boundary conditions will be satisifed.

Alejandro.

Which error estimator is useful?

Jafar — Thu, 02 Jul 2009 09:21:55 -0400

Dear Prof. Sukumar

I've applied Voronoi diagram for refinement process in which it's functional contains residuals of domain and boundaries. Which error estimator can be useful in adaptive refinement of meshfree methods?

best regards,

Jafar

it all depands on what you

seechew — Thu, 02 Jul 2009 03:35:58 -0400

it all depands on what you want to do.

FLAC is Fast Lagrangian Algorithm Code, and ABAQUS and COMSOL is finite element based. FLAC fundamentally uses finite difference technique to solve problems. Get the global force to balanced out. FEM of course uses weighted residual and Galerkin way.

I am from Geomechanics. FLAC is popular in Geo, because it some sense it simulate reality and are able to handle wide class of nonlinear problems, although for some, might question the validity of the solution. COMSOL (FEMLAB) is a nice FEM program for academia, not much mesh and robustness for industry class problem. It has some nice features though. However might need to take considerable learning before you get comfortable in nonlinear problem.

Abaqus of course, is robust commecial code. FEM based. You might want to take special attention on the boundary of your mesh if you are doing anything dynamics. Nothing bad about ABAQUS, maybe just expansive. If you are student, and wish to join industry after you graduate, it might be a good time to pick up some knowledge on ABAQUS.

Of course, for all nonlinear problems, you will still have to get a strong grib on it before you attemp to solve them using any method you wish.

In term of results, that is up to personal believe. Do you believe in the result FEM gives you anyway? the solution come with certain assumptions and are they reasonable?

I don't track FLAC for awhile, do they incoorporate multicore solver yet? Send an email to Peter Candle and his team to ask them. I think FLAC cost less, and it is more easier to understand in term of the way they solve problems.

I am FEM guy, but I use FLAC too. I think it depands on your problem at hand, and who is picking up the bills.

Stability

Mike W. Long — Thu, 02 Jul 2009 03:29:02 -0400

Dear Alejandro,

thank you very much for the information. I've read these topics more time and find them very usefull. I tried to consider all comments by constructing of my model. But i wonder how i can get it stable?

I use the MLPG where the shape function and test function are defined over different domains. The support domains of shape function for approximation of displacement overlap. As the test function the heaviside function is used, so that i get rid of the product of two basis function derivatives. The quadratur domains are the same as test domains. They don't overlap and don't include any nodes. There is also gap between test domains. Only for this setup of domain the model function. Is it right? Can they overlap and include orther nodes?

The quadratur domains are hexahedrons and for integration over every side of hexahedron i use about 30 points. After integration over every hexahedron the stiffness matrix is filled for every node. I think it must be enough for reproduction of linear field. The support domains are so large that at least the minimal amount of nodes is included. As you wrote it is very important for stability of model.

As you said the region used
to compute numerical integration (background cell) does not coincide
with the intersection of supports of two basis functions. What does it really mean for MLPG? The quadratur or in this case also the test domain should be large enough that the integration points contains minimal number of shape function in stiffness matrix. It force the matrix A of MLS to stay non-singular.

Ther are also cases that the deformation in my model changes in the opposite direction if i change the support size. The form of the deformation can remain. If i give the force on the lower edge of the body to deform it from bottom to top, it deforms in the opposite direction depending on the size of support or test domain. May be there is a mistake in the model?

Mike

MLPG

Mike W. Long — Thu, 02 Jul 2009 02:15:47 -0400

Sorry, there were technical problems to post the comment. I hope that it goes now.

Thanks a lot for your reply.

Excursion stays for the displacement or change of the displacement of the body under external forces. This result i'll get from my model. May be it's not the right word for that.

I suppose that by changing of the support domain the size of displacement changes because of the smoothing of weight function. By changing of the form of displacement the model does not converge. Is there any reason why it could be unstable for every support size?

I noted that the amount of gauss integration points also defines the size of the displacement. Is there any explanation?

seeking for a postdoctoral

hao.sun — Wed, 01 Jul 2009 22:01:45 -0400

seeking for a postdoctoral position in vibration control with piezoelectric materials

to arash

kajalschopra — Wed, 01 Jul 2009 16:54:23 -0400

Arash, you said where would we use this?-in FE formulations what is used is principle of virtual displacements,right?

Re: MLPG

Alejandro A. Ortiz — Wed, 01 Jul 2009 15:35:31 -0400

Dear Mike,

The issue of the support of the basis function in meshfree methods is not new. Here at Imechanica you can find several discussions on the same (see links provided below). The problems in meshfree methods which use Gaussian integration on a background cell arise from two specific points:

1) Basis functions are rational functions (non-polynomial) and hence they are not accurately integrated

2) The region used to compute numerical integration (background cell) does not coincide with the intersection of supports of two basis functions.

Point 2) is the most critical since it is present in the computation of the stiffness matrix. The latter involves the product of two basis functions derivatives which is much more complex to integrate than the basis function itself. An excellent article that discusses this issue is Numerical integration of Galerkin weak form in meshfree methods.

Now, moving to your problem. In the light of the above two issues, you can expect that several Gauss points (typically much more than in FE) are needed to get convergence of the solution and minimize the error in the numerical integration. This is the reason why you obtain different results for the displacement solution.

The instability you obtain for different basis function support size is due to a combination of number of Gauss points used and number of nodes that are covered by the meshfree basis function. Possibly, the second is more important. Let us assume that you always use the same number of Gauss points. This will leave us only with the issue of the support size of the basis function. Let us also assume that the basis functions are constructed so that they reproduce an arbitrary linear displacement field. Note that in 2D you need at least 3 points to reproduce a linear field. So, if for one Guass point evaluation there are less than three basis functions contributing at that Gauss point, there is no possibility of reproducing a linear displacement field in 2D. Thus, if the support size of the meshfree basis function is too small so that this minimum requirement is not met, non-convergence might arise or your numerical results might be totally damaged.

You can get much more information in the following posts:

http://www.imechanica.org/node/490

http://www.imechanica.org/node/1085

http://www.imechanica.org/node/402

http://www.imechanica.org/node/502

Hope this helps.

Alejandro

virtual work

Arash_Yavari — Wed, 01 Jul 2009 15:15:20 -0400

Dear Kajal:

I should first emphasize that your structure does not have to be determinate to use the result of your "notes". In the case of determinate structures you can directly calculate the displacements.

Instead of putting a virtual force on your structure, you could impose a virtual displacement and following a similar line of arguments find a very similar result: Work of real forces acting on virtual displacements is equal to the corresponding stored energy. In the proof you would start with your real forces and corresponding real displacements and then impose the (compatible) virtual displacements. Balance of energy then will give you everything. I don't know where you would use this but perhaps it can help in calculating stiffness matrices.

In short, what you see in those notes as "virtual work theorem" or any variants of it are all consequences of balance of energy.

Regards,
Arash

Reply to Kajal

Ajit R. Jadhav — Wed, 01 Jul 2009 11:35:58 -0400

Kajal,

I am genuinely surprised that anyone would want to confirm things of so straight-forward a nature after finishing his master's in structural engineering from India. Or, seek detailed work-outs.

Still, having said that, I ran the following query in Google and a majority of the first 10 hits it returned seems relevant: "Principle of Virtual Work in Solid Mechanics."

Out of those hits, Alan Bower's book is well-known to iMechanicians and seems to carry a detailed section on what you seek; IIT Madras' prescribed syllabus for the PhD aspirants in Applied Mechanics Department, in a way, goes to confirm that the surprise that I express above was right; from what I have browsed of J. N. Reddy's book on Energy Principles, it seems very well suited to what you seek; and while I have not yet had an opportunity to consult Holzapfel's book, I remember it being recommended by Zhigang (Suo) in the recent past at iMechanica.

All in all, I guess it would be a good (and pleasurable) exercise to work out what you seek through self-studies alone. (I am certain you could do it.)

----

If a system is statically determinate, why would one at all seek more complicated procedures like PVW or MWR (Method of Weighted Residuals)? (This question is rhetorical in nature.) ... OK, therefore to make it all a little bit interesting: It would be interesting to see how PVW, Principle of Stationary Total Potential Energy (PSTPE), and MWR work out in systems that are (a) overdetermined and (b) underdetermined. "...exercise left for the reader..."

Bye.

CEL analysis in Abaqus/Explicit

kunal_mecadcam — Wed, 01 Jul 2009 09:51:03 -0400

Hey.

I have done tha analysi succesfully..