A Comparison of the Performance of Hexahedral and Tetrahedral Elements in Finite Element Models of the Foot

2010 ◽  
Author(s):  
Srinivas C. Tadepalli ◽  
Ahmet Erdemir ◽  
Peter R. Cavanagh
Keyword(s):  
Finite Element ◽  
Mesh Generation ◽  
Complex Structure ◽  
Shear Loading ◽  
Superior Performance ◽  
Hexahedral Mesh ◽  
Tetrahedral Elements ◽  
Heel Pad ◽  
Hexahedral Elements ◽  
Foot Biomechanics

Characterization of the contact pressure patterns under the foot provides significant insight into pathological conditions such as diabetic peripheral neuropathy [1]. The finite element method (FEM) is widely used in foot biomechanics for predictive simulations of plantar pressures in barefoot and shod conditions [2–6]. In the analysis of the foot, mesh generation accounts for most of the labor in model development, due to the complex structure of the foot including highly partitioned, embedded, and branching geometries. In FEM, hexahedral elements are preferred over tetrahedral elements because of their superior performance in terms of convergence and accuracy of the solution [7]. This becomes more apparent as the convergence behavior of the simulations are hindered by large deformation, material incompressibility, and contact with friction, mechanical features which are commonly seen in foot biomechanics. Unfortunately, unlike tetrahedral meshing which is highly automated [8], hexahedral mesh generation is a time consuming process requiring considerable operator intervention. Despite their reputed advantages, the relative performance of tetrahedral meshes in foot models has not been well established; to our knowledge, there has not been a comprehensive study comparing the performance of hexahedral and tetrahedral elements when material and geometric nonlinearity are included combined with material incompressibility and shear force loading conditions. Hence, the objective of the present study was to evaluate various types of meshes that can be used to model the interaction of a bone-soft tissue construct and rigid floor complex under compressive and shear loading in a heel-pad analog model.

Finite Element Analysis in 3D Using the Penalty Boundary Method

2002 ◽  
Author(s):  
Brett W. Clark ◽  
David C. Anderson
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Boundary Conditions ◽  
Mesh Generation ◽  
Discretization Error ◽  
Finite Element Models ◽  
Element Analysis ◽  
Hexahedral Elements ◽  
Boundary Method ◽  
Time Required

Traditional methods for applying boundary conditions in finite element analysis require the mesh to conform to the geometry boundaries. This in turn requires complex meshing algorithms for automated mesh generation from CAD geometry, particularly when using quadrilateral and hexahedral elements. The 3D extension of the penalty boundary method (PBM) is presented as a method that significantly reduces the time required generating finite element models because the mesh is not required to conform to the CAD geometry. The PBM employs penalty methods to apply boundary conditions on a simple, regular mesh. The PBM also eliminates discretization error because boundary conditions are applied using CAD geometry directly rather than an approximation of the geometry.

New Algorithm for Full Hexahedral Finite Element Mesh Generation of Pipe Models With Multiple Corrosion Defects

2008 ◽  
Author(s):  
Alejandro Andueza ◽  
Segen F. Estefen
Keyword(s):  
Mesh Generation ◽  
Stress Fields ◽  
Complex Geometries ◽  
Accurate Analysis ◽  
Element Mesh ◽  
Simulation Techniques ◽  
Tetrahedral Elements ◽  
Hexahedral Elements ◽  
Hexahedral Element ◽  
Corrosion Defects

Analysis of corroded pipelines using simulation techniques has become an essential step for the evaluation of the residual ultimate strength of damaged pipes. Problems with multiple corrosion defects present highly complex geometries mainly when the defects are close enough to produce interacting stress fields. In such cases it is easier the mesh generation with all-tetrahedral elements using mature algorithms implemented in commercial programs like Ansys or Patran. The use of all-tetrahedral meshes in many applications yields to less accurate analysis results. Unfortunately, the algorithm for mesh generation of all-hexahedral elements is much more complex than the generation of all-tetrahedral element mesh. Currently, the problem associated with general all-hexahedral element mesh algorithm is a research subject in progress. This paper presents a new algorithm for the mesh generation of all-hexahedral elements to be used in the analysis of damaged pipelines. The algorithm is currently under development and was designed to deal with any number of corrosion defects of arbitrary shape. The application of the new methodology is demonstrated performing the mesh generation of models with one, two and three corrosion defects in order to demonstrate both efficiency and robustness of the new methodology. Finally, computer simulations for the generated models are performed in order to determine the failure pressure of the damaged pipes. The obtained results are compared to the values predicted by the standard DNV RP-F101.

Basic LOgical Bulk Shapes (BLOBs) for Finite Element Hexahedral Mesh Generation to Support Virtual Prototyping

1998 ◽  
Vol 120 (4) ◽  
pp. 728-735 ◽  
Author(s):  
S.-S. Liu ◽  
R. Gadh
Keyword(s):  
Finite Element ◽  
Mesh Generation ◽  
Virtual Prototyping ◽  
Solid Model ◽  
Hexahedral Mesh ◽  
Product Model ◽  
Element Analysis ◽  
Element Mesh ◽  
Automated Method ◽  
Finite Element Meshes

Manufacturability analysis of product design reduces the downstream problems of manufacturing. Such design approaches are referred to as Virtual Prototyping when performed on the computer. In the present research, Virtual Prototyping is facilitated by the use of an automated method of determining the finite element meshes needed to perform finite element analyses. Finite element analysis requires a finite element mesh of the product model as input. This mesh (an approximation of an object’s geometry and topology, composed in terms of a given individual unit, e.g., a tetrahedron, or a hexahedron), can be generated using a variety of methods. The research presented here offers an approach for automatic mesh generation that addresses some of the limitations in the mesh-generation technologies currently available. This article presents an approach for automatically generating hexahedral meshes from solid models. The mesh generating method presented in this paper involves four major steps. First, objects called Basic LOgical Bulk shapes (BLOBs) are determined from the solid model of a given part. Second, these BLOBs are used to decompose the solid model into its various sub-volumes. Third, a multiple-block structure (MBS), which is a group of hexahedral objects, is constructed to approximate the solid model. Finally, transfinite mapping is employed to project the faces of the MBS onto the surfaces of a model to generate the finite element meshes.

Study on Complex Structure Mesh Generating of Hexahedron Element Based on Improved Waveform Mesh Generating Method

2011 ◽  
Vol 462-463 ◽  
pp. 955-960
Author(s):  
Xu Fei Wang ◽  
Mamtimin Gheni ◽  
Masanori Kikuchi ◽  
Ju Rong Liu
Keyword(s):  
Mesh Generation ◽  
Complex Structure ◽  
Fem Simulation ◽  
Engineering Problem ◽  
Simulation Technique ◽  
Tetrahedral Mesh ◽  
Hexahedral Mesh ◽  
Generating Method ◽  
Complex Engineering ◽  
Mesh Models

Three-dimensional finite element method (FEM) is widely used as an effective numerical simulation technique to solve the complex engineering problem. Usually, the more complex engineering problem has more complex structure and shape; the FEM simulation technique is that needs to discrete the structure and shape of the problem by mesh. In addition, the correct generation of mesh is one of the most significant issues that directly affect to the accuracy of the FEM simulation. The hexahedral mesh is better than tetrahedral mesh in solving the complex engineering problem. The common methods of hexahedral automatic mesh generation have been used in some commercial soft already, but its adaptation is not enough to solve for practical applications of the complex engineering problems. A new method of mesh generation technique was proposed by improved waveform mesh generating method, and realized by C++ developing program in Linux OS. The method could generate some effective and smoothly mesh models by quadrilateral element or hexahedron element, and not only generated revolution curve surface meshes, but also generated random meshes according to free functions too. The results shown that the hexahedral mesh models of the complex shapes were generated as the shape function apply to regular mesh side as a waveform constraint.

An automatic hexahedral mesh generation method for hexahedral elements towards rotating machine

2005 ◽  
Vol 161 (1-2) ◽  
pp. 101-106 ◽  
Author(s):  
Toshihiro Maeda ◽  
So Noguchi ◽  
Hideo Yamashita ◽  
Vlatko Cingoski
Keyword(s):  
Mesh Generation ◽  
Hexahedral Mesh ◽  
Rotating Machine ◽  
Hexahedral Elements ◽  
Hexahedral Mesh Generation

scholarly journals custEM: Customizable finite-element simulation of complex controlled-source electromagnetic data

Geophysics ◽  
2019 ◽  
Vol 84 (2) ◽  
pp. F17-F33 ◽  
Author(s):  
Raphael Rochlitz ◽  
Nico Skibbe ◽  
Thomas Günther
Keyword(s):  
Finite Element ◽  
Open Source ◽  
Mesh Generation ◽  
Analytic Solutions ◽  
Superior Performance ◽  
Electromagnetic Modeling ◽  
Matrix Assembly ◽  
Controlled Source ◽  
Time Harmonic ◽  
Element Simulation

We have developed the open-source toolbox custEM (customizable electromagnetic modeling) for the simulation of complex 3D controlled-source electromagnetic (CSEM) problems. It is based on the open-source finite-element library FEniCS, which supports tetrahedral meshes, multiprocessing, higher order polynomials, and anisotropy. We use multiple finite-element approaches to solve the time-harmonic Maxwell equations, which are based on total or secondary electric field and gauged potential formulations. In addition, we develop a secondary magnetic field formulation, showing superior performance if only magnetic fields are required. Using Nédélec basis functions, we robustly incorporate the current density on the edges of the mesh for the total field formulations. The latter enable modeling of CSEM problems taking topography into account. We evaluate semianalytical 1D layered-earth solutions with the pyhed library, supporting arbitrary configurations of dipole or loop sources for secondary field calculations. All system matrices have been modified to be symmetric and solved in parallel with the direct solver MUMPS. Aside from the finite-element kernel, mesh generation, interpolation, and visualization modules have been implemented to simplify and automate the modeling workflow. We prove the capability of custEM, including validation against analytic-solutions, crossvalidation of all implemented approaches, and results for a model with 3D topography with four examples. The object-oriented implementation allows for customizable modifications and additions or to use only submodules designed for special tasks, such as mesh generation or matrix assembly. Therefore, the toolbox is suitable for crossvalidation with other codes and as the basis for developing 3D inversion routines.

scholarly journals MODIFICATION OF SURFACE MESH FOR THE GENERATION OF KNIFE ELEMENT FREE HEXAHEDRAL MESH

2011 ◽  
Vol 41 (2) ◽  
pp. 103-113
Author(s):  
Md. Shahidul Islam ◽  
Gazi Md. Khalil
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Surface Mesh ◽  
Hexahedral Mesh ◽  
Element Analysis ◽  
Hexahedral Elements ◽  
Detailed Method ◽  
Modification Procedure ◽  
Face Generation

Hexahedral elements provide greater accuracy and efficiency over tetrahedral elements for finite element analysis of solids and for this reason the all-hexahedral element auto meshing has a growing demand. The whisker-weaving based plastering algorithm developed by the authors can generate hexahedral mesh (HM) automatically. In this method the prerequisite for generating HM is quadrilateral surface mesh (SM). From the given SM, combinatorial dual cycles or whisker sheet loops for whisker weaving algorithm are generated to produce HM. Generation of good quality HM does not depend only on the quality of quadrilaterals of the SM but also on the quality of the dual cycles generated from it. If the dual cycles have self-intersection, it could cause the formation of degenerated hexahedron called knife element, which is not usable in finite element analysis. In this paper a detailed method is proposed to modify the SM to remove self-intersections from its dual loops. The SM modification procedure of this proposed method has three basic steps. These steps are (a) face collapsing, (b) new face generation and (c) template application. A fully automatic computer program is developed on the basis of this proposed method and a number of models are analyzed to show the effectiveness of the proposal.DOI: http://dx.doi.org/10.3329/jme.v41i2.7505

scholarly journals Improving the quality of hexahedral mesh generated by automatic mesh generators

2011 ◽  
Vol 8 (2) ◽  
pp. 121-128
Author(s):  
Md. Shahidul Islam
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Mesh Generation ◽  
Hexahedral Mesh ◽  
Element Analysis ◽  
Large Structures ◽  
Hexahedral Mesh Generation ◽  
Marine Engineering ◽  
Automatic Mesh

Automatic hexahedral mesh generation is a very deserving solution for better performance of finite element analysis of complex large structures. At present plastering, whisker weaving and whisker weaving based plastering algorithm are available to perform such tasks. As these hexahedral mesh generation processes are fully automatic, it is possible to form some elements, which don’t have high enough qualities for finite element analysis. For this reason, a reliable post-processing method is presented in this paper which can modify the shapes of the already generated hexahedrons. Four different structural models are tested and the results show that the proposed method can effectively modify the quality of the inverted hexahedrons and eliminate the invalid ones.Keywords: Doublet; triplet; quadruplet; Whisker weaving based plastering algorithm; hexahedral meshDOI: http://dx.doi.org/10.3329/jname.v8i2.5646Journal of Naval Architecture and Marine Engineering 8(2011) 121-128

Survey of Immersed Boundary Approaches for Finite Element Analysis

2020 ◽  
Vol 20 (4) ◽  
Author(s):  
Ashok V. Kumar
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Mesh Generation ◽  
Immersed Boundary ◽  
Uniform Mesh ◽  
Element Analysis ◽  
Hexahedral Elements ◽  
Boundary Method ◽  
Background Mesh ◽  
Plates And Shells

Abstract Mesh generation for traditional finite element analysis has proven to be very difficult to fully automate especially using hexahedral elements for complex 3D geometry. Several modifications to the finite element method (FEM), such as the meshless methods, have been proposed for avoiding mesh generation. An alternative approach has recently gained popularity where the geometry, created as a solid model in cad software, is embedded or immersed in a nonconforming background mesh for analysis. In this approach, referred to here as the immersed boundary approach, a background mesh that is independent of the geometry is used for piecewise interpolation or approximation of the solution. Therefore, a uniform mesh with regular-shaped or undistorted elements can be used, and such a mesh is easy to generate automatically. When the geometry is immersed in the background mesh, the boundary elements are often only partly inside the geometry and the nodes of the mesh may not be on the boundaries. Many new methods have been developed to integrate over partial elements and to apply boundary and interface conditions when the boundaries of the geometries do not conform to the background mesh. These methods are reviewed in this article with particular emphasis on the implicit boundary method and step boundary method for applying boundary conditions. In addition, B-spline elements and several applications of the immersed boundary approach are surveyed including composite microstructures and structural elements for plates and shells.

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