All-hexahedral Element Research Articles

Three-dimensional temperature and stress field simulation with all-hexahedral element mesh in a high efficiency cooling structure for the fabrication of amorphous ribbons

Planar flow casting is an advanced technology to produce amorphous and nanocrystalline ribbons in electrical application. At present, the utilization rate of roller surface is generally under 20% in industrial production. This work reports a new cooling structure that is designed to produce ribbons width 65 mm with the utilization rate of roller surface up to 65%. The cooling structure is simulated with the software ANSYS by employing three-dimensional temperature and stress field mathematic model incorporating actual production conditions with all-hexahedral element mesh. It is shown that the liquid velocity is uniform with consistent distribution of convective heat transfer coefficient in width direction between cooling water and rotating roller. The thermal expansion difference in the new cooling structure is only 0.0042 mm at the ribbon edge. In this case, it is unnecessary to make the slit with an upward bend. The new cooling structure is expected to be applied for industrial production at an ideal level.

TUM.GeoFrame: automated high-order hexahedral mesh generation for shell-like structures

This paper presents a fully automated high-order hexahedral mesh generation algorithm for shell-like structures based on enhanced sweeping methods. Traditional sweeping techniques create all-hexahedral element meshes for solid structures by projecting an initial single surface mesh along a specified trajectory to a specified target surface. The work reported here enhances the traditional method for thin solids by creating conforming high-order all-hexahedral finite element meshes on an enhanced surface model with surfaces intersecting in parallel, perpendicular and skew-angled directions. The new algorithm is based on cheap projection rules separating the original surface model into a set of disjoint single surfaces and a so-called interface skeleton. The core of this process is reshaping the boundary representations of the initial surfaces, generating new sweeping templates along the intersection curves and joining the single swept hex meshes in an independently generated interface mesh.

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

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

A control approach for pore size distribution in the bone scaffold based on the hexahedral mesh refinement

Tissue engineering is the application of that knowledge to the building or repairing of tissues. Generally, engineered tissue is a combination of living cells and a support structure called scaffolds. Modeling, design and fabrication of tissue scaffold with intricate architecture, porosity and pore size for desired tissue properties presents a challenge in tissue engineering. In this paper, a control approach for pore size distribution in the bone scaffold based on the hexahedral mesh refinement is presented. Firstly, the bone scaffold modeling approach based on the shape function in the finite element method is provided. The resulting various macroporous morphologies can be obtained. Then conformal refinement algorithm for all-hexahedral element mesh is illustrated. Finally, a modeling approach for constructing tissue engineering (TE) bone scaffold with defined pore size distribution is presented. Before the conformal refinement of all-hexahedral element mesh, a 3D mesh with various hexahedral elements must be provided. If all the pores in the bone scaffold need to be reduced, that means that the whole hexahedral mesh needs to be refined. Then the solid entity can be re-divided with altered subdivision parameters. If the pores in the local regions of bone need to be reduced, that means that 3D hexahedral mesh in the local regions needs to be refined. Based on SEM images, the pore size distribution in the normal bone can be obtained. Then, according to the conformal refinement of all-hexahedral element meshes, defined hexahedral size distribution can be gained, which leads to generate defined pore size distribution in the bone scaffold, for the pore morphology and size are controlled by various subdivided hexahedral elements. Compared to other methods such as varying processing parameters in supercritical fluid processing and multi-interior architecture design, the method proposed in this paper enjoys easy-controllability and higher accuracy.

A semi-staggered dilation-free finite volume method for the numerical solution of viscoelastic fluid flows on all-hexahedral elements

The dilation-free semi-staggered finite volume method presented in Sahin [M. Sahin, A preconditioned semi-staggered dilation-free finite volume method for the incompressible Navier–Stokes equations on all-hexahedral elements, Int. J. Numer. Methods Fluids 49 (2005) 959–974] has been extended for the numerical solution of viscoelastic fluid flows on all-quadrilateral (2D) / hexahedral (3D) meshes. The velocity components are defined at element node points, while the pressure term and the extra stress tensor are defined at element centroids. The continuity equation is satisfied exactly within each element. An upwind least square method is employed for the calculation of the extra stresses at control volume faces in order to maintain stability for hyperbolic constitutive equations. The time stepping algorithm used decouples the calculation of the extra stresses from the evaluation of the velocity and pressure fields by solving a generalised Stokes problem. The resulting linear systems are solved using the GMRES method provided by the PETSc library with an ILU( k) preconditioner obtained from the HYPRE library. We apply the method to both two- and three-dimensional flow of an Oldroyd-B fluid past a confined circular cylinder in a channel with blockage ratio 0.5.

Adaptive generation of hexahedral element mesh using an improved grid-based method

An improved grid-based algorithm for the adaptive generation of hexahedral finite element mesh is presented in this paper. It is named as the inside-out grid-based method and involves the following four steps. The first step is the generation of an initial grid structure which envelopes the analyzed solid model completely. And the elements size and density maps are constructed based on the surface curvature and local thickness of the solid model. Secondly, the core mesh is generated through removing all the undesired elements using even and odd parity rules. The third step is to magnify the core mesh in an inside-out manner through a surface node projection process using the closest position approach. To match the mesh to the characteristic boundary of the solid model, a minimal Scaled Jacobian criterion is employed. Finally, in order to handle the degenerated elements and improve the quality of the resulting mesh, two comprehensive techniques are employed: the insertion technique and collapsing technique. The present method was applied in the mesh construction of different engineering problems. Scaled Jacobian and Skew metrics are used to evaluate the hexahedral element mesh quality. The application results show that all-hexahedral element meshes which are well-shaped and capture all the geometric features of the original solid models can be generated using the inside-out grid-based method presented in this paper.

Adaptive refinement of all-hexahedral elements for three-dimensional metal forming analysis

In many 3-D forging simulations, the master-grid method or uniform-grid method is adopted as an effect tool for hexahedral element mesh generation, because the method is robust and reliable to construct the intermediate mesh during forging simulation. However, almost equal-sized element mesh is employed regardless of the local characteristics of the deforming region. In order to overcome this drawback, a new refinement technique for hexahedral element mesh is proposed by selecting the element regions to be refined and iteratively inserting the zero-thickness element layers into the necessary interfaces of elements. To generate refined mesh adaptive to the gradient of physical property or to the complexity of geometry, the desired mesh density is obtained from the Z – Z posteriori error analysis. In the course of expanding and smoothing the refined mesh to ensure the desired mesh density, the weighting factor based on mesh density of neighbor entities is introduced to the conventional Laplacian smoothing method. Comparative simulations of the selected forging processes have shown that the proposed refinement technique is effective from the viewpoint of computational economy of computations and accuracy.

All‐hexahedral element meshing: automatic elimination of self‐intersecting dual lines

AbstractThere has been some degree of success in all‐hexahedral meshing. Standard methods start with the object geometry defined by means of an all‐quadrilateral mesh, followed by the use of the combinatorial dual to the mesh in order to define the internal connectivities among elements. For all of the known methods using the dual concept, it is necessary to first prevent or eliminate self‐intersecting (SI) dual lines of the given quadrilateral mesh. The relevant features of SI lines are studied, giving a method to remove them, which avoids deforming the original geometry. Some examples of resulting meshes are shown where the current meshing method has been successfully applied. Copyright © 2002 John Wiley & Sons, Ltd.

All-hexahedral element meshing: Generation of the dual mesh by recurrent subdivision

The domain geometry is defined by means of a closed all-quadrilateral mesh. The outer mesh imposes very strong restrictions on the possible connectivities between the inner hexahedral elements. Following the guidelines of the outer topology, the inner one is almost entirely defined. Several ways may be decided for certain configurations, some of them requiring special considerations in order to achieve a valid FEM mesh. The process is entirely performed by constructing the (graph theoretical) dual of the hexahedral mesh, this means no metric information is handled until the final (positioning and smoothing) steps. The essential steps of this scheme are described by means of examples.