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An Equivalent Classical Plate Model of Corrugated Structures

1. 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.

2. 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)

4. 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 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.

5. 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.

6. 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.

Thanks,

Zheng

7. Hi Zheng,