• Structural Engineering and Mechanics
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• v.70 no.1
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• pp.33-41
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• 2019

The influence of two parameters on fatigue damage predictions of a variably loaded cantilever beam has been examined. The first parameter is the geometry of the cantilever beam and the weld connecting it to a rear panel. Variables of the geometry examined here include the cantilever length, the weld width on the critical cross-section and the angle of the critical cross-section. The second parameter is the safety factor, as set out by the Eurocode 3 standard. An analytical approach has been used to calculate the stresses at the critical cross-section and standard rainflow counting has been used for the extraction of the load cycles from the load history. The results here suggest that a change in the width and angle of the critical cross-section has a non-linear impact on the fatigue damage. The results also show that the angle of the critical cross-section has the biggest influence on the fatigue damage and can cause the weld to withstand fatigue better. The second parameter, the safety factor, is shown to have a significant effect on the fatigue damage calculation, whereby a slight increase in the endurance safety factor can cause the calculated fatigue damage to increase considerably.

• Journal of Educational Research in Mathematics
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• v.16 no.1
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• pp.1-23
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• 2006

It is regarded as critical to analyse and re-appreciate Euclidean geometry for the sake of improving school geometry This study, a critical analysis of demonstrative plane geometry in current secondary school mathematics with an eye to the viewpoints of 'Elements of Geometry', is conducted with this purpose in mind. Firstly, the 'Elements' is analysed in terms of its educational purpose, concrete contents and approaching method, with a review of the history of its teaching. Secondly, the 'Elemens de Geometrie' by Clairaut and the 'histo-genetic approach' in teaching geometry, mainly the one proposed by Branford, are analysed. Thirdly, the basic assumption, contents and structure of the current textbooks taught in secondary schools are analysed according to the hypothetical construction, ordering and grouping of theorems, presentations of proofs, statements of definitions and exercises. The change of the development of contents over time is also reviewed, with a focus on the proportional relations of geometric figures. Lastly, tile complementary way of integrating the two 'Elements' is explored.

• Korean Journal of Mathematics
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• v.23 no.3
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• pp.379-391
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• 2015

We investigate the existence of solutions of the nonlinear biharmonic equation with variable coefficient polynomial growth nonlinear term and Dirichlet boundary condition. We get a theorem which shows that there exists a bounded solution and a large norm solution depending on the variable coefficient. We obtain this result by variational method, generalized mountain pass geometry and critical point theory.

• Korean Journal of Mathematics
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• v.17 no.4
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• pp.419-428
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• 2009

We show the existence of at least one nontrivial solution of the homogeneous mixed type nonlinear elliptic problem. Here mixed type nonlinearity means that the nonlinear part contain the jumping nonlinearity and the critical growth nonlinearity. We first investigate the sub-level sets of the corresponding functional in the Soboles space and the linking inequalities of the functional on the sub-level sets. We next investigate that the functional I satisfies the mountain pass geometry in the critical point theory. We obtain the result by the mountain pass method, the critical point theory and variational method.

• Journal of Advanced Marine Engineering and Technology
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• v.19 no.2
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• pp.1-9
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• 1995

The processing paper has devoted to the theory of the flow equations, the basic derivative procedure, the meaning of a valve flow coefficient $C_v$, the valve Reynolds R$R_{ev}$ and its application for liquid control valves, which applicable under the condition of a non-critical flow and the case of piping geometry factor $F_p$=1.0. However there is no information on the effects of fittings, a critical flow and the flow resistance coefficient of a valve equivalent to that of pipe which is conveniently used in the piping design. Since the piping systems of plants or ships generally contain various fittings such as expanders and reducers due to different size between pipes and valves and there may occur a critical flow, that a mass flowrate is maintained to be constant, due to the pressure drop in a piping when a liquid is initially maintainder ar a saturated temperature or at nearby corresponding to upstream pressure, system designer should have a knowledge of the effect to flow due to fittings and the critical flow phenomenon of a liquid. This study is performed to inform system designers with the critical flow phenomenon of a liquid, a valve resistance coefficient, a valve geometry factor and their applications.

• Journal of Mechanical Science and Technology
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• v.18 no.7
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• pp.1222-1235
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• 2004

This study examines the influence of geometry on the internal flow and macroscopic behavior of the spray in Diesel nozzles. For this investigation, two bi-orifice nozzles were employed: one cylindrical and one conical. The first step is to use a non-destructive characterization method which is based on the production of silicone moulds so that the precise internal geometry of the two nozzles can be measured. At this stage the nozzles have been characterized dimensionally and therefore the internal flow can be studied using CFD calculations. The results gained from this experiment make it possible also to ascertain the critical cavitation conditions. Once the critical cavitation conditions have been identified, the macroscopic parameters of the spray can be studied in both cavitating and non-cavitating conditions using a test rig pressurized with nitrogen and with the help of a image acquisition system and image processing software. Consequently, research can be carried out to determine the influence that cavitation has on macroscopic spray behavior. From the point of view of the spray macroscopic behavior, the main conclusion of the paper is that cavitation leads to an increment of the spray cone angle. On the other hand, from the point of view of the internal flow, the hole outlet velocity increases when cavitation appears. This phenomenon can be explained by the reduction in the cross section of the liquid phase in the outlet section of the hole.

• Nuclear Engineering and Technology
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• v.5 no.2
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• pp.115-131
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• 1973

L.S. Pontryagin's maximum principle is applied to the minimum critical mass problem without any restriction on the ranges of uranium enrichment. For the analysis, two group diffusion equation is adopted for a cylindrical reactor neglecting the vertical axis consideration. The result shows that the three-zoned reactor turns out to be most optimal: the inner and outer zones with the minimum enrichment ; whereas the middle 3one with the maximum enrichment. With the given three-zoned reactor, critical condition is derived, which leads to the calculation of the determinant. By finding the roots of the determinant the numerical calculation of the minimum critical mass is carried out for the case of Kori reactor geometry changing the minimum or the maximum enrichment. It is found from many computed values that the least possible critical mass turns out to be the case of 1.2% maximum enrichment for the middle zone and 0.65% minimum enrichment for the inner and out zones.

• Proceedings of the IEEK Conference
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• 2005.11a
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• pp.663-666
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• 2005

The geometry stage, which performs the transformation and lighting operations of vertices, became the critical part in 3D graphics pipeline. In this paper, we have planned and designed the Geometry Processor for the better and more efficient way to process the real-time 3D using the floating point unit. We also designed a verification system for Geometry engine. It is implemented with Xilinx-Virtex2 and Visual C++.NET. In the Synopsis, we confirmed 100 MHz performance and 137107 cell area of Geometry Engine.

• Computers and Concrete
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• v.15 no.4
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• pp.673-686
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• 2015

R-curve based on the size effect law previously developed for geometrically similar specimens (geometry type III) is extended to geometries with variable depth (geometry type I) as well as with variable notch (geometry type II), where the R-curve is defined as the envelope of the family of critical strain energy release rates from specimens of different sizes. The results show that the extended R-curve for type I tends to be the same for different specimen configurations, while it is greatly dependent on specimen geometry in terms of the initial crack length. Furthermore, the predicted load-deflection responses from the suggested R-curve are found to agree well with the testing results on concrete and rock materials. Besides, maximum loads for type II specimen are predicted well from the extended R-curve.

• Biomaterials and Biomechanics in Bioengineering
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• v.3 no.2
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• pp.71-84
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• 2016

The finite element method is wide used in simulation in the biomechanical structures, but a lack of studies concerning finite element mesh quality in biomechanics is a reality. The present study intends to analyze the importance of the mesh quality in the finite element model results from humeral structure. A sensitivity analysis of finite element models (FEM) is presented for the humeral bone and cartilage structures. The geometry of bone and cartilage was acquired from CT scan and geometry reconstructed. The study includes 54 models from same bone geometry, with different mesh densities, constructed with tetrahedral linear elements. A finite element simulation representing the glenohumeral-joint reaction force applied on the humerus during $90^{\circ}$ abduction, with external load as the critical condition. Results from the finite element models suggest a mesh with 1.5 mm, 0.8 mm and 0.6 mm as suitable mesh sizes for cortical bone, trabecular bone and humeral cartilage, respectively. Relatively to the higher minimum principal strains are located at the proximal humerus diaphysis, and its highest value is found at the trabecular bone neck. The present study indicates the minimum mesh size in the finite element analyses in humeral structure. The cortical and trabecular bone, as well as cartilage, may not be correctly represented by meshes of the same size. The strain results presented the critical regions during the $90^{\circ}$ abduction.