• Structural Engineering and Mechanics
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• v.21 no.5
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• pp.571-590
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• 2005

An 8 node assumed stress hexahedral element with rotational degrees of freedom is proposed for static and free vibration analyses. The element formulation is based directly on an 8-node element. This direct formulation requires fewer computations than a similar element that is derived from an internal 20-node element in which the midside degrees of freedom are eliminated by expressing them in terms of displacements and rotations at corner nodes. The formulation is based on Hellinger-Reissner variational principle. Numerical examples are presented to show the validity and efficiency of the present element for static and free vibration analysis.

• Structural Engineering and Mechanics
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• v.11 no.1
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• pp.105-122
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• 2001

A new three-dimensional 13-node hexahedral element with rotational degrees of freedom, which is designated as MR-H13 element, is presented. The proposed element is established by adding five nodes to one of the six faces of basic 8-node hexahedral element. The new element can be effectively used in the connection between the refined mesh and the coarser mesh. The derivation of the current element in this paper is based on the variational principles in which the rotation and skew-symmetric stress are introduced as independent variables. Numerical examples show that the performance of the new element is satisfactory.

• Journal of Power System Engineering
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• v.16 no.1
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• pp.78-83
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• 2012

The authors suggest the algorithm for the static analysis of a three dimensional solid structure by using the finite element-transfer stiffness coefficient method (FE-TSCM) and the hexahedral element of the finite element method (FEM). MATLAB codes were made by both FE-TSCM and FEM for the static analysis of three dimensional solid structure. They were applied to the static analyses of a very thick plate structure and a three dimensional solid structure. In this paper, as we compare the results of FE-TSCM with those of FEM, we confirm that FE-TSCM introducing the hexahedral element for the static analysis of a three dimensional solid structure is very effective from the viewpoint of the computational accuracy, speed, and storage.

• Structural Engineering and Mechanics
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• v.17 no.1
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• pp.113-140
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• 2004

A mixed eight-node hexahedral element formulated via the Hu-Washizu principle as well as the field extrapolation technique is presented. The mixed element with only three translational degrees of freedom at each node can provide extremely accurate and reliable performance for popular benchmark problems such as spacial beams, plates, shells as well as general three-dimensional elasticity problems. Numerical calculations also show that when extremely skewed and coarse meshes and nearly incompressible materials are used, the proposed mixed element can still possess excellent behaviour. The mixed formulation starts with introduction of a parallelepiped domain associated with the given general eight-node hexahedral element. Then, the assumed strain field at the nodal level is constructed via the Hu-Washizu variational principle for that associated parallelepiped domain. Finally, the assumed strain field at the nodal level of the given hexahedral element is established by using the field extrapolation technique, and then by using the trilinear shape functions the assumed strain field of the whole element domain is obtained. All matrices involved in establishing the element stiffness matrix can be evaluated analytically and expressed explicitly; however, a 24 by 24 matrix has to be inverted to construct the displacement extrapolation matrix. The proposed hexahedral element satisfies the patch test as long as the element with a shape of parallelepiped.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.15 no.1
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• pp.57-65
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• 2011

In this paper, a good quality mesh generation for the finite element method is investigated for artificial hip joint simulations. In general, bad meshes with a large aspect ratio or mixed elements can give rise to excessively long computational running times and extremely high errors. Typically, hexahedral elements outperform tetrahedral elements during three-dimensional contact analysis using the finite element method. Therefore, it is essential to mesh biologic structures with hexahedral elements. Four meshing schemes for the finite element analysis of an artificial hip joint are presented and compared: (1) tetrahedral elements, (2) wedge and hexahedral elements, (3) open cubic box hexahedral elements, and (4) proposed hexahedral elements. The proposed meshing scheme is to partition a part before seeding so that we have a high quality three-dimensional mesh which consists of only hexahedral elements. The von Mises stress distributions were obtained and analyzed. We also performed mesh refinement convergence tests for all four cases.

• Proceedings of the KSME Conference
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• 2007.05a
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• pp.1637-1641
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• 2007

In this paper, we simulate a rotor pole cold forging process by a forging simulator with both tetrahedral and hexahedral element capabilities and compare the predictions obtained by the two approaches with the experiments. Hexahedral element capability runs manually while tetrahedral element capability runs automatically with help of an intelligent remeshing technique. It is shown that the tetrahedral element capability can give quite accurate solution if assisted by the intelligent remeshing technique even though the tetrahedral element itself is not theoretically and numerically clear.

• Nuclear Engineering and Technology
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• v.51 no.6
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• pp.1479-1486
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• 2019

The purpose of the present study is to develop the 3D static and noise simulator based on Galerkin Finite Element Method (GFEM) using the unstructured hexahedral elements. The 3D, 2G neutron diffusion and noise equations are discretized using the unstructured hexahedral by considering the linear approximation of the shape function in each element. The validation of the static calculation is performed via comparison between calculated results and reported data for the VVER-1000 benchmark problem. A sensitivity analysis of the calculation to the element type (unstructured hexahedral or tetrahedron elements) is done. Finally, the neutron noise calculation is performed for the neutron noise source of type of variable strength using the Green function technique. It is shown that the error reduction in the static calculation is considerable when the unstructured tetrahedron elements are replaced with the hexahedral ones. Since the neutron flux distribution and neutron multiplication factor are appeared in the neutron noise equation, the more accurate calculation of these parameters leads to obtaining the neutron noise distribution with high accuracy. The investigation of the changes of the neutron noise distribution in axial direction of the reactor core shows that the 3D neutron noise analysis is required instead of 2D.

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 2004.10a
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• pp.79-82
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• 2004

In this study, a new refinement technique for 3-dimensional hexahedral element mesh is proposed, which is aimed at the control of mesh density. With the proposed scheme the mesh is refined adaptively to the elemental error which is estimated by 'a posteriori' error estimator based on the energy norm. A desired accuracy of an analysis i.e. a limit of error defines the new desired mesh density map on the current mesh. To obtain the desired mesh density, the refinement procedure is repeated iteratively until no more elements to be refined exist. In the algorithm, at first the regions of mesh to be refined are defined and, then, the zero-thickness element layers are inserted into the interfaces between the regions. All the meshes in the regions, in which the zero-thickness layers are inserted, are to be regularized in order to improve the shape of the slender elements on the interfaces. This algorithm is tested on a simple shape of 2-d quadrilateral element mesh and 3-d hexahedral element mesh. A numerical example of elastic deformation of a plate with a hole shows the effectiveness of the proposed refinement scheme.

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 2003.05a
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• pp.323-326
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• 2003

This paper presents a new algorithm that can refine hexahedral elements while maintaining the appropriate connectivity. In the algorithm, at first the regions of mesh to be refined are defined and, then, the zero-thickness element layers inserted into the interfaces between the regions. All the meshes in the regions, in which the zero-thickness layers are inserted, are to be regularized in order to improve the shape of the slender elements on the interfaces. This algorithm is applied to the analysis of plastic deformation process. The results show that the refined mesh gives smaller relative errors than the original mesh.

• Transactions of Materials Processing
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• v.12 no.4
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• pp.334-339
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• 2003

This paper presents a new algorithm that enables the refinement of hexahedral elements while maintaining the appropriate connectivity. In the algorithm, at first the regions of mesh to be refined are defined and, then, the zero-thickness element layers are inserted into the interfaces between the regions. All the meshes in the regions, in which the zero-thickness layers are inserted, are to be regularized in order to improve the shape of the slender elements on the interfaces. This algorithm is applied to the analysis of plastic deformation process. The results show that the refined mesh gives smaller relative errors than the original mesh.