이상 시의 4차원 시공간 설계 및 건축 : 「삼차각설계도」와 「건축무한육면각체」의 연결, 그리고 차원 확장

오상현 ( Oh¸ Maverick S. H. ),이수정 ( Lee¸ Soo-jong ) 한국어문학국제학술포럼 2021 Journal of Korean Culture Vol.54 No.-

This paper is a trial to establish the foundation of more concrete and coherent understanding of two series poems of Yi-Sang, Three-Dimensional Angle Blueprint(삼차각설계도, 三次角設計圖,) and Building Infinite Hexahedral-Angle Bodies(건축무한육면각체, 建築無限六面角體). Yi-Sang, based on his understanding on contemporary physics theories, wrote about his attempt to design and build arbitrary four-dimensional bodies on the poems. He coined and used the terms ‘three-dimensional angle’ and ‘hexahedral-angle body’. In this paper, it is explained that a three-dimensional angle is the set of three angular values from expressing the physical position of an object in four-dimensional space using the hyperspherical coordinate system, and a ‘hexahedral angle’ is the hyper-solid angle calculated from the integration of a three-dimensional angle as well as the angle made with six intersecting planes. Also, it is shown that a body that has n vertices and corresponding hexahedral angles can be called as n-hexahedral-angle body, which is followed by the notion that an ‘infinite-hexahedral-angle body’ is an arbitrary body in the four-dimensional space. On top of that, the dimension expansion that appears in Memorendum on lines 1 and AU MAGASIN DE NOUVEAUTES is covered. Summary video: https://youtu.be/hoH1GrumJ58

A new polyhedral element for the analysis of hexahedral-dominant finite element models and its application to nonlinear solid mechanics problems

Nguyen-Hoang, Son,Sohn, Dongwoo,Kim, Hyun-Gyu Elsevier 2017 Computer methods in applied mechanics and engineer Vol.324 No.-

<P><B>Abstract</B></P> <P>A hexahedral-dominant finite element mesh can be easily constructed by cutting regular hexahedral elements in a simple block with CAD surfaces representing outer surfaces of a geometric model. Polyhedral elements with straight edges but possibly non-planar faces are generated at the domain boundaries, while regular hexahedral elements remain in the interior region. Shape functions for polyhedral elements are derived from moving least square approximation based on a tetrahedral subdivision of polyhedral domains by a centroid-based subdivision technique. The polyhedral shape functions in this study have similar properties to conventional finite element shape functions in terms of continuity and completeness within elements, compatibility across inter-element boundaries and the Kronecker-delta property. Furthermore, the present approach using hexahedral-dominant meshes with polyhedral elements at domain boundaries is successfully applied to solve large deformation problems of hyperelastic and elastic–plastic materials.</P>

Hexahedral Mesh Quality Improvement with Geometric Constraints

Wei Peng,Xinyu Mei,Kun Shao,ChenXin Song,Xinguang Wu 한국정밀공학회 2023 International Journal of Precision Engineering and Vol.24 No.12

Hexahedral mesh is of great value in the analysis of mechanical structure, and the mesh quality has an important impact on the efficiency and accuracy of the analysis. This paper presents a quality improvement method for hexahedral meshes, which consists of node classification, geometric constraints based single hexahedron regularization and local hexahedral mesh stitching. The nodes are divided into different types and the corresponding geometric constraints are established in single hexahedron regularization to keep the geometric shapes of original mesh. In contrast to the global optimization strategies, we perform the hexahedral mesh stitching operation within a few local regions surrounding elements with undesired quality, which can effectively improve the quality of the mesh with less consuming time. Several mesh quality improvements for hexahedral meshes generated by a variety of methods are introduced to demonstrate the effectiveness of our method.

Quadrilateral Mesh Fitting that Preserves Sharp Features based on Multi-Normals for Laplacian Energy

Yusuke Imai,Shogo Moriya,Hiroyuki Hiraoka,Hiroshi Kawaharada (사)한국CDE학회 2013 한국CAD/CAM학회 국제학술발표 논문집 Vol.2010 No.8

Nowadays, manufacturers use computer-aided design for simulations. The reason is that the cost of performance test using actual products is expensive, so the cost of performance simulation using CAD models is lower than it. In this paper, we think about hexahedral meshes for finite element analysis, because simulations with hexahedral mesh are more accurate than those with tetrahedral meshes. Our purpose is automatic hexahedral mesh generation with sharp features to precisely represent the corresponding features of a target shape. Our hexahedral mesh is generated by a voxel-based algorithm. Thus, in our previous works, we fit the surface of the voxels to the target surface using Laplacian energy minimization. We used normal vector in the fitting for preserving sharp features. However, the method can not represent concave sharp features precisely. Thus, we improve the previous Laplacian energy by adding a term that depends on multi-normal vectors instead of a term using normal vectors. Furthermore, we accentuate convex/concave subset of surface to represent concave sharp features.

High accurate three-dimensional neutron noise simulator based on GFEM with unstructured hexahedral elements

Seyed Abolfazl Hosseini 한국원자력학회 2019 Nuclear Engineering and Technology Vol.51 No.6

The purpose of the present study is to develop the 3D static and noise simulator based on Galerkin FiniteElement Method (GFEM) using the unstructured hexahedral elements. The 3D, 2G neutron diffusion andnoise equations are discretized using the unstructured hexahedral by considering the linear approximationof the shape function in each element. The validation of the static calculation is performed viacomparison between calculated results and reported data for the VVER-1000 benchmark problem. Asensitivity 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 typeof variable strength using the Green function technique. It is shown that the error reduction in the static calculation is considerable when the unstructuredtetrahedron elements are replaced with the hexahedral ones. Since the neutron flux distribution andneutron multiplication factor are appeared in the neutron noise equation, the more accurate calculationof these parameters leads to obtaining the neutron noise distribution with high accuracy. The investigationof the changes of the neutron noise distribution in axial direction of the reactor core shows thatthe 3D neutron noise analysis is required instead of 2D.

플래스터링을 이용한 육면체 요소망의 자동생성

한재녕(Jae-nyung Han),박정수(Jung-Su Park),채수원(Soo-won Chae) 대한기계학회 2006 대한기계학회 춘추학술대회 Vol.2006 No.11

This paper presents a full hexahedral mesh generation by plastering for three-dimensional geometries. In this method, hexahedral elements are generated inward by offsetting from initial boundary mesh. When the elements intersect with each other after offsetting, overlapped elements are improved by node relocation method. In order to construct conforming mesh, pyramid elements are added to all hexahedral elements on the meshing front. With this process unmeshed regions are covered with triangular elements and tetrahedral elements are then generated at unmeshed regions. Finally pyramid and tetrahedral elements are subdivided into hexahedral elements using the Geode algorithm. Sample meshes for several geometries are presented to demonstrate the effectiveness of the proposed algorithm.

Hybrid Three-dimensional Mesh Generation from Quad-dominant Surface Meshes

한재녕,조남정,채수원,최영 한국자동차공학회 2008 International journal of automotive technology Vol.9 No.5

A hybrid mesh generation algorithm using a modified plastering method for three-dimensional objects with variable thickness is presented. The method starts with a quad-dominant surface mesh and generates layered elements with variable thickness by using adaptive offsetting, resulting in hex-tet dominant mesh generation. Hexahedral and prismatic meshes are generated by the inward offsetting of the initial boundary mesh. In order to generate a conforming mesh, pyramid elements are constructed on top of hexahedral elements, and tetrahedral elements are generated for the remaining domain by using an advancing front method. This method is applied to several different geometries, and the effectiveness of the proposed algorithm is demonstrated. A hybrid mesh generation algorithm using a modified plastering method for three-dimensional objects with variable thickness is presented. The method starts with a quad-dominant surface mesh and generates layered elements with variable thickness by using adaptive offsetting, resulting in hex-tet dominant mesh generation. Hexahedral and prismatic meshes are generated by the inward offsetting of the initial boundary mesh. In order to generate a conforming mesh, pyramid elements are constructed on top of hexahedral elements, and tetrahedral elements are generated for the remaining domain by using an advancing front method. This method is applied to several different geometries, and the effectiveness of the proposed algorithm is demonstrated.

New Development of Hexahedral Type Vibration Motor Used for Mobile Phones

Hwang, Gun-Yong,Hwang, Sang-Moon,Chung, Shi-Uk,Kang, Beom-Soo,Hwang, I-Cheol The Korean Society of Mechanical Engineers 2002 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.16 No.8

Mobile communication industry powered by electronics and information technology is building a transforming way for human communication. The latest electronics is so saturated to forget the difficulty in size reduction of electronic parts. However, mechanical parts, such as dynamic speakers and vibration motors, are intrinsically not easy to realize size reduction due to their construction. In this paper, a hexahedral type with simpler configuration is introduced to substitute for the conventional vibration motors. For uneven magnetic field analysis of the hexahedral type, FEM was used to determine magnetic flux density. After an analysis of magnetic and mechanical characteristics, it is shown that the coil configuration is the most important parameter to increase the output torque, and thus vibration. For optimization, genetic algorithm is used to find the optimal configuration of coil to maximize the output torque. Experimental results are also followed to confirm the validity of the proposed design.

Mixed formulated 13-node hexahedral elements with rotational degrees of freedom: MR-H13 elements

Choi, Chang-Koon,Chung, Keun-Young,Lee, Eun-Jin Techno-Press 2001 Structural Engineering and Mechanics, An Int'l Jou Vol.11 No.1

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.

Quadrilateral mesh fitting that preserves sharp features based on multi-normals for Laplacian energy

Imai, Yusuke,Hiraoka, Hiroyuki,Kawaharada, Hiroshi Society for Computational Design and Engineering 2014 Journal of computational design and engineering Vol.1 No.2

Because the cost of performance testing using actual products is expensive, manufacturers use lower-cost computer-aided design simulations for this function. In this paper, we propose using hexahedral meshes, which are more accurate than tetrahedral meshes, for finite element analysis. We propose automatic hexahedral mesh generation with sharp features to precisely represent the corresponding features of a target shape. Our hexahedral mesh is generated using a voxel-based algorithm. In our previous works, we fit the surface of the voxels to the target surface using Laplacian energy minimization. We used normal vectors in the fitting to preserve sharp features. However, this method could not represent concave sharp features precisely. In this proposal, we improve our previous Laplacian energy minimization by adding a term that depends on multi-normal vectors instead of using normal vectors. Furthermore, we accentuate a convex/concave surface subset to represent concave sharp features.