• Research in Mathematical Education
• /
• v.14 no.3
• /
• pp.263-279
• /
• 2010

Teachers' personal knowledge (PK) is an element in their pedagogic-practical knowledge. This study exposes the PK of primary school mathematics teachers regarding solid geometry through reflection. Students are exposed to solid geometry on various levels, from kindergarten age and above. Previous studies attested to the fact that students encounter difficulties-strong dislike and fear engendered by geometry. A good number of teachers have strong dislike to solid geometry, as well. Therefore, those engaged in teaching the subject must address the problem and try to overcome these difficulties. In this paper we have introduced the reflective process among teachers in primary school, including application of Van-Hiele's theory to solid geometry.

• Journal of the Korea Computer Graphics Society
• /
• v.3 no.2
• /
• pp.77-84
• /
• 1997

Solid modeling refers to techniques for unambiguous representations of three- dimensional objects. The most widely used techniques for solid modeling have been Constructive Solid Geometry (CSG) and Boundary Representation (BRep). Contemporary solid modeling systems typically support both representations, and bilateral conversions between CSG and BRep are essential. However, computing a CSG from a BRep is largely an open problem. This paper presents 3D geometric reasoning algorithms for converting a BRep into a special CSG, called Destructive Solid Geometry (DSG) whose Boolean operations are all subtractions. The major application area of BRep-to-DSG conversion is feature recognition, which is essential for integrating CAD and CAM.

• Research in Mathematical Education
• /
• v.16 no.1
• /
• pp.31-50
• /
• 2012

The present study explored whether the implementation of focused activities (intervention programme) can enhance 22 pre-service mathematics teachers' proficiency in solid geometry thinking level as well as change for the better their feelings in this discipline. Over a period of 6 weeks the pre-service teachers participated in activities and diversified experiences with 3D shapes, using illustration aids and actual experience of building 3D shapes in relation to the various spatial thinking levels. The research objectives were to investigate whether the intervention programme, comprising task-oriented activities of solid geometry, enhance mathematics pre-service teachers' mastery of their geometric thinking levels as well as examine their feelings towards this discipline before and after the intervention programme. The findings illustrate that learners' levels of geometric thinking can be promoted, entailing control on higher thinking levels as well as a more positive attitude towards this field.

• International Journal of Fuzzy Logic and Intelligent Systems
• /
• v.4 no.2
• /
• pp.193-198
• /
• 2004

This paper describes an automatic finite element (FE) mesh generation for three-dimensional structures consisting of tree-form surfaces. This mesh generation process consists of three subprocesses: (a) definition of geometric model, (b) generation of nodes, and (c) generation of elements. One of commercial solid modelers is employed for three-dimensional solid structures. Node is generated if its distance from existing node points is similar to the node spacing function at the point. The node spacing function is well controlled by the fuzzy knowledge processing. The Voronoi diagram method is introduced as a basic tool for element generation. Automatic generation of FE meshes for three-dimensional solid structures holds great benefits for analyses. Practical performances of the present system are demonstrated through several mesh generations for three-dimensional complex geometry.

• Journal of Hydrogen and New Energy
• /
• v.30 no.4
• /
• pp.330-337
• /
• 2019

Effects of cyclone and freeboard geometry on solid entrainment loss were investigated with two different types of cyclones and bubbling beds in a gas-solid fluidized bed system. The solid entrainment loss was measured by collected fines during continuous solid circulation condition. Bubbling bed which has an expanded freeboard showed less solid entrainment than the bubbling bed which has a straight freeboard. The cyclone which has a wide gas-solid mixture inlet showed less solid entrainment loss than the cyclone which has a narrow gas-solid mixture inlet. Moreover, the cyclone has a wide gas-solid mixture inlet can capture smaller particles.

• Korean Journal of Computational Design and Engineering
• /
• v.4 no.3
• /
• pp.180-189
• /
• 1999

Solid freeform fabrication technology, widely known as rapid prototyping an rapid tooling, can create physical part directly from digital model by accumulating layers of a given material. Providing a tremendous flexibility of a part geometry that they can fabricate, these technologies present a opportunity or the creation of new products that can not be made with existing technologies. For this to be possible, however, various design environments including different fabrication processes needs to be considered at the time of design, and finding an appropriate design solution for the new product by combining necessary design communications become increasingly complex as environmental condition become diverse. This paper proposes a geometric modeling paradigm for design and fabrication of a new product, honeycomb structural geometry.

• International Journal of Fuzzy Logic and Intelligent Systems
• /
• v.6 no.2
• /
• pp.144-149
• /
• 2006

This paper describes a novel automated analysis system for bellows of piping system. An automatic finite element (FE) mesh generation technique, which is based on the fuzzy theory and computational geometry technique, is incorporated into the system, together with one of commercial FE analysis codes and one of commercial solid modelers. In this system, a geometric model, i.e. an analysis model, is first defined using a commercial solid modelers for 3-D shell structures. Node is generated if its distance from existing node points is similar to the node spacing function at the point. The node spacing function is well controlled by the fuzzy knowledge processing. The Delaunay triangulation technique is introduced as a basic tool for element generation. The triangular elements are converted to quadrilateral elements. Practical performances of the present system are demonstrated through several analysis for bellows of piping system.

• International Journal of Fuzzy Logic and Intelligent Systems
• /
• v.6 no.1
• /
• pp.58-63
• /
• 2006

This paper describes a novel automated analysis system for bellows of piping system. An automatic finite element (FE) mesh generation technique, which is based on the fuzzy theory and computational geometry technique, is incorporated into the system, together with one of commercial FE analysis codes and one of commercial solid modelers. In this system, a geometric model, i.e. an analysis model, is first defined using a commercial solid modelers for 3-D shell structures. Node is generated if its distance from existing node points is similar to the node spacing function at the point. The node spacing function is well controlled by the fuzzy knowledge processing. The Delaunay triangulation technique is introduced as a basic tool for element generation. The triangular elements are converted to quadrilateral elements. Practical performances of the present system are demonstrated through several analysis for bellows of piping system.

• Advances in aircraft and spacecraft science
• /
• v.6 no.4
• /
• pp.333-348
• /
• 2019

Low fuel regression rate is the main drawback of hybrid rocket which should be overcome. One of the improvement techniques to this problem is usage of a solid fuel grain with a complicated geometry port, which has been promoted owing to the recent development of additive manufacturing technologies. In the design of a hybrid rocket fuel grain with a complicated geometry port, the understanding of fuel regression behavior is very important. Numerical investigations of fuel regression behavior requires a capturing method of solid fuel surface, i.e. gas-solid interface. In this study, level set method is employed as such a method and the preliminary numerical tool for capturing a hybrid rocket solid fuel surface is developed. At first, to test the adequacy of the numerical modeling, the simulation results for circular port are compared to the experimental results in open literature. The regression rates and oxidizer to fuel ratios show good agreements between the simulations and the experiments, after passing enough time. However, during the early period of combustion, there are the discrepancies between the simulations and the experiments, owing to transient phenomena. Second, the simulations of complicated geometry ports are demonstrated. In this preliminary step, a star shape is employed as complicated geometry of port. The slot number effect in star port is investigated. The regression rate decreases with increasing the slot number, except for the star port with many slots (8 slots) in the latter half of combustion. The oxidizer to fuel ratio increases with increasing the slot number.

• Journal of Hydrogen and New Energy
• /
• v.30 no.4
• /
• pp.312-319
• /
• 2019

Effect of loop seal geometry on solid circulation characteristics was investigated with two different types of upper loop seals and lower loop seals in a gas-solid fluidized bed system. Upper loop seal which has a wide gap between solid intake and outlet parts requires more fluidization gas to maintain smooth solid circulation. Moreover, the lower loop seal which has a wide gap requires more fluidization gas to achieve the same solid circulation rate. These results can be explained by results of minimum fluidization velocity in the lower loop seals. Consequently, if a loop seal has a wide gap between solid intake and outlet parts, more fluidization gases should be fed to ensure enough solid circulation rate and smooth solid circulation.