iMechanica - Comments for "Transformation Cloaking in Elastic Plates"
https://imechanica.org/node/24589
Comments for "Transformation Cloaking in Elastic Plates"enRe: Cloaking in plates
https://imechanica.org/comment/30525#comment-30525
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<p><em>In reply to <a href="https://imechanica.org/node/24589">Transformation Cloaking in Elastic Plates</a></em></p>
<div class="field field-name-comment-body field-type-text-long field-label-hidden"><div class="field-items"><div class="field-item even"><p>Dear Michele:</p>
<p>Thank you for your message. I was not aware of your PML paper and just read it. In Eq. (17) of your PML paper the transformed elastic constants are correct. You cited your older papers but I wonder why the discrepancy between the two transformed elastic constants was not discussed? The continuity conditions on the PML boundary (your Eq. (30)) are correct. However, this will not make your cloaking formulation in your previous papers work. There are still some constraints (coming from matching the different terms in the governing equations of the virtual and physical plates) that will ultimately force the cloaking map (or your "transformation" map) to be the identity. Exact cloaking is not possible. I am not claiming that approximate cloaking is not possible. However, it should be formulated properly as an optimization problem. </p>
<p>Regards,</p>
<p>Arash</p>
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</ul>Tue, 17 Nov 2020 23:14:14 +0000Arash_Yavaricomment 30525 at https://imechanica.orgCloaking in plates
https://imechanica.org/comment/30524#comment-30524
<a id="comment-30524"></a>
<p><em>In reply to <a href="https://imechanica.org/node/24589">Transformation Cloaking in Elastic Plates</a></em></p>
<div class="field field-name-comment-body field-type-text-long field-label-hidden"><div class="field-items"><div class="field-item even"><p>Dear Arash Yavari,</p>
<p>thank you for your interesting work.<br />Concerning your criticisms on our work concerning your eqs. (1.1) and (1.2), they were already solved in the paper I published in (2018), i.e. <a title="Perfectly matched layers for flexural waves in Kirchhof–Love plates" href="https://www.sciencedirect.com/science/article/pii/S0020768317305140?via%3Dihub">https://www.sciencedirect.com/science/article/pii/S0020768317305140?via%3Dihub</a></p>
<p>Transformed equations and interface/boundary conditions have been reported in Section 4.</p>
<p>In Section 5, we propose the eigenfrequency analysis as a tool in order to check the transformation.</p>
<p>There, higher order polynomials were implemented in order to respect interface conditions between untransformed and transformed domains.</p>
<p> </p>
<p>Anyway, concerning the formulation reported in <br />1) D. J. Colquitt, M. Brun, M. Gei, A. B. Movchan, N. V. Movchan, and I. S. Jones. Transformation elastodynamics and cloaking for flexural waves. Journal of the Mechanics and Physics of Solids, 72:131–143, 2014. </p>
<p>2) M. Brun, D. Colquitt, I. Jones, A. Movchan, and N. Movchan. Transformation cloaking and radial approximations for flexural waves in elastic plates. New Journal of Physics, 16(9):093020, 2014.</p>
<p>and </p>
<p>3) I. Jones, M. Brun, N. Movchan, and A. Movchan. Singular perturbations and cloaking illusions for elastic waves in membranes and kirchhoff plates. International Journal of Solids and Structures, 69:498–506, 2015.</p>
<p>the comparison between untransformed and transformed domain show an excellent agreement apart from the neighbourhood of the interface between untransformed and transformed domains. The difference between solutions in the reference and transformed domains was considered quantitatively in (1) through the scattering measure.<br />Anyway, the difference is small.</p>
<p>May you guess why?</p>
<p> </p>
<p>Best,</p>
<p>Michele Brun </p>
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</ul>Sun, 15 Nov 2020 18:54:23 +0000Michele Bruncomment 30524 at https://imechanica.orgShells
https://imechanica.org/comment/30489#comment-30489
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<p><em>In reply to <a href="https://imechanica.org/comment/30488#comment-30488">Re: Plates and Shells</a></em></p>
<div class="field field-name-comment-body field-type-text-long field-label-hidden"><div class="field-items"><div class="field-item even"><p>Dear Arash,</p>
<p>Thank you for you comment. I am looking for the definition of the p.d.e in (r,s) natural coordinates (or r,s,t) of the curved shell midsurface. You have cited the p.d.e in (x,y) cartesian coordinate of a plane plate which is developed in its plane. There are envelopes theory and cylindric envelopes theory where these domains are known as shells in finite elements. The finite elements is an efficient method which uses interpolations functions and different methods are used to program plates and shells where curved domains can be approximated with several plane plates or with curved shells but this is a numerical method. In this method a plate with membrane effects (quadrilateral element) + bending effects (plate element) is equivalent to a shell elemnt with five to six degrees of freedom.</p>
<p>Mohammed Lamine</p>
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</ul>Fri, 18 Sep 2020 21:04:41 +0000mohamedlaminecomment 30489 at https://imechanica.orgRe: Plates and Shells
https://imechanica.org/comment/30488#comment-30488
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<p><em>In reply to <a href="https://imechanica.org/comment/30487#comment-30487">Plates and Shells</a></em></p>
<div class="field field-name-comment-body field-type-text-long field-label-hidden"><div class="field-items"><div class="field-item even"><p>Dear Mohammed:</p>
<p>In Kirchhoff-Love plate theory shear deformations are ignored (this is a theory of thin plates). Assuming that energy of a shell depends on the first and the second fundamental forms of its mid surface one is implicitly ignoring shear deformations. To take into account shear deformations one would need to consider director fields at each point of the mid surface. Mindin (or Mindlin-Reissner) plate theory would be a special case of plates with director fields.</p>
<p>Arash</p>
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</ul>Thu, 17 Sep 2020 19:50:05 +0000Arash_Yavaricomment 30488 at https://imechanica.orgPlates and Shells
https://imechanica.org/comment/30487#comment-30487
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<p><em>In reply to <a href="https://imechanica.org/node/24589">Transformation Cloaking in Elastic Plates</a></em></p>
<div class="field field-name-comment-body field-type-text-long field-label-hidden"><div class="field-items"><div class="field-item even"><p>Dear Arash Yavari,</p>
<p>Golgoon is using in your cited paper plate elements and after he call them shell elements. The partial differential equation of plates is shown. </p>
<p>There are two theories for plates elements Kirchoff theory and Mindlin theory which includes the shear deformation energy effect. When the plate element has a great thickness, the Mindlin theory is used. The plate element is considered as a shell element when it has a small thickness and the theory of shell elements can also be used. Shell theory is developed with the midplane of the elements. Is there a relation between these two names in the cited developments ?</p>
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</ul>Thu, 17 Sep 2020 17:50:21 +0000mohamedlaminecomment 30487 at https://imechanica.org