There are elements which use shear stabilization, discrete Kirchhoff theory (DKT), mixed interpolation of tensorial components (MITC) etc. I wonder which one is most robust in avoiding locking? Any test with real life problems?
Hi Huajiang Ouyang and Amin Khajeh, Thanks for suggesting the QUAD elements. However, I have following observations about these.
CQUAD4 element in NASTRAN .(NEi NASTRAN) uses DKT (Discrete Kirchhoff Theory) for improved performance.
Possibly Amin Khajeh is referring ABAQUS S4R5 element, which is 4 nodes QUAD element having reduced integration feature for improving results.
Bathe and his group has suggested MITC (mixed interpolation of tensorial components) type element (in ADINA) for improved performance.
In fact, I have a well-developed open source FEA software (ELMER), which has 3 nodes triangle and 4 node quad elements with shear stabilization. These give some spurious deflection when applied to highly curved components. Since the source code was available, I was trying to improve its performance by using some additional feature like DKT, Reduced integration, MITC. I was wondering if somebody has used element with any of these features to improve the performance of doubly curved shell structures and tested it as benchmark problem.
Dear Engineer,
If you would like to do your analysis by Abaqus, choose 5 integrity nodes,quad, structural. Without a doubt, you would achieve high precision.
Regards,
Hi Huajiang Ouyang and Amin Khajeh, Thanks for suggesting the QUAD elements. However, I have following observations about these.
CQUAD4 element in NASTRAN .(NEi NASTRAN) uses DKT (Discrete Kirchhoff Theory) for improved performance.
Possibly Amin Khajeh is referring ABAQUS S4R5 element, which is 4 nodes QUAD element having reduced integration feature for improving results.
Bathe and his group has suggested MITC (mixed interpolation of tensorial components) type element (in ADINA) for improved performance.
In fact, I have a well-developed open source FEA software (ELMER), which has 3 nodes triangle and 4 node quad elements with shear stabilization. These give some spurious deflection when applied to highly curved components. Since the source code was available, I was trying to improve its performance by using some additional feature like DKT, Reduced integration, MITC. I was wondering if somebody has used element with any of these features to improve the performance of doubly curved shell structures and tested it as benchmark problem.
CQUAD4 in Nastran is generally known to be accurate. For people who do FEA, that is good enough. However, for you as a researcher and expert studying finite elements as a research topic, knowing this is apparently not good enough. I am afraid that is beyond me.
Dear Prof,
In case you are working on shell composite and your step analysis determined for thermal analysis, the number of integration while you are layup your composites is highly effects on results. It be advised to consider minimum 5 integration if you are use Abaqus software.
Regards.
Thanks Amin Khajeh for suggesting more number of integration points. There is an optimum number of integration points depending upon the order of terms in stiffness matrix and for second order terms 4 point integration is possibly minimum. If there are still higher order terms in the matrix in complex formulation, even more number of points may be required. Thus it depends very much on the formulation used in the element. But paradoxically it is also reported number of times that a lower order of integration (less number of points), sometimes gives better results (shell elements based on Reduced integration). In some cases boundary conditions also play important role in accuracy obtained. So I am still at loss to know which linear element will be best with the current state of knowledge so that I use it in my formulation.
Dear Prof,
Absolutely, you are right. The most or only accurate way to FEA continuous shell part is linear, quad, structured way.
I have a question, when the model was sent to mesh module in abaqus, what was the color of model?
Agree with Dr Gupta ---- fewer-point integration when computing stiffness matrix can be more accurate.
The other thing is that even though more-point integration may give more accurate stiffness matrix it involves more computational workload.
So overall, lower-point integration should be used in the first instance.
Dear Mr Amin Khajeh,
Unfortunately I am not using ABAQUS and as I had written earlier I am using the open source software ELMER, although I had used ANSYS quite sometimes back. However I went through the description of ABAQUS and Nastran to find out the background of the shell elements there and the basic formulation is derived from the similar research papers on this topic. Due to variety of assumptions and approximations used in formulation, ultimately the one which satisfies the known results in most of the cases should be the best. This is the reason why i was more interested to see the applications of the elements to practical examples.
Regarding Mr Huajiang Ouyang's point I agree in principle, but there is a minimum order of integration for proper integration of stiffness matrix beyond which the effort may be a waste (Yet I am not sure.)
I found the paper on QUAD4 in NAstran I read a numebr of years ago. I think it might be interesting to Dr Gupta.
http://www.ewp.rpi.edu/hartford/~ewingb/AFEA/Reading/ASimpleQuadShellElem_MacNeal.pdf
Thanks Dr. Huajiang Ouyang for the reference provided. The work seems to be an extension of standard displacement formulation with extensive modifications to overcome the deficiencies of simple displacement formulation. I have included this paper in my compilation of the articles on shell elements. I shall go through it more thoroughly later on. Zienkiewicz in his book (FEM, 4th ed., vol. 2) has reported MacNeal’s subsequent work. Currently I am working on DKT (Discrete Kirchhoff Theory) triangular element, which has been reported to show promise as an accurate shell element.
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