• School Mathematics
• /
• v.13 no.1
• /
• pp.107-125
• /
• 2011

In this paper, we investigated how the GSP environments impact students' conjecturing of geometric properties. And we wanted to draw some implication in teaching and learning geometry in dynamic geometric environments. As results, we conclude that when students were given the problem situations which almost has no condition, they were not successful, and rather when the problem situations had appropriate conditions students were able to generate many conditions which were not given in the original problem situations, and consequently they were more successful in conjecturing geometric properties. And the geometric properties conjectured in GSP environments are more complex and difficult to prove than those in paper and pencil environments. Also the function of moving screen with 'Alt' key is frequently used in conjecturing geometric properties with functions of measurement and calculation of GSP. And students felt happier when they discovered geometric properties than when they could prove geometric properties.

• Proceedings of the Computational Structural Engineering Institute Conference
• /
• 2004.04a
• /
• pp.217-224
• /
• 2004

This paper proposed a new impact equation by analyzing the form of the proposal section 1 and section 2 proposed by Korea Highway Corporation, F-type, NJ-type and SS-type with HVOSM program Because the impact equation proposed by Ministry Construction ＆ Transportation(1992) considered an only impact velocity, the values of impact loads calculated by HVOSM program are 21.5∼44 times as large as those using equation of MCT. The values of HVOSM program are 1.4 times as large as those of Olson's model because Olson's equation consider impact vehicle, impact velocity and impact angle. But, it does not consider geometric characters, while HVOSM program considers characters. Considering the shapes of sections and the conditions of colliding, HVOSM program can calculate imuact load. As Multiple Regression Analysis is conducted with the calculated values, the R² values of the proposed equations are 0.984 in SB1∼SB3 and 0.958 in SB4∼SB6. After all, the equation proposed in this study have better results than Olson's equation.

• The Journal of the Acoustical Society of Korea
• /
• v.35 no.2
• /
• pp.158-165
• /
• 2016

Many researches for improving detection performance in the reverberation environment have been conducted in active sonar systems. Especially the type of active pulse makes an impact on the detection performance in the reverberation environment. Thus, this paper describes the detection performance of PTFM (Pulse Trains of Frequency Modulated waveform), Costas, and Geometric Comb pulses which are known for their outstanding performance against the reverberation. Sea trial data of those pulses was analyzed and it was figured out that the range resolution of PTFM pulse was deteriorated by its sub-pulses. Costas pulse showed performance degradations of the doppler resolution by multipath signals. Geometric Comb pulse showed the best doppler resolution.

• Proceedings of the Korean Society For Composite Materials Conference
• /
• 2000.04a
• /
• pp.38-42
• /
• 2000

In this study, the low velocity impact behavior of the composite laminates has been described by using 3 dimensional nonlinear finite elements. To describe the geometric nonlinearity due to large deformation, the dynamic contact problem is formulated using the exterior penalty finite element method on the base of Total Lagrangian formulation. The incremental decomposition is introduced, and the converged solution is attained by Newton-Raphson Method. The Newmark's constant-acceleration time integration algorithm is used. To make verification of the finite element program developed in this study, the solution of the nonlinear static problem with occurrence of large deformation is compared with ABAQUS, and the solution of the static contact problem with indentation is compared with the Hertz solution. And, the solution of low velocity impact problem for isotropic material is verificated by comparison with that of LS-DYNA3D. Finally the contact force of impact response from the nonlinear analysis are compared with those from the linear analysis.

• The Mathematical Education
• /
• v.52 no.4
• /
• pp.531-547
• /
• 2013

The purpose of the study is to examine how effects of activities using Google SketchUp on students' spatial ability and 3D geometric thinking in measuring the volume of solid figures. By comparing the results from pre- and post-tests between the experimental group and control group, we found that activities using Google SketchUp help students improve their spatial ability in the spatial orientation and visualization. In addition, more than half students in the experimental group moved from level 4 up to level 7 in thinking process of measuring the volume in terms of Battista(2004)'s levels. This study suggests that the instruction with Google SketchUp can help to improve students' spatial ability and 3D geometric thinking in the regular class in middle school. In addition, SketchUp can be an advanced technological tool to support students' self-directed learning, which create an efficient educational environment and a great opportunity to learn geometry in an effective manner.

• Steel and Composite Structures
• /
• v.50 no.2
• /
• pp.149-158
• /
• 2024

Considering that different boundary conditions can have an important impact on structural vibration characteristics. In this paper, the nonlinear forced vibration behavior of functionally graded material (FGM) doubly curved shells with initial geometric imperfections under different boundary conditions is studied. Considering initial geometric imperfections and von Karman geometric nonlinearity, the nonlinear governing equations of FGM doubly curved shells are derived using Reissner's first order shear deformation (FOSD) theory. Three different boundary conditions of four edges simply supported (SSSS), four edges clamped (CCCC), clamped-clamped-simply-simply (CCSS) were studied, and a system of nonlinear ordinary differential equations was obtained with the help of Galerkin principle. The nonlinear forced vibration response of the FGM doubly curved shell is obtained by using the modified Lindstedt Poincare (MLP) method. The accuracy of this method was verified by comparing it with published literature. Finally, the effects of curvature ratio, power law index, void coefficient, prestress, and initial geometric imperfections on the resonance of FGM doubly curved shells under different boundary conditions are fully discussed. The relevant research results can provide certain guidance for the design and application of doubly curved shell.

• Ocean Systems Engineering
• /
• v.9 no.4
• /
• pp.349-368
• /
• 2019

Triceratops is one of the new generations of offshore compliant platforms suitable for ultra-deepwater applications. Apart from environmental loads, the offshore structures are also susceptible to accidental loads. Due to the increase in the risk of collision between ships and offshore platforms, the accurate prediction of structural response under impact loads becomes necessary. This paper presents the numerical investigations of the impact response of the buoyant leg of triceratops usually designed as an orthogonally stiffened cylindrical shell with stringers and ring frames. The impact analysis of buoyant leg with a rectangularly shaped indenter is carried out using ANSYS explicit analysis solver under different impact load cases. The results show that the shell deformation increases with the increase in impact load, and the ring stiffeners hinder the shell damage from spreading in the longitudinal direction. The response of triceratops is then obtained through hydrodynamic response analysis carried out using ANSYS AQWA. From the results, it is observed that the impact load on single buoyant leg causes periodic vibration in the deck in the surge and pitch degrees of freedom. Since the impact response of the structure is highly affected by the geometric and material properties, numerical studies are also carried out by varying the strain rate, and the location of the indenter and the results are discussed.

• Journal of Educational Research in Mathematics
• /
• v.26 no.4
• /
• pp.769-789
• /
• 2016

Pattern activities are useful to develop functional thinking of young students, but there has been lack of research on how to teach patterns. This study explored teaching methods of geometric patterns for developing functional thinking of elementary school students, and then analyzed the lessons in which such methods were implemented. For this, three classrooms of fourth grades in elementary schools were selected and three teachers taught geometric patterns on the basis of the same lesson plan. The lessons emphasized noticing the commonality of a given pattern, expanding the noti ce for the commonality, and representing the commonality. The results of this study showed that experience of analyzing the structure of a geometric pattern had a significant impact on how the fourth graders reasoned about the generalized rules of the given pattern and represented them in various methods. This paper closes with several implications to teach geometric patterns in a way to foster functional thinking.

• Steel and Composite Structures
• /
• v.48 no.6
• /
• pp.693-708
• /
• 2023

Composite beams, two materials joined together, have become more common in structural engineering over the past few decades because they have better mechanical and structural properties. The shear connectors between their layers exhibit some deformability with finite stiffness, resulting in interfacial shear slip, a phenomenon known as partial shear interaction. Such a partial shear interaction contributes significantly to the composite beams. To provide precise predictions of the geometric nonlinear behavior shown by two-layered composite beams with interfacial shear slips, a robust analytical model has been developed that incorporates the influence of significant displacements. The application of a higher-order beam theory to the two material layers results in a third-order adjustment of the longitudinal displacement within each layer along the depth of the beam. Deformable shear connectors are employed at the interface to represent the partial shear interaction by means of a sequence of shear connectors that are evenly distributed throughout the beam's length. The Von-Karman theory of large deflection incorporates geometric nonlinearity into the governing equations, which are then solved analytically using the Navier solution technique. Suggested model exhibits a notable level of agreement with published findings, and numerical outputs derived from finite element (FE) model. Large displacement substantially reduces deflection, interfacial shear slip, and stress values. Geometric nonlinearity has a significant impact on beams with larger span-to-depth ratio and a greater degree of shear connector deformability. Potentially, the analytical model can accurately predict the geometric nonlinear responses of composite beams. The model has a high degree of generality, which might aid in the numerical solution of composite beams with varying configurations and shear criteria.

• Steel and Composite Structures
• /
• v.47 no.5
• /
• pp.615-631
• /
• 2023

Steel corrosion induces structural deterioration of concrete-filled steel tubes (CFSTs), and any potential extreme action on a corroded CFST would pose a severe threat. This paper presents a comprehensive investigation on the lateral impact behaviour of CFSTs suffering from localised pitting corrosion damage. A refined finite element analysis model is developed for the simulation of locally corroded CFSTs subjected to lateral impact loads, which takes into account the strain rate effects on concrete and steel materials as well as the random nature of corrosion pits, i.e., the distribution patterns and the geometric characteristics. Full-range nonlinear analysis on the lateral impact behaviour in terms of loading and deforming time-history relations, nonlinear material stresses, composite actions, and energy dissipations are presented for CFSTs with no corrosion, uniform corrosion and pitting corrosion, respectively. Localised pitting corrosion is found to pose a more severe deterioration on the lateral impact behaviour of CFSTs due to the plastic deformation concentration, the weakened confinement and the reduction in energy absorption capacity of the steel tube. An extended parametric study is then carried out to identify the influence of the key parameters on the lateral impact behaviour of CFSTs with localised pitting corrosion. Finally, simplified design methods considering the features of pitting corrosion are proposed to predict the dynamic flexural capacity of locally pitted CFSTs subjected to lateral impact loads, and reasonable accuracy is obtained.