Area Bubble Functions for Stabilization of Mixed Finite Tetrahedral Elements

2009 ◽  
Author(s):  
R. Mahnken ◽  
I. Caylak ◽  
G. Laschet
Keyword(s):  
Tetrahedral Elements ◽  
Bubble Functions

Stability and Convergence of Two Three-Field Finite Element Formulations for Elasticity

2014 ◽  
Vol 14 (3) ◽  
pp. 305-316
Author(s):  
A. Chama ◽  
B. D. Reddy
Keyword(s):  
Saddle Point Problem ◽  
Three Dimensions ◽  
Stability And Convergence ◽  
Point Problem ◽  
Well Posedness ◽  
Tetrahedral Elements ◽  
Enhanced Strain ◽  
Uniformly Convergent ◽  
Bubble Functions ◽  
Special Case

Abstract.In this work analyses are carried out to verify the well-posedness of two three-field formulations for linear elasticity that have been shown to work well in practice, but for which analyses are absent. Both are formulated in three dimensions on tetrahedral elements. The first has as primary unknowns the displacement, pressure, and dilatation, and the second is a formulation with primary unknowns the displacement, pressure and enhanced strain, with the space of enhanced strains spanned by functions that are bubble functions on a surface of the element. It is shown that the first-mentioned formulation is a special case of a general three-field formulation, for which well-posedness conditions have been established. These conditions are used here to show that the pressure-dilatation-displacement formulation is uniformly convergent in the incompressible limit. The pressure-enhanced strain-displacement formulation is not amenable to such an approach; instead, it is reformulated in the form of a standard discrete saddle point problem, and the uniform convergence of the formulation established directly by verifying the ellipticity and inf-sup conditions.

scholarly journals 3D Simulation of acoustic waves propagating through porous domain using PUFEM tetrahedral elements

2020 ◽  
Vol 1605 ◽  
pp. 012016
Author(s):  
Mingming Yang ◽  
Cyrille Breard ◽  
Yipeng Cen ◽  
Jean-Daniel Chazot
Keyword(s):  
Acoustic Waves ◽  
3D Simulation ◽  
Tetrahedral Elements ◽  
Porous Domain

Tetrahedral elements for fluid flow

1992 ◽  
Vol 33 (6) ◽  
pp. 1251-1267 ◽  
Author(s):  
F. H. Bertrand ◽  
M. R. Gadbois ◽  
P. A. Tanguy
Keyword(s):  
Fluid Flow ◽  
Tetrahedral Elements

On the Reduction of the Pre-Processing Effort and the Application of a Contact Meshing Approach for Complex Jet Engine Component Assemblies

2014 ◽  
Author(s):  
W. Hufenbach ◽  
A. Hornig ◽  
H. Böhm ◽  
A. Langkamp ◽  
A. Keskin
Keyword(s):  
Significant Proportion ◽  
Work Effort ◽  
Positive Effects ◽  
Tetrahedral Elements ◽  
Automated Method ◽  
Geometry Decomposition ◽  
Hexahedral Meshes ◽  
Complex Structural ◽  
Processing Effort ◽  
Pressure Compressor

A significant proportion of the work effort for finite element (FE) analysis is spent for pre-processing activities, especially for complex structural components and component assemblies. An exclusive use of hexahedron (hex) elements increases the meshing effort substantially compared to tetrahedral elements. An automated method to generate high quality hexahedral meshes for an arbitrary geometry does not exist. In this work, commercially available FE software tools for meshing were investigated with the focus on an advantageous pre-processing effort. The evaluation showed that the software package NX (Siemens PLM Software) offers robust advanced semiautomatic hex meshing capabilities. Furthermore, a Contact Meshing Approach (CMA) was elaborated to reduce the effort of the challenging and time-consuming geometry decomposition significantly. Using the example of an intermediate pressure compressor it can be shown that the pre-processing effort time can be reduced up to 75%. Due to the independent meshes, element transitions in the geometry become redundant. This results in lower total element numbers and higher mesh qualities and subsequently leads to more efficient calculations. Moreover, the increased element quality has positive effects on the result quality.

Elastic solution of a polyhedral particle with a polynomial eigenstrain and particle discretization

2021 ◽  
pp. 1-35
Author(s):  
Chunlin Wu ◽  
Liangliang Zhang ◽  
Huiming Yin
Keyword(s):  
Taylor Series ◽  
Three Dimensional ◽  
Stress Singularity ◽  
Elastic Field ◽  
Analytical Form ◽  
Tetrahedral Elements ◽  
Equivalent Inclusion Method ◽  
Equivalent Inclusion ◽  
Eshelby’S Tensor ◽  
Domain Discretization

Abstract The paper extends the recent work (JAM, 88, 061002, 2021) of the Eshelby's tensors for polynomial eigenstrains from a two dimensional (2D) to three dimensional (3D) domain, which provides the solution to the elastic field with continuously distributed eigenstrain on a polyhedral inclusion approximated by the Taylor series of polynomials. Similarly, the polynomial eigenstrain is expanded at the centroid of the polyhedral inclusion with uniform, linear and quadratic order terms, which provides tailorable accuracy of the elastic solutions of polyhedral inhomogeneity by using Eshelby's equivalent inclusion method. However, for both 2D and 3D cases, the stress distribution in the inhomogeneity exhibits a certain discrepancy from the finite element results at the neighborhood of the vertices due to the singularity of Eshelby's tensors, which makes it inaccurate to use the Taylor series of polynomials at the centroid to catch the eigenstrain at the vertices. This paper formulates the domain discretization with tetrahedral elements to accurately solve for eigenstrain distribution and predict the stress field. With the eigenstrain determined at each node, the elastic field can be predicted with the closed-form domain integral of Green's function. The parametric analysis shows the performance difference between the polynomial eigenstrain by the Taylor expansion at the centroid and the 𝐶0 continuous eigenstrain by particle discretization. Because the stress singularity is evaluated by the analytical form of the Eshelby's tensor, the elastic analysis is robust, stable and efficient.

Tetrahedral elements in self-consistent parallel 3D Monte Carlo simulations of MOSFETs

2008 ◽  
Vol 7 (3) ◽  
pp. 201-204 ◽  
Author(s):  
M. Aldegunde ◽  
A. J. García-Loureiro ◽  
A. Martinez ◽  
K. Kalna
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Tetrahedral Elements ◽  
Self Consistent ◽  
3D Monte Carlo

Establishing 3D Mandible FEA Model via Clinical CT Images

2010 ◽  
Vol 44-47 ◽  
pp. 1952-1956 ◽  
Author(s):  
Wen Zheng Wu ◽  
Ya Dong Chen ◽  
Kun Peng Cui ◽  
Xing Jun Qin ◽  
Wan Shan Wang
Keyword(s):  
3D Model ◽  
Biomechanical Analysis ◽  
Mandible Reconstruction ◽  
Element Analysis ◽  
Boundary Constraints ◽  
Reconstruction Surgery ◽  
Tetrahedral Meshes ◽  
Fea Model ◽  
Tetrahedral Elements ◽  
Force Range

Aiming at the filature of titanium plates and screws after defective mandible reconstruction surgery, a method named Finite Element Analysis （FEA）was conducted in this paper through FEA software Abaqus with which a 3D model of defective mandible was established. The mandible 3D model was input into the Magics and remeshed. The mandible model was output in the format of .inp file from the Magics and import to Abaqus for converting from triangular meshes to tetrahedral meshes. The tetrahedral meshes totally had 71057 tetrahedral elements and 10720 nodes. The boundary constraints of the mandible 3D model were arranged. The force was applied separately in the direction of vertical, 15° and 30° with the occluding plane (teeth force range when occluding) to analyze the force. The mandible 3D model was established and prepared to be done a biomechanical analysis.

Sign in / Sign up

Export Citation Format

Share Document