Modeling Stress Concentrations with FEM

[wnmascare]

Hi everyone!

I was modeling a stress concentration feature and I was warned that FEM is not the best tool to do that. Then, I was reading Cook´s book (Cook, R. D.; Malkus, D. S.; Plesha, M. E.; Witt, R. J. Concepts and Applications of Finite Element Analysis) and they said exactly this: "FEA is not well-suited to economical modeling of these small details unless special elements are used. If each stress raiser is surrounded by a profusion of small elements, meshing becomes tedious and computational demands become large".

On the other hand, Peterson´s book (Peterson´s Stress Concentration Factors) says exactly this: "The analysis of stress concentration and the design to avoid harmful stress concentrations can be efficiently accomplished using this numerical tool (finite element). The universality of the finite element method allows the analysis of even complicated geometries".

Can someone here tell me who is right? Is it really true that FEM is not well-suited to model stress-strain field around a geometric discontinuity?

Thanks in advance!

 

[jhardy1]

Cook et al is a 1974 text. Back then, models with thousands of elements took super-computer power to process. Today, we can quickly and efficiently solve models with hundreds of thousands of elements on consumer-grade laptop computers - and many low-cost FEA packages have the kinds of "special" element formulations which enable complex geometry and discontinuities to be modelled.

(Having said that, poorly configured meshes - including those generated by the automatic meshers which are built into many CAD packages - are capable of generating utterly meaningless analysis results in the hands of people who are not proficient with the techniques that should be employed to build and check such models.)

http://julianh72.blogspot.com

 

[nlgyro]

I think the key word from Cook's text is "economical modeling".

In the bad old days, when computers were small, it was necessary to use all kinds of esoteric math and accept approximations if you needed to solve large size problems. Today, when one can buy truly huge computers for a fraction of the cost that those old turkeys cost, you just see engineers doing huge problems using straight-forward solutions and few approximations.

 

[wnmascare]

Thank you guys for your answers.

From Cook et al book, I believe that they were more concerned about the processing time required to run an analysis, because in the 70's, the computational resources were limited. Since a very fine mesh is usually required to determine with good accuracy the stress-strain state around a geometric discontinuity, then too large meshes were avoided, because of the limited resources. As a consequence, poor or meaningless results could be obtained.

 

[StressRook]

It is perfectly acceptable to use the finite element method to capture the effects of stress concentrations in a structure. I have modeled numerous stress concentrations with finite elements and validated my results against classical theory and tests. The trick is using the right elements and mesh quality for the type of detail you are trying to model. If you can do the validation, the confidence in your model and analysis techniques is established and you can shut down any argument that would challenge you. For example, early in my career when I started modeling holes and holes in close proximity to other holes and part edges with quads, I performed a trade study to verify techniques and methods. It took a little work, but I was able to establish a standard for modeling those types of details. I even validated my models against testing. Once I had the method and substantiating data, I was able to model and analyze any similar details, and defend the validity of my work. Similar approaches are needed depending on your situation.

So from the two references you mentioned above, Peterson is correct. With the proliferation of computing power, a highly detailed model is easy to build and process without a significant cost in processing time which I believe Cook was attempting to address.

 

[rb1957]

agreed, i immediately wondered when Cook made his comments ... todays FEA is Much more capable than the 70s.

a point from my experience, make sure you extract the surface node stress.

model something easy to start with ... a hole in tension is easy enough, then a shoulder on a bar, then a step on a rectangle.

Quando Omni Flunkus Moritati

 

[wnmascare]

StressRook and rb1957

Thank you very much for your comments.

This issue came out when I was trying to model an offshore component with a prominent fillet radius and I was warned that FEM is not the best tool to do that. Then, I started researching why FEM would not be suited to model geometric discontinuity and I have found anything which prevents me from continuing to use FEM to model stress concentrations. As an alternative way, I was suggested that I should model it by using submodeling instead. Is submodeling strategy more effective than mesh refinement?

Thanks in advance.

 

[corus]

Submodelling is probably the best way to model small features if there's no appropriate scf available from text books. Model the global geometry without the features and select appropriate faces away from the feature as the 'driving nodes' for the sub model. You get odd results at the faces where the sub model extracts results from the global model, but if these faces are at a reasonable distance from the feature then that shouldn't affect the results too much.

 

[rb1957]

certainly to capture a stress concentration you need a very fine mesh. submodelling is a way, mesh refinement is a way ... they'll both accomplish much the same result.

but why not use your FEA to give you the general stress level in the structure, and use Kt geometry solutions to add the stress concentration effect ?

but this is an offshore structure ... i'd've thought you'd design to the endurance limit (of the steel) ? (so you won't have to worry about Kt) ??

Quando Omni Flunkus Moritati

 

[wnmascare]

corus and rb1957, thank you very much for your comments.

In the beginning, when I was warned that FEM was not the best tool to model stress concentration features, I thought it could be a problem of the method itself. But, the comments above helped me to understand that this "deficiency" is much more related to computational resources availability. I am going to recommend revision of the offshore standard we use to follow for stress analyses of our offshore structures, because it references Cook's book and states that FEM is not good at calculation of peak stresses at stress concentration features.

Thank you very much.

 

[rb1957]

of course you allow other methods (like local geometry Kt, like from Petersen) ?

you're just looking to delete the advice not to use FEA ??

Quando Omni Flunkus Moritati

 

[rb1957]

and of course you'll add something like that the FEA needs to be validated (how do you know that the model is detecting the peak stress ??)

Quando Omni Flunkus Moritati

 

[wnmascare]

The offshore standard I mentioned states exactly this: "the analyst shall be warned that FEM is not good at calculation of peak stress at holes, fillets and other stress raisers (see Cook et al[]), thus the straightforward use of extreme FE-predicted stresses as hot spot stresses is discouraged (...)". The standard still recommends other methods found in other offshore standard, which include the application of a SCF.

As a matter of fact, I was going to recommend the complete removal of this paragraph, since, according to the previous comments, there is nothing which prevents us from using FEM for stress analysis of stress raisers regions.

 

[corus]

The problem with using SCFs from Peterson etc. is that you need to identify the nominal stress, and in some cases that can be difficult where the overall stress distribution is complex, say in the region of other features. In other cases the geometry of the feature might itself be beyond the scope of text book classification. The problem with FEM however is that the stresses tend to be underestimated and whether these stress concentrations can be modelled 'efficiently' is a matter of debate. Both methods are appropriate, in the right circumstances, and personally I'd opt for text book determination of an SCF in the first place, but where inappropriate, opt for FEM using mesh convergence to verify the results.

 

[rb1957]

as written it sounds like a reasonable word of caution (rather than a prohibition).

maybe something like "the analyst shall be cautioned about the issues with verifying an FEA (eg convergence study) for determining peak stresses at stress concentrations".

IMO FEA is no better or worse than Kt solutions (eg Petersen) at estimating stress concentrations.

whatever method is used, the closer the method is to a real fatigue test result the better.

Quando Omni Flunkus Moritati

 

[jhardy1]

I would be inclined to change the section that says:
"the analyst shall be warned that FEM is not good at calculation of peak stress at holes, fillets and other stress raisers (see Cook et al[]), thus the straightforward use of extreme FE-predicted stresses as hot spot stresses is discouraged (...)"

to something which highlights the importance of appropriate meshing, element type selection, mesh convergence, validation, expert / peer review, etc.

There is no reason why these problems can't be solved using FEA, but you have to use the right methods and techniques, know how to de-bug / validate the results, and how to APPLY the results (particularly in conjunction with design codes and standards, and "Classical" solutions). For example, you would not generally perform a detailed FEA of a member, and then simply limit the peak tensile stresses to be no greater than 2/3 F[sub]y[/sub], for example.)

http://julianh72.blogspot.com

 

[ESPcomposites]

Peterson's or FEM can work, but each have pitfalls. For simple problems, both should converge. For example, a plate with a hole.

A little background. Many of the Peterson results are determined via mathematical solutions (such as series solutions with conformal mapping, etc.). Some problems are easier to solve than others via these mathematical approaches (some present convergence issues or were difficult to solve via the computation power at the time of the solution). Some solutions also use experimental methods (such as photoeslastic), which can be subject to error.

FEM has many pitfalls, but if done correctly, should yield very good results. For most solutions, it is quite easy to locally refine the mesh at the location of interest and get good results. This is because the computation power of today is very good and not really a limiting factor if done "economically".

As an example, this is a FEM with a very high stress gradient (p. 139 of PDF = p. 126 of document). The FEM converged to nearly exact solution done via mathematical methods (bound collacation and conformal mapping).

https://dspace.uta.edu/bitstream/handle/10106/767/umi-uta-1969.pdf?sequence=1

However, there can be some challenging problems. For example, a pin in a hole is such a challenge. This has been done experimentally in Peterson's, mathetically, and via FEM in various literature. The solutions do not sync up very well. This has to do with issues of how to model contact in FEM, how to calculate and effective distribution mathematically (i.e. assumed cosine distribution often), or shortcomings of photoelastic measurements in high stress gradient regions.

But long story short, I do agree that today Cook's statement would not be valid. FEM is quite good at calculating stress concentrations and the fatigue analysts sometimes like it specifically for that purpose. Actually, the p-element codes are often very good at this as increasing the element order is very efficient at capturing peak stresses.

Brian

http://www.espcomposites.com