Browsing by Subject "mesh-free methods"

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Access status: Open Access ,
Uogólnienia metody elementów skończonych w inżynierskich symulacjach numerycznych ośrodka nieciągłego i dyskretnego
(Wydawnictwa AGH, 2010) Jakubowski, Jacek
Traditional finite element method is efficient and universal numerical simulation method, and implemented with many available software packages, also easy to use. Applied to simulations of discontinuities and discontinuous rock mass, it has got serials limitations. For the last several years some generalizations of this method have been developed with the use of new approximation techniques, particularly partition of unity. As a result of these developments mesh-free methods (MFree), enriched approximation methods (GFEM, XFEM) and numerical manifold method has been developed, basing on finite element method and finite difference method approaches. All the three groups of methods listed above have ability to model discontinuities without challenging and expensive remeshing. All of them can simulate continuous medium, discontinuous medium and model disintegration within a single numerical schema (each of them within different one). Completed with contact detection algorithms, they meet criteria of discrete element method. The above mentioned methods are still in their very early stages of development and many theoretical and practical problems need to be solved before they will be used in Civil Engineering and Rock Mechanics for practical applications. In the future, due to their advantages, they can offer an alternative for finite element method, distinct element method and other popular engineering simulation methods. The article presents the above mentioned methods and their possible applications for discontinuous and discrete medium simulation, particularly for the simulation of discontinuous rock mass.