Modeling Stress Concentrations with FEM
Modeling Stress Concentrations with FEM
(OP)
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!
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!





RE: Modeling Stress Concentrations with FEM
(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
RE: Modeling Stress Concentrations with FEM
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.
RE: Modeling Stress Concentrations with FEM
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.
RE: Modeling Stress Concentrations with FEM
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.
RE: Modeling Stress Concentrations with FEM
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
RE: Modeling Stress Concentrations with FEM
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.
RE: Modeling Stress Concentrations with FEM
RE: Modeling Stress Concentrations with FEM
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
RE: Modeling Stress Concentrations with FEM
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.
RE: Modeling Stress Concentrations with FEM
you're just looking to delete the advice not to use FEA ??
Quando Omni Flunkus Moritati
RE: Modeling Stress Concentrations with FEM
Quando Omni Flunkus Moritati
RE: Modeling Stress Concentrations with FEM
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.
RE: Modeling Stress Concentrations with FEM
RE: Modeling Stress Concentrations with FEM
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
RE: Modeling Stress Concentrations with FEM
"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 Fy, for example.)
http://julianh72.blogspot.com
RE: Modeling Stress Concentrations with FEM
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/...
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
www.espcomposites.com