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Ettore Barbieri's picture

Extremely Curved Cracks

 

The word "extreme" seems to be "trending" a lot these days, see the recent discussions on the new journal Extreme Mechanics Letters.

My collaborator Ruben Sevilla at Swansea and I were interested in very curved crack paths that develop in nature and have been replicated experimentally in thin films attached to elastic substrates.

farzad64's picture

Mesh free coupled with FEM

Hi All

 

I would like to know , If part of our model has geometrical complexity , is it reasonable to use meshfree method for that area ? does it fasten or ease the analysis ? how to couple it with FEM ? 

General query regarding MLPG method

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I have few general queries regarding MLPG meshfree method

1. Can the trial and test functions be taken same for solving a problem

2. In the problem if there are zones with different properties, for example different Coeffiencient of Permeability in the aquifers (Plan view-wise), how to handle the interface between the zones and assemble the global matrix

Ettore Barbieri's picture

DPhil Studentship at University of Oxford - funded by Rolls-Royce

Dear All,

we have a DPhil studentship available in the Solid Mechanics and Materials Engineering Group, within the Impact Engineering Laboratory led by Prof Nik Petrinic.

Meshfree Analysis of Elastic Bar

 This may be usefull for learning meshfree methods

 

Meshfree Analysis of Elastic Bar

 

 https://www.lap-publishing.com/catalog/details/store/gb/book/978-3-8443-...

regards.

Question about how to determine support radius..

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Hi, everyone.

I'm going to employ the meshfree method to analyze composite model.

But, I can't understand how to determine the support radius although I have read some references.

I will use the circular support domain.

Please explain how to determine the support radius.

Need help with understanding Thin Plate Splines as Radial Basis function for Meshfree simulation

I want to try applying TPS as the RBF for the simulation of groundwater flow and transport. but the i'm getting error because of zeros in diagonal elements in the global matrix. Please help with the shape function

How to deal with noisy data in a mesh free Galerkin method

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I'm currently working with a particle tracking velocimetry method, specifically trying to extract shear and vorticity data from the non-gridded velocity results. Of several methods used, the most efficient and accurate was based on a non-Sibsonian element free method. Unlike a more typical Galerkin problem which finds displacements by solving a PDE, this method uses the displacements of natural neighbors to find local flow gradients. 

CMMSE 2010 - Call for papers - Minisymposium on Sampling theory and meshfree methods

Please note the Minisymposium on Sampling theory and meshfree methods as a part of

the International Conference on Computational and Mathematical methods in Science and Engineering
CMMSE 2010, 26-30 June 2010, Almeria, Andalucia, Spain
--   http://gsii.usal.es/~CMMSE  --

 This mini-symposium aims to bring together such related areas of
mathematics and computational mechanics as Sampling Theory and Meshfree
Numerical Methods.

UK Newton Post-Doc Fellowship in Computational Mechanics

 
Dear All,

A new multi-million pound initiative to fund research collaborations and improve links between UK and overseas researchers has been launched.

The Newton International Fellowships aim to attract the most promising, early stage, post-doctoral researchers working overseas, who do not hold UK citizenship, in the fields of humanities, engineering, natural
and social sciences.

Ettore Barbieri's picture

The Future of Meshless Methods

I joined imechanica almost a year ago and I've been frequently following its interesting discussions, even the most animated ones. I think that a place like this is ideal to foster the exchange of ideas in the scientific community;

Moreover it is fantastic as a simple student like me can interact and easily ask questions to the most important researcher in the field of mechanics.

N. Sukumar's picture

Epi-convergence (max-ent bases), crack growth

In the attached paper, we have used Variational Analysis techniques (in particular, the theory of epi-convergence) to prove the continuity of maximum-entropy basis functions. In general, for non-smooth functionals, moving objectives and/or constraints, the tools of Newton-Leibniz calculus (gradient, point-convergence) prove to be insufficient; notions of set-valued mappings, set-convergence, etc., are required. Epi-convergence bears close affinity to Gamma- or Mosco-convergence (widely used in the mathematical treatment of martensitic phase transformations). The introductory material on convex analysis and epi-convergence had to be omitted in the revised version; hence the material is by no means self-contained. Here are a few more pointers that would prove to be helpful. Our main point of reference is Variational Analysis by RTR and RJBW; the Princeton Classic Convex Analysis by RTR provides the important tools in convex analysis. For convex optimization, the text Convex Optimization by SB and LV (available online) is excellent. The lecture slides provide a very nice (and gentle) introduction to some of the important concepts in convex analysis. The epigraphical landscape is very rich, and many of the applications would resonate with mechanicians.

On a different topic (non-planar crack growth), we have coupled the x-fem to a new fast marching algorithm. Here are couple of animations on growth of an inclined penny crack in tension (unstructured tetrahedral mesh with just over 12K nodes): larger `time' increment and smaller `time' increment. This is joint-work with Chopp, Bechet and Moes (NSF-OISE project). I will update this page as and when more relevant links are available.

N. Sukumar's picture

3. Meshfree methods and the patch test

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We are in the framework of small-strain two-dimensional linear elasticity without any body forces. Consider a domain that is discretized by a union of triangles and/or quadrilaterals (`patch of elements').  For C0 conforming approximations such as triangular/quadrilateral finite elements, the finite element approximation can exactly reproduce an arbitrary linear displacement field. Hence, if the exact solution is linear, then the finite element solution must match (within machine precision) the exact solution. In simple terms, passing the patch test for linear elasticity with standard conforming finite elements provides verification of one's implementation and is used to assess the same when new elements are proposed. For conforming elements, it is a sufficient condition for convergence (2nd order PDEs), and hence is the first problem that is solved when a new element/method is proposed. To carry out the patch test, the following steps are performed:

N. Sukumar's picture

2. Is a mesh required in meshfree methods?

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In meshfree (this is more in vogue than the term meshless) methods, two key steps need to be mentioned: (A) construction of the trial and test approximations; and (B) numerical evaluation of the weak form (Galerkin or Rayleigh-Ritz procedure) integrals, which lead to a linear system of equations (Kd = f). In meshfree Galerkin methods, the main departure from FEM is in (A): meshfree approximation schemes (linear combination of basis functions) are constructed independent of an underlying mesh (union of elements).

However, since a Galerkin method is typically used in solid mechanics applications, (B) arises and the weak form integrals need to be evaluated. Three main directions have been pursued to evaluate these integrals:

Zhigang Suo's picture

Where can I read about the basic ideas of the meshfree methods?

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For someone with a background in solid mechanics and finite element methods, where should he go to read up on the elementary ideas of the meshfree methods?

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