Invariant Hermitian finite elements for thin Kirchhoff rods. II: The linear three-dimensional case

2012 ◽  
Vol 213-216 ◽  
pp. 458-485 ◽  
Author(s):  
F. Armero ◽  
J. Valverde
Keyword(s):  
Finite Elements ◽  
Three Dimensional ◽  
Dimensional Case ◽  
Kirchhoff Rods

scholarly journals Solving the hourglass instability problem using rare mesh variation-difference schemes

2021 ◽  
Vol 2099 (1) ◽  
pp. 012003
Author(s):  
D T Chekmarev ◽  
Ya A Dawwas
Keyword(s):  
Finite Elements ◽  
High Efficiency ◽  
Three Dimensional ◽  
Dimensional Case ◽  
Two Dimensional ◽  
Explicit Difference Scheme ◽  
Slow Convergence ◽  
Instability Problem ◽  
Instability Effect ◽  
2D And 3D

Abstract The hourglass instability effect is characteristic of the Wilkins explicit difference scheme or similar schemes based on two-dimensional 4-node or three-dimensional 8-node finite elements with one integration point in the element. The hourglass effect is absent in schemes with cells in the form of simplexes (triangles in two-dimensional case, tetrahedrons in three-dimensional case). But they have another well-known drawback - slow convergence. One of the authors proposed a rare mesh scheme, in which elements in the form of a tetrahedron are located one at a time in the centers of the cells of a hexahedral grid. This scheme showed the absence “hourglass” effect and other drawbacks with high efficiency. This approach was further developed for solving 2D and 3D problems.

Topology optimization using non-conforming finite elements: three-dimensional case

2005 ◽  
Vol 63 (6) ◽  
pp. 859-875 ◽  
Author(s):  
Gang-Won Jang ◽  
Sangkeun Lee ◽  
Yoon Young Kim ◽  
Dongwoo Sheen
Keyword(s):  
Topology Optimization ◽  
Finite Elements ◽  
Three Dimensional ◽  
Dimensional Case

The Development of an Automatic Three-Dimensional Mesh Generator via Modified Ray Casting

1992 ◽  
Author(s):  
Cengiz Yeker ◽  
Ibrahim Zeid
Keyword(s):  
Finite Elements ◽  
Cell Structure ◽  
Three Dimensional ◽  
Ray Casting ◽  
Solid Object ◽  
Casting Technique ◽  
Element Size ◽  
A Cell ◽  
Conforming Meshes ◽  
Representation Scheme

Abstract A fully automatic three-dimensional mesh generation method is developed by modifying the well-known ray casting technique. The method is capable of meshing objects modeled using the CSG representation scheme. The input to the method consists of solid geometry information, and mesh attributes such as element size. The method starts by casting rays in 3D space to classify the empty and full parts of the solid. This information is then used to create a cell structure that closely models the solid object. The next step is to further process the cell structure to make it more succinct, so that the cells close to the boundary of the solid object can model the topology with enough fidelity. Moreover, neighborhood relations between cells in the structure are developed and implemented. These relations help produce better conforming meshes. Each cell in the cell structure is identified with respect to a set of pre-defined types of cells. After the identification process, a normalization process is developed and applied to the cell structure in order to ensure that the finite elements generated from each cell conform to each other and to other elements produced from neighboring cells. The last step is to mesh each cell in the structure with valid finite elements.

Thermal jet drilling of granite rock: a numerical 3D finite-element study

2021 ◽  
Vol 379 (2196) ◽  
pp. 20200128
Author(s):  
Timo Saksala ◽  
Reijo Kouhia ◽  
Ahmad Mardoukhi ◽  
Mikko Hokka
Keyword(s):  
Finite Elements ◽  
Numerical Study ◽  
Thermal Flux ◽  
Three Dimensional ◽  
Numerical Approach ◽  
Mass Scaling ◽  
Granite Rock ◽  
Fracture Dynamics ◽  
Rock Heterogeneity ◽  
Thermal Drilling

This paper presents a numerical study on thermal jet drilling of granite rock that is based on a thermal spallation phenomenon. For this end, a numerical method based on finite elements and a damage–viscoplasticity model are developed for solving the underlying coupled thermo-mechanical problem. An explicit time-stepping scheme is applied in solving the global problem, which in the present case is amenable to extreme mass scaling. Rock heterogeneity is accounted for as random clusters of finite elements representing rock constituent minerals. The numerical approach is validated based on experiments on thermal shock weakening effect of granite in a dynamic Brazilian disc test. The validated model is applied in three-dimensional simulations of thermal jet drilling with a short duration (0.2 s) and high intensity (approx. 3 MW m −2 ) thermal flux. The present numerical approach predicts the spalling as highly (tensile) damaged rock. Finally, it was shown that thermal drilling exploiting heating-forced cooling cycles is a viable method when drilling in hot rock mass. This article is part of the theme issue ‘Fracture dynamics of solid materials: from particles to the globe’.

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