• Journal of Educational Research in Mathematics
• /
• v.23 no.2
• /
• pp.173-192
• /
• 2013

It may be replacement proofs with understanding and explaining geometrical properties that was a remarkable change in school geometry of 2009 revised national curriculum for mathematics. That comes from the difficulties which students have experienced in learning proofs. This study focuses on one of those difficulties which are caused by the forms of proofs: using letters for designating some sides or angles in writing proofs and understanding some long sentences of proofs. To overcome it, this study aims to investigate the applicability of Byrne's method which uses coloured diagrams instead of letters. For this purpose, the proofs of three geometrical properties were taught to middle school students by Byrne's visual method using the original source, dynamic representations, and the teacher's manual drawing, respectively. Consequently, the applicability of Byrne's method was discussed based on its strengths and its weaknesses by analysing the results of students' worksheets and interviews and their teacher's interview. This analysis shows that Byrne's method may be helpful for students' understanding of given geometrical proofs rather than writing proofs.

• Textile Coloration and Finishing
• /
• v.9 no.4
• /
• pp.28-38
• /
• 1997

Peach skin fabrics were washed by the general and ultrasonic washing systems using different conditions. The physical properties of the washed fabrics were estimated. The following results were obtained through experimental data and their analysis. The tensile properties were changed due to fabric running speed and washing methods. The lower the running speed, the higher the extensibility and resilience and the lower the linearity and tensile energy. In the general washing method, the extensibility and resilience had lower values than those of the ultrasonic washing method and the linearity and tensile energy had the higher values than those of the ultrasonic washing system. The bending properties, bending moment and histeresis, were estimated. These values were generally lower in the ultrasonic washing system than those of the general washing system. The faster the washing speed, the higher the value of hysterisis. The shear properties were affected by the fabric running speed and washing methods. Shear stiffness and hysteresis of shear forces increased according to the increase of the fabric running speed. The values were higher in the general washing system than those of the ultrasonic washing system. The compressional energy was affected by the fabric running speed. The higher the fabric speed the higher the compressional energy. The ultrasonic washing system had lower compressional energy than the general washing system. The higher the running speed, the lower the coefficient of friction and geometrical roughness. The values of geometrical roughness were infienced by the removal of the sizing agent. The higher the remaining sizing agent, the higher the fabric weight and the thicker the thickness of fabric.

• Honam Mathematical Journal
• /
• v.29 no.1
• /
• pp.75-81
• /
• 2007

The Fisher information matrix plays a significant role in statistical inference in connection with estimation and properties of variance of estimators. In this paper, the parameter space of the normal distribution using its Fisher's matrix is defined. The Riemannian curvature and J-divergence to parameter space are calculated.

• Proceedings of the KIEE Conference
• /
• 1996.07c
• /
• pp.1479-1481
• /
• 1996

The Purpose of this paper is to produce air core inductor and measure its electrical properties for high frequency. Especially we focused attention on the effect of geometrical parameters such as coil width, distance between coils, turn number. In addition, the influence of film morphology at inductor was investigated. Increase of coil width and decrease of turn number resulted in promotion of electric properties.

• Honam Mathematical Journal
• /
• v.28 no.3
• /
• pp.433-438
• /
• 2006

The Fisher information matrix plays a significant role in statistical inference in connection with estimation and properties of variance of estimators. In this paper, the parameter space of the t-distribution using its Fisher's matrix is defined. The Riemannian and scalar curvatures to parameter space are calculated.

• Advances in Computational Design
• /
• v.2 no.4
• /
• pp.257-271
• /
• 2017

There are many plain concrete arch bridges in Iran that have been used as railway bridges for more than seventy years. Owe to the fact that these bridges have not been designed seismically, and even may be loaded under high-speed trains, evaluation of fundamental frequencies of the bridges against earthquake and high-speed train vibrations is necessary for considering dynamics effects. To evaluate complex behavior of these bridges, results of field tests are useful. Since it is not possible to perform field tests for all arch bridges, these structures should be simulated correctly by computers for structural assessment. Several parameters are employed to describe the bridges, such as number of spans, length of spans, geometrical and material properties. In this study, results of field tests are used for modal analysis and adapted for 64 three dimensional finite element models with various physical parameters. Computer simulations show length of spans has important effect on fundamental frequencies of plain concrete arch bridge and modal deformations of bridges is in longitudinal and transverse directions. Also, these results demonstrate that fundamental frequencies of bridges decrease after increasing span length and number of spans. Plus, some relations based in the number of spans (n) and span length (l) are proposed for calculation of fundamental frequencies of plain concrete arch bridge.

• Structural Engineering and Mechanics
• /
• v.67 no.6
• /
• pp.565-578
• /
• 2018

This research article reported the nonlinear finite solutions of the nonlinear flexural strength and stress behaviour of nano sandwich graded structural shell panel under the combined thermomechanical loading. The nanotube sandwich structural model is derived mathematically using the higher-order displacement polynomial including the full geometrical nonlinear strain-displacement equations via Green-Lagrange relations. The face sheets of the sandwich panel are assumed to be carbon nanotube-reinforced polymer composite with temperature dependent material properties. Additionally, the numerical model included different types of nanotube distribution patterns for the sandwich face sheets for the sake of variable strength. The required equilibrium equation of the graded carbon nanotube sandwich structural panel is derived by minimizing the total potential energy expression. The energy expression is further solved to obtain the deflection values (linear and nonlinear) via the direct iterative method in conjunction with finite element steps. A computer code is prepared (MATLAB environment) based on the current higher-order nonlinear model for the numerical analysis purpose. The stability of the numerical solution and the validity are verified by comparing the published deflection and stress values. Finally, the nonlinear model is utilized to explore the deflection and the stresses of the nanotube-reinforced (volume fraction and distribution patterns of carbon nanotube) sandwich structure (different core to face thickness ratios) for the variable type of structural parameter (thickness ratio, aspect ratio, geometrical configurations, constraints at the edges and curvature ratio) and unlike temperature loading.

• Steel and Composite Structures
• /
• v.33 no.6
• /
• pp.837-847
• /
• 2019

A type of hybrid core made up of thin-walled square carbon fiber reinforced polymer (CFRP) honeycomb and Polymethacrylimide (PMI) foam fillers was proposed and prepared. Numerical model of the core under quasi static compression was established and validated by corresponding experimental results. The compressive properties of the core with different configurations were analyzed through numerical simulations. The effect of the geometrical parameters and foam fillers on the compressive response and energy absorption of the core were analyzed. The results show that the PMI foam fillers can significantly improve the compressive strength and energy absorption capacity of the square CFRP honeycomb. The geometrical parameters have marked effects on the compressive properties of the core. The research can give a reference for the application of PMI foam materials in energy absorbing structures and guide the design and optimization of lightweight and energy efficient cores of sandwiches.

• Proceeding of EDISON Challenge
• /
• 2014.03a
• /
• pp.472-474
• /
• 2014

Carbon nanotubes (CNTs) have been intensively investigated since they have been considered as building blocks of nanoscience and nanotechnology. Theoretical and computational studies on CNTs have revealed their physical and chemical properties and helped researchers build various experimental devices to study them in depth. However, there have been only few systematic studies on detailed changes in electronic structures of CNTs due to geometrical structure modifications. In this regard, it is necessary to perform systematic investigations of the modifications in electronic structures of CNTs, as their geometrical configurations are altered, using the first-principles density functional theory. In other words, it is essential to determine the true equilibrium structure of CNTs. We are going to construct different atomic configurations of each nanotube by maintaining the original symmetries, but changing all the other bonding types one by one. Furthermore, as for CNTs, for example, the way the graphene sheet is wrapped is represented by a pair of indices (n,m) and electronic structures of CNTs vary depending on different indices. Therefore, we plan to study and discuss all the significant couplings between electronic and geometric structures in CNTs.

• Structural Engineering and Mechanics
• /
• v.89 no.1
• /
• pp.13-22
• /
• 2024

The nonlinear snap-through buckling of functionally graded (FG) carbon nanotube reinforced composite (CNTRC) curved tubes is analytically investigated in this research. It is assumed that the FG-CNTRC curved tube is supported on a three-parameter nonlinear elastic foundation and is subjected to the uniformly distributed pressure and thermal loads. Properties of the curved nanocomposite tube are distributed across the radius of the pipe and are given by means of a refined rule of mixtures approach. It is also assumed that all thermomechanical properties of the nanocomposite tube are temperature-dependent. The governing equations of the curved tube are obtained using a higher-order shear deformation theory, where the traction free boundary conditions are satisfied on the top and bottom surfaces of the tube. The von Kármán type of geometrical non-linearity is included into the formulation to consider the large deflection in the curved tube. Equations of motion are solved using the two-step perturbation technique for nanocomposite curved tubes which are simply-supported and clamped. Closed-form expressions are provided to estimate the snap-buckling resistance of FG-CNTRC curved pipes rested on nonlinear elastic foundation in thermal environment. Numerical results are given to explore the effects of the distribution pattern and volume fraction of CNTs, thermal field, foundation stiffnesses, and geometrical parameters on the instability of the curved nanocomposite tube.