I have read the paper entitled (An Equivalent Classical Plate Model of Corrugated Structures). I am very interested in the proposed model. I have read the example of section 7.1 (Sinusoidal Shape). Could you please help me by answering the attached questions.
1. In Example 7.1, Did you use Eq (33) or Eq(39) to calculate the equivalent plate stiffnesses?
None of the above. Please use Eq(11) to do the calculation
2. Could you please help me in calculating the following items for the sinusoidal shape:
•
•
•
It is easy to use Mathematica to do this calculation numerically
(please check the attached file for detail script)
My name is Nhan and I'm reading your article [1] which is about homogenization methods for corrugated plates. It gives me a good overview of essential methods in literature. Based on your equivalent formula, I also find out how to compute I1, and I2 (in Xia's method [2]) for sinusoidal corrugated plate. Now I want to make some simulations to compare the efficiency and accuracy of different homogenization methods. I have some questions that need your help.
You mentioned in the article [1] that there was available a static analysis of a square sinusoidally corrugated plate (11 corrugations) subjected to a uniformly distributed pressure in [3] and there was a comparison between the result of your method with those of ANSYS shell modeling. This analysis suits my need and it's convenient for me to reuse it. Unfortunately, I can't find this analysis in [3] although I have tried my best. I only see an analysis for a trapezoidally corrugated plate. Could you help me locate it?
In your paper [1], you have introduced Xia’s method by rewritten the bending and extensional stiffness terms using your new operator <>. I have checked them and see that all of them except _A22 is correct. Could you help me recheck the formula for _A22? (Please see the attached filefor detail)
Thank you.
Best regards,
Nhan
Reference:
[1] Z. Ye, V. L. Berdichevsky, and W. Yu, “An equivalent classical plate model of corrugated structures,” Int. J. Solids Struct., vol. 51, no. 11–12, pp. 2073–2083, Jun. 2014.
[2] Y. Xia, M. I. Friswell, and E. I. S. Flores, “Equivalent models of corrugated panels,” Int. J. Solids Struct., vol. 49, no. 13, pp. 1453–1462, 2012.
[3] Y. Zheng, “Enhance Variational Asymptotic Method for Unit Cell Homogenization,” Utah State University, 2013.
My name is Nhan and I'm reading your article [1] which is about homogenization methods for corrugated plates. It gives me a good overview of essential methods in literature. Based on your equivalent formula, I also find out how to compute I1, and I2 (in Xia's method [2]) for sinusoidal corrugated plate. Now I want to make some simulations to compare the efficiency and accuracy of different homogenization methods. I have some questions that need your help.
1. You mentioned in the article [1] that there was available a static analysis of a square sinusoidally corrugated plate (11 corrugations) subjected to a uniformly distributed pressure in [3] and there was a comparison between the result of your method with those of ANSYS shell modeling. This analysis suits my need and it's convenient for me to reuse it. Unfortunately, I can't find this analysis in [3] although I have tried my best. I only see an analysis for a trapezoidally corrugated plate. Could you help me locate it?
2. In your paper [1], you have introduced Xia’s method with the bending and extensional stiffness terms rewritten using your new operator < >. I have checked them and see that all of them except _A22 is correct. Could you help me recheck the formula for _A22? (Please see the attached file for detail)
Thank you.
Best regards,
Nhan
Reference:
[1] Z. Ye, V. L. Berdichevsky, and W. Yu, “An equivalent classical plate model of corrugated structures,” Int. J. Solids Struct., vol. 51, no. 11–12, pp. 2073–2083, Jun. 2014.
[2] Y. Xia, M. I. Friswell, and E. I. S. Flores, “Equivalent models of corrugated panels,” Int. J. Solids Struct., vol. 49, no. 13, pp. 1453–1462, 2012.
[3] Y. Zheng, “Enhance Variational Asymptotic Method for Unit Cell Homogenization,” Utah State University, 2013.
This is exactly the place where I would like you to raise questions. You must have done a lot of studies on this topic, which led you here.
Answer for Q1: You can refer to P.125-127 in [3] for a 9 corrugations example. I upload a previous version [4] of this paper which has 11 corrugations example as I referred (section 7.1). This previous version also have several other examples, which can help you validate the theory. Actually, I prefer this old version to the truncated published one.
Answer for Q2: Your derivation is correct. For the comparison, I have the comments in P.12 of this previous version [4] regarding to your question. Xia's equations are correct under certain case, such as symmetric corrugated plate or shallow corrugated plate case, but you will find VAM is a more general theory without ad-hoc assumptions.
Nabeel @ on — Edited @ on
I have read the paper entitled (An Equivalent Classical Plate Model of Corrugated Structures). I am very interested in the proposed model. I have read the example of section 7.1 (Sinusoidal Shape). Could you please help me by answering the attached questions.
Equivalent_plate_model.docx
20 KBClick to download
Equivalent_plate_model.docx
20 KBClick to download
Zheng Ye @ on
1. In Example 7.1, Did you use Eq (33) or Eq(39) to calculate the equivalent plate stiffnesses?
None of the above. Please use Eq(11) to do the calculation
2. Could you please help me in calculating the following items for the sinusoidal shape: • • • It is easy to use Mathematica to do this calculation numerically (please check the attached file for detail script)
Re_-_Equivalent_plate_model.docx
44 KBClick to download
Wenbin Yu @ on
Dear Zheng, thanks a lot for your answer.
Nhan Minh Nguyen @ on
Hi Zheng, Wenbin and Nabeel,
My name is Nhan and I'm reading your article [1] which is about homogenization methods for corrugated plates. It gives me a good overview of essential methods in literature. Based on your equivalent formula, I also find out how to compute I1, and I2 (in Xia's method [2]) for sinusoidal corrugated plate. Now I want to make some simulations to compare the efficiency and accuracy of different homogenization methods. I have some questions that need your help.
You mentioned in the article [1] that there was available a static analysis of a square sinusoidally corrugated plate (11 corrugations) subjected to a uniformly distributed pressure in [3] and there was a comparison between the result of your method with those of ANSYS shell modeling. This analysis suits my need and it's convenient for me to reuse it. Unfortunately, I can't find this analysis in [3] although I have tried my best. I only see an analysis for a trapezoidally corrugated plate. Could you help me locate it?
In your paper [1], you have introduced Xia’s method by rewritten the bending and extensional stiffness terms using your new operator <>. I have checked them and see that all of them except _A22 is correct. Could you help me recheck the formula for _A22? (Please see the attached file for detail)
Thank you.
Best regards,
Nhan
Reference:
[1] Z. Ye, V. L. Berdichevsky, and W. Yu, “An equivalent classical plate model of corrugated structures,” Int. J. Solids Struct., vol. 51, no. 11–12, pp. 2073–2083, Jun. 2014.
[2] Y. Xia, M. I. Friswell, and E. I. S. Flores, “Equivalent models of corrugated panels,” Int. J. Solids Struct., vol. 49, no. 13, pp. 1453–1462, 2012.
[3] Y. Zheng, “Enhance Variational Asymptotic Method for Unit Cell Homogenization,” Utah State University, 2013.
ask-zheng-question-2.docx
35 KBClick to download
Nhan Minh Nguyen @ on
Hi Zheng, Wenbin and Nabeel,
My name is Nhan and I'm reading your article [1] which is about homogenization methods for corrugated plates. It gives me a good overview of essential methods in literature. Based on your equivalent formula, I also find out how to compute I1, and I2 (in Xia's method [2]) for sinusoidal corrugated plate. Now I want to make some simulations to compare the efficiency and accuracy of different homogenization methods. I have some questions that need your help.
1. You mentioned in the article [1] that there was available a static analysis of a square sinusoidally corrugated plate (11 corrugations) subjected to a uniformly distributed pressure in [3] and there was a comparison between the result of your method with those of ANSYS shell modeling. This analysis suits my need and it's convenient for me to reuse it. Unfortunately, I can't find this analysis in [3] although I have tried my best. I only see an analysis for a trapezoidally corrugated plate. Could you help me locate it?
2. In your paper [1], you have introduced Xia’s method with the bending and extensional stiffness terms rewritten using your new operator < >. I have checked them and see that all of them except _A22 is correct. Could you help me recheck the formula for _A22? (Please see the attached file for detail)
Thank you.
Best regards,
Nhan
Reference:
[1] Z. Ye, V. L. Berdichevsky, and W. Yu, “An equivalent classical plate model of corrugated structures,” Int. J. Solids Struct., vol. 51, no. 11–12, pp. 2073–2083, Jun. 2014.
[2] Y. Xia, M. I. Friswell, and E. I. S. Flores, “Equivalent models of corrugated panels,” Int. J. Solids Struct., vol. 49, no. 13, pp. 1453–1462, 2012.
[3] Y. Zheng, “Enhance Variational Asymptotic Method for Unit Cell Homogenization,” Utah State University, 2013.
ask-zheng-question-2.docx
35 KBClick to download
Zheng Ye @ on
Hello Nhan,
This is exactly the place where I would like you to raise questions. You must have done a lot of studies on this topic, which led you here.
Answer for Q1: You can refer to P.125-127 in [3] for a 9 corrugations example. I upload a previous version [4] of this paper which has 11 corrugations example as I referred (section 7.1). This previous version also have several other examples, which can help you validate the theory. Actually, I prefer this old version to the truncated published one.
Answer for Q2: Your derivation is correct. For the comparison, I have the comments in P.12 of this previous version [4] regarding to your question. Xia's equations are correct under certain case, such as symmetric corrugated plate or shallow corrugated plate case, but you will find VAM is a more general theory without ad-hoc assumptions.
Hopefully these are helpful.
Thanks,
Zheng
Homogenization-of-periodically-corrugated-plate-20131002.pdf
1 MBClick to download
Nhan Minh Nguyen @ on
Hi Zheng,
Your answers are clear and they help me a lot.
I have found the analysis of the sinusoidal corrugated plate in your attached article.
Actually, I don’t understand much about your method. I will read the articles and inquire further.
Thank you very much and wish you a good day.
Best regards,
Nhan