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https://imechanica.org/node/469
Comments for "Where can I read about the basic ideas of the meshfree methods?"enwhere can I find that book
https://imechanica.org/comment/24854#comment-24854
<a id="comment-24854"></a>
<p><em>In reply to <a href="https://imechanica.org/comment/7441#comment-7441">Mesh Free Methods: Moving Beyond the Finite Element Method</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>
where can I find that book ?... if you kindly post the link then it will be of much help.
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abby_dutt
</p>
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</ul>Fri, 23 Aug 2013 08:23:10 +0000abbyduttcomment 24854 at https://imechanica.orgAbsolutely, the books of
https://imechanica.org/comment/14571#comment-14571
<a id="comment-14571"></a>
<p><em>In reply to <a href="https://imechanica.org/node/469">Where can I read about the basic ideas of the meshfree methods?</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>
Absolutely, the books of the Prof. G.R. Lui are a very important guide to understand MFREE METHODS.
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</p>
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</ul>Tue, 11 May 2010 17:58:36 +0000hkm.mecomment 14571 at https://imechanica.orglink to introductory MLS tutorial
https://imechanica.org/comment/10760#comment-10760
<a id="comment-10760"></a>
<p><em>In reply to <a href="https://imechanica.org/node/469">Where can I read about the basic ideas of the meshfree methods?</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>
Hello Everyone,
</p>
<p>
Beginners may like the introductory document I put together regarding moving least squares basis functions (MLS). These basis functions are common in meshfree methods. In the document I include definitions of common terminology, the derivation of MLS basis functions, derivation of first derivatives, and derivation of 2nd derivatives.
</p>
<p>
Here is the link to the document <a href="http://people.wallawalla.edu/~louie.yaw/otherfiles/introTo_MLS.pdf">http://people.wallawalla.edu/~louie.yaw/otherfiles/introTo_MLS.pdf</a>
</p>
<p>
regards,
</p>
<p>
Louie
</p>
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</ul>Thu, 07 May 2009 20:56:20 +0000yawloucomment 10760 at https://imechanica.orgMesh Free Methods: Moving Beyond the Finite Element Method
https://imechanica.org/comment/7441#comment-7441
<a id="comment-7441"></a>
<p><em>In reply to <a href="https://imechanica.org/node/469">Where can I read about the basic ideas of the meshfree methods?</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><span> If you are searching for a book, this book seems to be one of the best choices. G.R. Liu is a famous face in meshfree methods and the book is very attractive and integrative.</span><span></span></p>
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</ul>Tue, 13 May 2008 22:27:28 +0000RoozbehSanaeicomment 7441 at https://imechanica.orgRecent Meshfree review paper
https://imechanica.org/comment/7435#comment-7435
<a id="comment-7435"></a>
<p><em>In reply to <a href="https://imechanica.org/comment/477#comment-477">Hello Zhigang,
You could</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 Zhigang,</p>
<p>You could also take a look at our recent meshfree review paper, which is written from a different angle to that of Thomas-Peter Fries, which you can find here: </p>
<p> <a href="http://dx.doi.org/10.1016/j.matcom.2008.01.003">doi:10.1016/j.matcom.2008.01.003</a></p>
<p>Our goal is to present global-weak form based methods in a very simple way by explaining their implementation, through a very simple MATLAB code that we will send you.</p>
<p> Let me know if you need more help, I or someone in my group will be happy to provide it,</p>
<p>Stephane </p>
<p> </p>
<p>Dr Stephane Bordas</p>
<p><a href="http://people.civil.gla.ac.uk/~bordas">http://people.civil.gla.ac.uk/~bordas</a> </p>
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</ul>Tue, 13 May 2008 16:52:47 +0000Stephane Bordascomment 7435 at https://imechanica.orglrpim matlab code
https://imechanica.org/comment/6670#comment-6670
<a id="comment-6670"></a>
<p><em>In reply to <a href="https://imechanica.org/node/469">Where can I read about the basic ideas of the meshfree methods?</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>
</p>
<p>
hello to every body
</p>
<p>
My thesis is about the lrpim method apllying to the 2d beam analysis. but i could not construct the codes in matlab.if anyone has this codes written in matlab and send to the this mail I would be too happy. thank you
</p>
<p>
<a href="mailto:mahmutpekedis@hotmail.com">mahmutpekedis@hotmail.com</a>
</p>
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</ul>Sat, 01 Mar 2008 16:05:03 +0000cokosklovakyacomment 6670 at https://imechanica.org
hello to every
https://imechanica.org/comment/6669#comment-6669
<a id="comment-6669"></a>
<p><em>In reply to <a href="https://imechanica.org/node/469">Where can I read about the basic ideas of the meshfree methods?</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>
</p>
<p>
hello to every body
</p>
<p>
My thesis is about the lrpim method apllying to the 2d beam analysis. but i could not construct the codes in matlab.if anyone has this codes written in matlab and send to the this mail I would be too happy. thank you
</p>
<p>
<a href="mailto:mahmutpekedis@hotmail.com">mahmutpekedis@hotmail.com</a>
</p>
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</ul>Sat, 01 Mar 2008 16:04:47 +0000cokosklovakyacomment 6669 at https://imechanica.orgHello Zhigang,
You could
https://imechanica.org/comment/477#comment-477
<a id="comment-477"></a>
<p><em>In reply to <a href="https://imechanica.org/node/469">Where can I read about the basic ideas of the meshfree methods?</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>Hello Zhigang,</p>
<p>You could find in, <a href="http://www.civil.gla.ac.uk/~bordas/phu.html">http://www.civil.gla.ac.uk/~bordas/phu.html</a>, my simple Matlab codes for EFG, enriched EFG for one and two dimentions problems.</p>
<p>By contacting Stephane Bordas at <a href="mailto:stephane.bordas@gmail.com">stephane.bordas@gmail.com</a>, you are also be able to get a document in meshless methods with details on computer implementation.</p>
<p>Phu </p>
<p> </p>
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</ul>Sun, 10 Dec 2006 13:30:01 +0000phunguyencomment 477 at https://imechanica.orgBasics on meshfree methods
https://imechanica.org/comment/323#comment-323
<a id="comment-323"></a>
<p><em>In reply to <a href="https://imechanica.org/node/469">Where can I read about the basic ideas of the meshfree methods?</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>Zhigang,</p>
<p>I think the best source for an introduction (not from the very basics though) to meshfree methods is via some of the review articles. The paper by Belytschko et al. (1996) and the report by Fries and Mathies (2004) are well-written and serve as good introductions; in my <a href="/node/402" target="_blank" title="Meshfree approximation schemes ...">earlier post</a> I have provided links to these articles. Many of the monographs on meshfree methods that are available might not be sufficiently detailed and gentle to be readily accessible to a beginner who is familiar with finite elements. I'll try to provide in brief the essentials as I see it:</p>
<p>1. In moving from FEM to meshfree approximations, it is beneficial to think in terms of approximating a function as a linear combination of <em>basis functions. </em>In FEM, <em>shape functions</em> are more commonly used---they are the local restriction of basis functions to an element. In meshfree methods, the basis functions are constructed by using the nodal coordinates and by assigning some means to define neighbor relationships (known as <em>basis function supports</em>). For instance, particular choices are made in Moving Least Squares (MLS) or natural neighbor interpolants (Voronoi diagram).</p>
<p>2. Once the approximation is defined, then a standard Galerkin method is adopted (<em>plain vanilla version</em>). As <a href="/node/467" target="_blank" title="If I have meshfree shape functions . . . ">John</a> has alluded to in his post, depending on the particular meshfree basis function that is under consideration, some additional modifications may be required to correctly impose essential boundary conditions. This applies to second-order PDEs (elasticity) as well as higher-order PDEs (thin-plate problems or gradient elasticity).</p>
<p>3. Assuming that 1. and 2. have been taken care of, then the next step is numerical integration of the weak form integrals. Unlike FEM, there is no mapping involved to compute meshfree basis functions. Typically, a higher-order Gaussian quadrature rule is used to compute the weak form. So, in essence a <em>mesh structure</em> is required in this case for the purpose of numerical integration. The derivatives of the basis functions are required (strain-displacement matrix, <strong>B</strong>), which are directly evaluated. Note that each Gauss point <strong>x</strong> may now have a variable number of neighbors; this is unlike the FEM where for each Gauss point inside an element (say a triangle), the number of neighbors is always three and hence the benefits of constructing an element stiffness matrix in the FEM.</p>
<p>4. Once modifications in the system matrices have been performed (to impose essential boundary conditions, if need be), then the linear system is solved: <strong>Ku </strong>= <strong>f</strong></p>
<p>5. The approximation at any point is determined via: <strong>u</strong>h(<strong>x</strong>)= φa(<strong>x</strong>)<strong>u</strong>a (sum on <em>a</em>).</p>
<p>Of course, I have skipped many intermediate steps. So, please feel free to edit this response and fix (subscript/superscript is mangled) as well as improve my remarks.</p>
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</ul>Tue, 21 Nov 2006 08:01:10 +0000N. Sukumarcomment 323 at https://imechanica.org