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Tetrahedral Elements (tetrahedral + element)
Kinds of Tetrahedral Elements Selected AbstractsAdvanced 4-node tetrahedronsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 12 2006Rong Tian Abstract Tetrahedral elements are indispensable to complex finite element structural analysis. Two existing and two newly developed advanced 4-node tetrahedrons are studied in this paper. The existing elements that use complicated displacement fields are significantly simplified. The spurious zero-energy modes typical of all these elements are identified to be rigid-body-alike modes and are found to be naturally suppressible, making it possible to avoid any stabilization techniques and unknown parameters in formulation. Through the simplified form, we connect these four tetrahedrons and view them in a general framework of the partition-of-unity-based approximation. This general view allows us to reveal many promising features of the newly developed tetrahedrons by comparing them with their existing counterparts: the newly developed tetrahedrons have straightforward formulation, no unsuppressed zero-energy modes, no stabilization required, no unknown parameters contained, and a high consistency in implementation, in addition to good accuracy and extremely straightforward mesh generation. Copyright © 2006 John Wiley & Sons, Ltd. [source] Non-locking tetrahedral finite element for surgical simulationINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 7 2009Grand Roman Joldes Abstract To obtain a very fast solution for finite element models used in surgical simulations, low-order elements, such as the linear tetrahedron or the linear under-integrated hexahedron, must be used. Automatic hexahedral mesh generation for complex geometries remains a challenging problem, and therefore tetrahedral or mixed meshes are often necessary. Unfortunately, the standard formulation of the linear tetrahedral element exhibits volumetric locking in case of almost incompressible materials. In this paper, we extend the average nodal pressure (ANP) tetrahedral element proposed by Bonet and Burton for a better handling of multiple material interfaces. The new formulation can handle multiple materials in a uniform way with better accuracy, while requiring only a small additional computation effort. We discuss some implementation issues and show how easy an existing Total Lagrangian Explicit Dynamics algorithm can be modified in order to support the new element formulation. The performance evaluation of the new element shows the clear improvement in reaction forces and displacements predictions compared with the ANP element in case of models consisting of multiple materials. Copyright © 2008 John Wiley & Sons, Ltd. [source] A uniform nodal strain tetrahedron with isochoric stabilizationINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 4 2009M. W. Gee Abstract A stabilized node-based uniform strain tetrahedral element is presented and analyzed for finite deformation elasticity. The element is based on linear interpolation of a classical displacement-based tetrahedral element formulation but applies nodal averaging of the deformation gradient to improve mechanical behavior, especially in the regime of near-incompressibility where classical linear tetrahedral elements perform very poorly. This uniform strain approach adopted here exhibits spurious modes as has been previously reported in the literature. We present a new type of stabilization exploiting the circumstance that the instability in the formulation is related to the isochoric strain energy contribution only and we therefore present a stabilization based on an isochoric,volumetric splitting of the stress tensor. We demonstrate that by stabilizing the isochoric energy contributions only, reintroduction of volumetric locking through the stabilization can be avoided. The isochoric,volumetric splitting can be applied for all types of materials with only minor restrictions and leads to a formulation that demonstrates impressive performance in examples provided. Copyright © 2008 John Wiley & Sons, Ltd. [source] Generalized nodes and high-performance elementsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 15 2005Rong Tian Abstract The paper concerns the development of robust and high accuracy finite elements with only corner nodes using a partition-of-unity-based finite-element approximation. Construction of the partition-of-unity-based approximation is accomplished by a physically defined local function of displacements. A 4-node quadratic tetrahedral element and a 3-node quadratic triangular element are developed. Eigenvalue analysis shows that linear dependencies in the partition-of-unity-based finite-element approximation constructed for the new elements are eliminable. Numerical calculations demonstrate that the new elements are robust, insensitive to mesh distortion, and offer quadratic accuracy, while also keeping mesh generation extremely simple. Copyright © 2005 John Wiley & Sons, Ltd. [source] Fringe element reconstruction for front tracking for three-dimensional incompressible flow analysisINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 6 2005Du-Soon Choi Abstract Fringe element reconstruction technique for tracking the free surface in three-dimensional incompressible flow analysis was developed. The flow field was calculated by the mixed formulation based on a four-node tetrahedral element with a bubble function at the centroid (P1+/P1). Since an Eulerian approach was employed in this study, the flow front interface was advected by the flow through a fixed mesh. For accurate modelling of interfacial movement, a fringe element reconstruction method developed can provide not only an accurate treatment of material discontinuity but also surface tension across the interface. The effect of surface tension was modelled by imposing tensile stress directly on the constructed surface elements at the flow front interface. To verify the numerical approach developed, the developed algorithm was applied to two examples whose solutions are available in references. Good agreement was obtained between the simulation results and these solutions. Copyright © 2005 John Wiley & Sons, Ltd. [source] Implementation of the finite element method in the three-dimensional discontinuous deformation analysis (3D-DDA)INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 15 2008Roozbeh Grayeli Abstract A modified three-dimensional discontinuous deformation analysis (3D-DDA) method is derived using four-noded tetrahedral elements to improve the accuracy of current 3D-DDA algorithm in practical applications. The analysis program for the modified 3D-DDA method is developed in a C++ environment and its accuracy is illustrated through comparisons with several analytical solutions that are available for selected problems. The predicted solutions for these problems using the modified 3D-DDA approach all show satisfactory agreement with the corresponding analytical results. Results presented in this paper demonstrate that the modified 3D-DDA method with discontinuous modeling capabilities offers a useful computational tool to determine stresses and deformations in practical problems involving fissured elastic media with reasonable accuracy. Copyright © 2008 John Wiley & Sons, Ltd. [source] Sloshing analysis of a liquid storage container using level set X-FEMINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 4 2009Toshio Nagashima Abstract The extended finite element method (X-FEM), in conjunction with the level set method, is applied to sloshing analysis of a rigid container filled with liquid. The governing equations for liquid with a free surface based on the potential flow theory are discretized using the framework of level set X-FEM. Once the space domain of a container is modeled by tetrahedral elements, sloshing analysis for arbitrary liquid levels and configurations can be performed without remeshing. Natural frequencies of free surface sloshing motion in rigid containers of various shapes were computed by the proposed method and the results were compared with those obtained by theoretical solutions and experiments. The proposed method was demonstrated to perform sloshing analysis efficiently for rigid containers with various liquid levels and configurations. Copyright © 2008 John Wiley & Sons, Ltd. [source] A parallel implicit/explicit hybrid time domain method for computational electromagneticsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 8 2009Z. Q. Xie Abstract The numerical solution of Maxwell's curl equations in the time domain is achieved by combining an unstructured mesh finite element algorithm with a cartesian finite difference method. The practical problem area selected to illustrate the application of the approach is the simulation of three-dimensional electromagnetic wave scattering. The scattering obstacle and the free space region immediately adjacent to it are discretized using an unstructured mesh of linear tetrahedral elements. The remainder of the computational domain is filled with a regular cartesian mesh. These two meshes are overlapped to create a hybrid mesh for the numerical solution. On the cartesian mesh, an explicit finite difference method is adopted and an implicit/explicit finite element formulation is employed on the unstructured mesh. This approach ensures that computational efficiency is maintained if, for any reason, the generated unstructured mesh contains elements of a size much smaller than that required for accurate wave propagation. A perfectly matched layer is added at the artificial far field boundary, created by the truncation of the physical domain prior to the numerical solution. The complete solution approach is parallelized, to enable large-scale simulations to be effectively performed. Examples are included to demonstrate the numerical performance that can be achieved. Copyright © 2009 John Wiley & Sons, Ltd. [source] A uniform nodal strain tetrahedron with isochoric stabilizationINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 4 2009M. W. Gee Abstract A stabilized node-based uniform strain tetrahedral element is presented and analyzed for finite deformation elasticity. The element is based on linear interpolation of a classical displacement-based tetrahedral element formulation but applies nodal averaging of the deformation gradient to improve mechanical behavior, especially in the regime of near-incompressibility where classical linear tetrahedral elements perform very poorly. This uniform strain approach adopted here exhibits spurious modes as has been previously reported in the literature. We present a new type of stabilization exploiting the circumstance that the instability in the formulation is related to the isochoric strain energy contribution only and we therefore present a stabilization based on an isochoric,volumetric splitting of the stress tensor. We demonstrate that by stabilizing the isochoric energy contributions only, reintroduction of volumetric locking through the stabilization can be avoided. The isochoric,volumetric splitting can be applied for all types of materials with only minor restrictions and leads to a formulation that demonstrates impressive performance in examples provided. Copyright © 2008 John Wiley & Sons, Ltd. [source] Localized remeshing techniques for three-dimensional metal forming simulations with linear tetrahedral elementsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 5 2006Il-Heon Son Abstract The localized remeshing technique for three-dimensional metal forming simulations is proposed based on a mixed finite element formulation with linear tetrahedral elements in the present study. The numerical algorithm to generate linear tetrahedral elements is developed for finite element analyses using the advancing front technique with local optimization method which keeps the advancing fronts smooth. The surface mesh generation using mesh manipulations of the boundary elements of the old mesh system was made to improve mesh quality of the boundary surface elements, resulting in reduction of volume change in forming simulations. The mesh quality generated was compared with that obtained from the commercial CAD package for the complex geometry like lumbar. The simulation results of backward extrusion and bevel gear and spider forgings indicate that the currently developed simulation technique with the localized remeshing can be used effectively to simulate the three-dimensional forming processes with a reduced computation time. Copyright © 2006 John Wiley & Sons, Ltd. [source] Hierarchic finite element bases on unstructured tetrahedral meshesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 14 2003Mark Ainsworth Abstract The problem of constructing hierarchic bases for finite element discretization of the spaces H1, H(curl), H(div) and L2 on tetrahedral elements is addressed. A simple and efficient approach to ensuring conformity of the approximations across element interfaces is described. Hierarchic bases of arbitrary polynomial order are presented. It is shown how these may be used to construct finite element approximations of arbitrary, non-uniform, local order approximation on unstructured meshes of curvilinear tetrahedral elements. Copyright © 2003 John Wiley & Sons, Ltd. [source] Fully-automated hex-dominant mesh generation with directionality control via packing rectangular solid cellsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 15 2003Soji Yamakawa Abstract A new fully automatic hex-dominant mesh generation technique of an arbitrary 3D geometric domain is presented herein. The proposed method generates a high-quality hex-dominant mesh by: (1) controlling the directionality of the output hex-dominant mesh; and (2) avoiding ill-shaped elements induced by nodes located too closely to each other. The proposed method takes a 3D geometric domain as input and creates a hex-dominant mesh consisting mostly of hexahedral elements, with additional prism and tetrahedral elements. Rectangular solid cells are packed on the boundary of and inside the input domain to obtain ideal node locations for a hex-dominant mesh. Each cell has a potential energy field that mimics a body-centred cubic (BCC) structure (seen in natural substances such as NaCl) and the cells are moved to stable positions by a physically based simulation. The simulation mimics the formation of a crystal pattern so that the centres of the cells provide ideal node locations for a hex-dominant mesh. Via the advancing front method, the centres of the packed cells are then connected to form a tetrahedral mesh, and this is converted to a hex-dominant mesh by merging some of the tetrahedrons. Copyright © 2003 John Wiley & Sons, Ltd. [source] Parallel adaptive refinement for unsteady flow calculations on 3D unstructured grids,INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 1 2004Jacob Waltz Abstract A parallel adaptive refinement algorithm for three-dimensional unstructured grids is presented. The algorithm is based on an hierarchical h -refinement/derefinement scheme for tetrahedral elements. The algorithm has been fully parallelized for shared-memory platforms via a domain decomposition of the mesh at the algebraic level. The effectiveness of the procedure is demonstrated with applications which involve unsteady compressible fluid flow. A parallel speedup study of the algorithm also is included. Published in 2004 by John Wiley & Sons, Ltd. [source] Three-dimensional numerical simulation of injection molding filling of optical lens and multiscale geometry using finite element methodPOLYMER ENGINEERING & SCIENCE, Issue 9 2006Sang-Woo Kim This article presents the development, verification, and validation of three-dimensional (3-D) numerical simulation for injection molding filling of 3-D parts and parts with microsurface features. For purpose of verification and comparison, two numerical models, the mixed model and the equal-order model, were used to solve the Stokes equations with three different tetrahedral elements (Taylor-Hood, MINI, and equal-order). The control volume scheme with tetrahedral finite element mesh was used for tracking advancing melt fronts and the operator splitting method was selected to solve the energy equation. A new, simple memory management procedure was introduced to deal with the large sparse matrix system without using a huge amount of storage space. The numerical simulation was validated for mold filling of a 3-D optical lens. The numerical simulation agreed very well with the experimental results and was useful in suggesting a better processing condition. As a new application area, a two-step macro,micro filling approach was adopted for the filling analysis of a part with a micro-surface feature to handle both macro and micro dimensions while avoiding an excessive number of elements. POLYM. ENG. SCI., 46:1263,1274, 2006. © 2006 Society of Plastics Engineers [source] | ||||||||||