Thesis (MSc)--Stellenbosch University, 2011. / ENGLISH ABSTRACT: FLAC3D is a three-dimensional explicit nite difference program for solving a variety of
solid mechanics problems, both linear and non-linear. The development of the algorithm
and its initial implementation were performed by Itasca Consulting Group Inc. The main
idea of the algorithm is to discritise the domain of interest into a Lagrangian grid where
each cell represents an element of the material. Each cell can then deform according to a
prescribed stress/strain law together with the equations of motion. An in-depth study of
the algorithm was performed and implemented in Java. During the implementation, it was
observed that the type of boundary conditions typically used has a major in uence on the
accuracy of the results, especially when boundaries are close to regions with large stress
variations, such as in mining excavations. To improve the accuracy of the algorithm, a
new type of boundary condition was developed where the FLAC3D domain is embedded
in a linear elastic material, named the Boundary Node Shell (BNS). Using the BNS
shows a signi cant improvement in results close to excavations. The FLAC algorithm is
also quite amendable to paralellization and a multi-threaded version that makes use of multiple Central Processing Unit (CPU) cores was developed to optimize the speed of the
algorithm. The nal outcome is new non-commercial Java source code (JFLAC) which
includes the Boundary Node Shell (BNS) and shared memory parallelism over and above
the basic FLAC3D algorithm. / AFRIKAANSE OPSOMMING: FLAC3D is 'n eksplisiete eindige verskil program wat 'n verskeidenheid liniêre en nieliniêre soliede meganika probleme kan oplos. Die oorspronklike algoritme en die implimentasies
daarvan was deur Itasca Consulting Group Inc. toegepas. Die hoo dee van die
algoritme is om 'n gebied te diskritiseer deur gebruik te maak van 'n Lagrangese rooster,
waar elke sel van die rooster 'n element van die rooster materiaal beskryf. Elke sel kan
dan vervorm volgens 'n sekere spannings/vervormings wet. 'n Indiepte ondersoek van
die algoritme was uitgevoer en in Java geïmplimenteer. Tydens die implementering was
dit waargeneem dat die grense van die rooster 'n groot invloed het op die akkuraatheid
van die resultate. Dit het veral voorgekom in areas waar stress konsentrasies hoog is,
gewoonlik naby areas waar myn uitgrawings gemaak is. Dit het die ontwikkelling van 'n
nuwe tipe rand kondisie tot gevolg gehad, sodat die akkuraatheid van die resultate kon
verbeter. Die nuwe rand kondisie, genaamd die Grens Node Omhulsel (GNO), aanvaar
dat die gebied omring is deur 'n elastiese materiaal, wat veroorsaak dat die grense van die
gebied 'n elastiese reaksie het op die stress binne die gebied. Die GNO het 'n aansienlike verbetering in die resultate getoon, veral in areas naby myn uitgrawings. Daar was ook
waargeneem dat die FLAC algoritme parralleliseerbaar is en het gelei tot die implentering
van 'n multi-SVE weergawe van die sagteware om die spoed van die algoritme te optimeer.
Die nale uitkomste is 'n nuwe nie-kommersiële Java weergawe van die algoritme
(JFLAC), wat die implimentering van die nuwe GNO randwaardekondisie insluit, asook
toelaat vir die gebruik van multi- Sentrale Verwerkings Eenheid (SVE) as 'n verbetering
op die basiese FLAC3D algoritme.
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:sun/oai:scholar.sun.ac.za:10019.1/17957 |
| Date | 12 1900 |
| Creators | Basson, Gysbert |
| Contributors | Smit, Francois, Stellenbosch University. Faculty of Science. Dept. of Mathematical Sciences. Applied Mathematics Division |
| Publisher | Stellenbosch : Stellenbosch University |
| Source Sets | South African National ETD Portal |
| Language | en_ZA |
| Detected Language | Unknown |
| Type | Thesis |
| Format | 110 p. : ill. |
| Rights | Stellenbosch University |
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