Simulation of Large Deformations of Rubbers by the RKPM Method

<!DOCTYPE html> <html lang="en" dir="ltr"> <head>  <script async src="https://www.googletagmanager.com/gtag/js?id=G-P63WKM1TM1"></script> <script> window.dataLayer = window.dataLayer || []; function gtag(){dataLayer.push(arguments);} gtag('js', new Date()); gtag('config', 'G-P63WKM1TM1'); </script>  <script type="text/javascript" > (function(m,e,t,r,i,k,a){m[i]=m[i]||function(){(m[i].a=m[i].a||[]).push(arguments)}; m[i].l=1*new Date(); for (var j = 0; j < document.scripts.length; j++) {if (document.scripts[j].src === r) { return; }} k=e.createElement(t),a=e.getElementsByTagName(t)[0],k.async=1,k.src=r,a.parentNode.insertBefore(k,a)}) (window, document, "script", "https://mc.yandex.ru/metrika/tag.js", "ym"); ym(55165297, "init", { clickmap:false, trackLinks:true, accurateTrackBounce:true, webvisor:false }); </script> <noscript><div><img src="https://mc.yandex.ru/watch/55165297" style="position:absolute; left:-9999px;" alt="" /></div></noscript>    <title> Simulation of Large Deformations of Rubbers by the RKPM Method </title> <meta name="description" content=" Simulation of Large Deformations of Rubbers by the RKPM Method "> <meta name="keywords" content="RKPM, large deformations, transformation, essentialboundary conditions."> <meta name="viewport" content="width=device-width, initial-scale=1, minimum-scale=1, maximum-scale=1, user-scalable=no"> <meta charset="utf-8"> <meta name="citation_title" content=" Simulation of Large Deformations of Rubbers by the RKPM Method "> <meta name="citation_author" content="M. Foroutan"> <meta name="citation_author" content="H. Dalayeli"> <meta name="citation_author" content="M. Sadeghian"> <meta name="citation_publication_date" content="2007/02/23"> <meta name="citation_journal_title" content="International Journal of Mathematical and Computational Sciences"> <meta name="citation_volume" content="1"> <meta name="citation_issue" content="2"> <meta name="citation_firstpage" content="137"> <meta name="citation_lastpage" content="141"> <meta name="citation_pdf_url" content="https://publications.waset.org/5792/pdf"> <link href="https://cdn.waset.org/favicon.ico" type="image/x-icon" rel="shortcut icon"> <link href="https://cdn.waset.org/static/plugins/bootstrap-4.2.1/css/bootstrap.min.css" rel="stylesheet"> <link href="https://cdn.waset.org/static/plugins/fontawesome/css/all.min.css" rel="stylesheet"> <link href="https://cdn.waset.org/static/css/site.css?v=150220211555" rel="stylesheet"> </head> <body> <header> <div class="container"> <nav class="navbar navbar-expand-lg navbar-light"> <a class="navbar-brand" href="https://waset.org"> <img src="https://cdn.waset.org/static/images/wasetc.png" alt="Open Science Research Excellence" title="Open Science Research Excellence" /> </a> <button class="d-block d-lg-none navbar-toggler ml-auto" type="button" data-toggle="collapse" data-target="#navbarMenu" aria-controls="navbarMenu" aria-expanded="false" aria-label="Toggle navigation"> <span class="navbar-toggler-icon"></span> </button> <div class="w-100"> <div class="d-none d-lg-flex flex-row-reverse"> <form method="get" action="https://waset.org/search" class="form-inline my-2 my-lg-0"> <input class="form-control mr-sm-2" type="search" placeholder="Search Conferences" value="" name="q" aria-label="Search"> <button class="btn btn-light my-2 my-sm-0" type="submit"><i class="fas fa-search"></i></button> </form> </div> <div class="collapse navbar-collapse mt-1" id="navbarMenu"> <ul class="navbar-nav ml-auto align-items-center" id="mainNavMenu"> <li class="nav-item"> <a class="nav-link" href="https://waset.org/conferences" title="Conferences in 2024/2025/2026">Conferences</a> </li> <li class="nav-item"> <a class="nav-link" href="https://waset.org/disciplines" title="Disciplines">Disciplines</a> </li> <li class="nav-item"> <a class="nav-link" href="https://waset.org/committees" rel="nofollow">Committees</a> </li> <li class="nav-item dropdown"> <a class="nav-link dropdown-toggle" href="#" id="navbarDropdownPublications" role="button" data-toggle="dropdown" aria-haspopup="true" aria-expanded="false"> Publications </a> <div class="dropdown-menu" aria-labelledby="navbarDropdownPublications"> <a class="dropdown-item" href="https://publications.waset.org/abstracts">Abstracts</a> <a class="dropdown-item" href="https://publications.waset.org">Periodicals</a> <a class="dropdown-item" href="https://publications.waset.org/archive">Archive</a> </div> </li> <li class="nav-item"> <a class="nav-link" href="https://waset.org/page/support" title="Support">Support</a> </li> </ul> </div> </div> </nav> </div> </header> <main> <div class="container mt-4"> <div class="row"> <div class="col-md-9 mx-auto"> <form method="get" action="https://publications.waset.org/search"> <div id="custom-search-input"> <div class="input-group"> <i class="fas fa-search"></i> <input type="text" class="search-query" name="q" placeholder="Author, Title, Abstract, Keywords" value=""> <input type="submit" class="btn_search" value="Search"> </div> </div> </form> </div> </div> <div class="row mt-3"> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Commenced</strong> in January 2007</div> </div> </div> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Frequency:</strong> Monthly</div> </div> </div> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Edition:</strong> International</div> </div> </div> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Paper Count:</strong> 33093</div> </div> </div> </div> <div class="card publication-listing mt-3 mb-3"> <h5 class="card-header" style="font-size:.9rem"> Simulation of Large Deformations of Rubbers by the RKPM Method </h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=M.%20Foroutan">M. Foroutan</a>, <a href="https://publications.waset.org/search?q=H.%20Dalayeli"> H. Dalayeli</a>, <a href="https://publications.waset.org/search?q=M.%20Sadeghian"> M. Sadeghian</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>In this paper processes including large deformations of a rubber with hyperelastic material behavior are simulated by the RKPM method. Due to the loss of kronecker delta properties in the mesh less shape functions, the imposition of essential boundary conditions consumes significant CPU time in mesh free computations. In this work transformation method is used for imposition of essential boundary conditions. A RKPM material shape function is used in this analysis. The support of the material shape functions covers the same set of particles during material deformation and hence the transformation matrix is formed only once at the initial stages. A computer program in MATLAB is developed for simulations.</p> <iframe src="https://publications.waset.org/5792.pdf" style="width:100%; height:400px;" frameborder="0"></iframe> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=RKPM" title="RKPM">RKPM</a>, <a href="https://publications.waset.org/search?q=large%20deformations" title=" large deformations"> large deformations</a>, <a href="https://publications.waset.org/search?q=transformation" title=" transformation"> transformation</a>, <a href="https://publications.waset.org/search?q=essentialboundary%20conditions." title=" essentialboundary conditions."> essentialboundary conditions.</a> </p> <p class="card-text"><strong>Digital Object Identifier (DOI):</strong> <a href="https://doi.org/10.5281/zenodo.1061707" target="_blank">doi.org/10.5281/zenodo.1061707</a> </p> <a href="https://publications.waset.org/5792/simulation-of-large-deformations-of-rubbers-by-the-rkpm-method" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/5792/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/5792/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/5792/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/5792/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/5792/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/5792/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/5792/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/5792/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/5792/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/5792/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/5792.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">1893</span> </span> <p class="card-text"><strong>References:</strong></p> <p><br>[1] T. Belytschko, Y.Y.Lu, L.Gu ''Element-free Galerking methods", Internat. J. Numer. Methods in Eng., vol.37, 1994, pp. 229 -256. <br>[2] P. Lancaster, K. Salkauskas ''Surface Generated by Moving Least Squares Methods", Math. Comput., vol. 37, 1981, pp.141-158. <br>[3] W. K. Liu, S. Li, T. Belytschko, ''Moving Least Square Reproducing Kernel Methods (I) Methodology and Convergence" Comp. Methods. Appl. Mech. Eng., 1996. <br>[4] W. K. Liu, S. Jun, S. Li, J. Adee, T. Belytschko, "Reproducing Kernel Particle Methods for Structural Dynamics'', Internat.J.Numer.Methods Engrg., vol.38, 1995, pp.1655-1679. <br>[5] W. K. Liu, S. Jun, Y. F. Zhang, "Reproducing Kernel Particle Methods", Internat. J. Numer. Methods Fluids, vol.20, 1995, pp.1081-1106. <br>[6] J. S. Chen, C.Pan, C.T.Wu, W.K.Liu "Reproducing Kernel Particle Methodes Large Deformation analysis of non-linear structures'' Comp.Methods.Appl. Mech Eng., vol. 139, 1996, pp.195-227. <br>[7] J.S. Chen, H. P. Wang "New Boundary Condition Treatment in Mesh-free Computation of Contact Problems'', Compul.Methods Appl Mech. Engrg, vol.187, 2000, pp.441-468. <br>[8] J.S. Chen, C. Pan, C. T. Wu, "Large Deformation Analysis of Rubber based on a Reproducing Kernel Particle Method'', Compul. Mech., vol.19, 1997, pp.211-227. <br>[9] W.R.Penn "Volume chenges accompanying the extension of rubber'' Trans. Soc. Rheo.vol. 14, 1970, pp.509-517</p> </div> </div> </div> </main> <footer> <div id="infolinks" class="pt-3 pb-2"> <div class="container"> <div style="background-color:#f5f5f5;" class="p-3"> <div class="row"> <div class="col-md-2"> <ul class="list-unstyled"> About <li><a href="https://waset.org/page/support">About Us</a></li> <li><a href="https://waset.org/page/support#legal-information">Legal</a></li> <li><a target="_blank" rel="nofollow" href="https://publications.waset.org/static/files/WASET-16th-foundational-anniversary.pdf">WASET celebrates its 16th foundational anniversary</a></li> </ul> </div> <div class="col-md-2"> <ul class="list-unstyled"> Account <li><a href="https://waset.org/profile">My Account</a></li> </ul> </div> <div class="col-md-2"> <ul class="list-unstyled"> Explore <li><a href="https://waset.org/disciplines">Disciplines</a></li> <li><a href="https://waset.org/conferences">Conferences</a></li> <li><a href="https://waset.org/conference-programs">Conference Program</a></li> <li><a href="https://waset.org/committees">Committees</a></li> <li><a href="https://publications.waset.org">Publications</a></li> </ul> </div> <div class="col-md-2"> <ul class="list-unstyled"> Research <li><a href="https://publications.waset.org/abstracts">Abstracts</a></li> <li><a href="https://publications.waset.org">Periodicals</a></li> <li><a href="https://publications.waset.org/archive">Archive</a></li> </ul> </div> <div class="col-md-2"> <ul class="list-unstyled"> Open Science <li><a target="_blank" rel="nofollow" href="https://publications.waset.org/static/files/Open-Science-Philosophy.pdf">Open Science Philosophy</a></li> <li><a target="_blank" rel="nofollow" href="https://publications.waset.org/static/files/Open-Science-Award.pdf">Open Science Award</a></li> <li><a target="_blank" rel="nofollow" href="https://publications.waset.org/static/files/Open-Society-Open-Science-and-Open-Innovation.pdf">Open Innovation</a></li> <li><a target="_blank" rel="nofollow" href="https://publications.waset.org/static/files/Postdoctoral-Fellowship-Award.pdf">Postdoctoral Fellowship Award</a></li> <li><a target="_blank" rel="nofollow" href="https://publications.waset.org/static/files/Scholarly-Research-Review.pdf">Scholarly Research Review</a></li> </ul> </div> <div class="col-md-2"> <ul class="list-unstyled"> Support <li><a href="https://waset.org/page/support">Support</a></li> <li><a href="https://waset.org/profile/messages/create">Contact Us</a></li> <li><a href="https://waset.org/profile/messages/create">Report Abuse</a></li> </ul> </div> </div> </div> </div> </div> <div class="container text-center"> <hr style="margin-top:0;margin-bottom:.3rem;"> <a href="https://creativecommons.org/licenses/by/4.0/" target="_blank" class="text-muted small">Creative Commons Attribution 4.0 International License</a> <div id="copy" class="mt-2">© 2024 World Academy of Science, Engineering and Technology</div> </div> </footer> <a href="javascript:" id="return-to-top"><i class="fas fa-arrow-up"></i></a> <div class="modal" id="modal-template"> <div class="modal-dialog"> <div class="modal-content"> <div class="row m-0 mt-1"> <div class="col-md-12"> <button type="button" class="close" data-dismiss="modal" aria-label="Close"><span aria-hidden="true">×</span></button> </div> </div> <div class="modal-body"></div> </div> </div> </div> <script src="https://cdn.waset.org/static/plugins/jquery-3.3.1.min.js"></script> <script src="https://cdn.waset.org/static/plugins/bootstrap-4.2.1/js/bootstrap.bundle.min.js"></script> <script src="https://cdn.waset.org/static/js/site.js?v=150220211556"></script> <script> jQuery(document).ready(function() { /*jQuery.get("https://publications.waset.org/xhr/user-menu", function (response) { jQuery('#mainNavMenu').append(response); });*/ jQuery.get({ url: "https://publications.waset.org/xhr/user-menu", cache: false }).then(function(response){ jQuery('#mainNavMenu').append(response); }); }); </script> </body> </html>

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Simulation of Large Deformations of Rubbers by the RKPM Method