• Steel and Composite Structures
• /
• v.41 no.6
• /
• pp.787-803
• /
• 2021

The size-dependent nonlinear thermomechanical vibration analysis of pre- and post-buckled tapered two-directional functionally graded (2D-FG) microbeams is presented in this study. In the context of the modified couple stress theory, the formulations are derived based on the parabolic shear deformation beam theory and von Karman nonlinear strains. Different thermomechanical material properties are assumed to be temperature-dependent and smoothly vary in both length and thickness directions using the power law and the physical neutral axis concept is employed. The nonlinear governing equations are derived using the Hamilton principle and the resulting variable coefficient equations of motion are solved using the differential quadrature method (DQM) and iterative Newton's method for clamped-clamped and simply supported boundary conditions. Comparison studies are presented to validate the derived model and solution procedure. The impacts of induced thermal moments, temperature power index, two gradient indices, nonuniform cross-section, and microstructure length scale parameter on the frequency-temperature configurations are explored for both clamped and simply supported microbeams.

• Journal of Elementary Mathematics Education in Korea
• /
• v.20 no.1
• /
• pp.105-129
• /
• 2016

The elements of mathematical processes include mathematical reasoning, mathematical problem-solving, and mathematical communications. Proportion reasoning is a kind of mathematical reasoning which is closely related to the ratio and percent concepts. Proportion reasoning is the essence of primary mathematics, and a basic mathematical concept required for the following more-complicated concepts. Therefore, the study aims to analyze the proportion reasoning ability of sixth graders of primary school who have already learned the ratio and percent concepts. To allow teachers to quickly recognize and help students who have difficulty solving a proportion reasoning problem, this study analyzed the characteristics and patterns of proportion reasoning of sixth graders of primary school. The purpose of this study is to provide implications for learning and teaching of future proportion reasoning of higher levels. In order to solve these study tasks, proportion reasoning problems were developed, and a total of 22 sixth graders of primary school were asked to solve these questions for a total of twice, once before and after they learned the ratio and percent concepts included in the 2009 revised mathematical curricula. Students' strategies and levels of proportional reasoning were analyzed by setting up the four different sections and classifying and analyzing the patterns of correct and wrong answers to the questions of each section. The results are followings; First, the 6th graders of primary school were able to utilize various proportion reasoning strategies depending on the conditions and patterns of mathematical assignments given to them. Second, most of the sixth graders of primary school remained at three levels of multiplicative reasoning. The most frequently adopted strategies by these sixth graders were the fraction strategy, the between-comparison strategy, and the within-comparison strategy. Third, the sixth graders of primary school often showed difficulty doing relative comparison. Fourth, the sixth graders of primary school placed the greatest concentration on the numbers given in the mathematical questions.

• Education of Primary School Mathematics
• /
• v.25 no.1
• /
• pp.57-79
• /
• 2022

Current mathematics It is necessary to ensure that ratio and proportion concept is not distorted or broken while being treated as if they were easy to teach and learn in school. Therefore, the purpose of this study is to analyze the activities presented in the textbook. Based on prior work, this study reinterpreted the proportional reasoning task from the proportional perspective of Beckmann and Izsak(2015) to the multiplicative structure of Vergnaud(1996) in four ways. This compared how they interpreted the multiplicative structure and relationships between two measurement spaces of ratio and rate units and proportional expression and proportional distribution units presented in the revised textbooks of 2007, 2009, and 2015 curriculum. First, the study found that the proportional reasoning task presented in the ratio and rate section varied by increasing both the ratio structure type and the proportional reasoning activity during the 2009 curriculum, but simplified the content by decreasing both the percentage structure type and the proportional reasoning activity. In addition, during the 2015 curriculum, the content was simplified by decreasing both the type of multiplicative structure of ratio and rate and the type of proportional reasoning, but both the type of multiplicative structure of percentage and the content varied. Second, the study found that, the proportional reasoning task presented in the proportional expression and proportional distribute sections was similar to the previous one, as both the type of multiplicative structure and the type of proportional reasoning strategy increased during the 2009 curriculum. In addition, during the 2015 curriculum, both the type of multiplicative structure and the activity of proportional reasoning increased, but the proportional distribution were similar to the previous one as there was no significant change in the type of multiplicative structure and proportional reasoning. Therefore, teachers need to make efforts to analyze the multiplicative structure and proportional reasoning strategies of the activities presented in the textbook and reconstruct them according to the concepts to teach them so that students can experience proportional reasoning in various situations.

• Communications of Mathematical Education
• /
• v.29 no.3
• /
• pp.553-571
• /
• 2015

Mathematical, verbal, and spatial abilities are known as three important indicators for the success in the STEM disciplines. In this study, Purdue Spatial Visualization Test-Rotation, College Entrance Scholastic Aptitude Test- Math and Verbal score of engineering freshmen students have been used to find the relationships among these areas. In addition, gender differences in spatial visualization, verbal achievement and mathematical achievement have been investigated, too. In this research, I found that gender difference was highest in spatial visualization ability, followed by verbal achievement and smallest in mathematical achievement. Substantial number of male students possess high level of spatial abilities, but only half of female students were at the same level where their male colleagues were. The correlation between spatial ability and mathematical ability was negligible, contrary to former researches on elementary and middle school students. But the correlation was stronger for female students than male students. The correlation between mathematical achievement and verbal achievement was negative. It reflects the fact that when one section of SAT score is low, score of other sections should be higher to get admitted to college. Gender difference in mathematics was smallest for high achieving spatial ability group. For low spatial ability group gender difference in mathematics achievement has been observed, too. To find the combined contribution of spatial and verbal abilities to mathematics achievement, students were divided into 4 ability groups. Mathematics achievement decreased in the order of (1) high spatial -low verbal group, (2) low spatial - low verbal group, (3) high spatial - high verbal group, (4) low spatial - high verbal group.

• Kyungpook Mathematical Journal
• /
• v.13 no.2
• /
• pp.235-240
• /
• 1973

A k-dimensional vector bundle is a bundle ${\xi}=(E,P,B,F^k)$ with fibre $F^k$ satisfying the local triviality, where F is the field of real numbers R or complex numbers C ([1], [2] and [3]). Let $Vect_k(X)$ be the set consisting of all isomorphism classes of k-dimensional vector bundles over the topological space X. Then $Vect_F(X)=\{Vect_k(X)\}_{k=0,1,{\cdots}}$ is a semigroup with Whitney sum (${\S}1$). For a pair (X, A) of topological spaces, a difference isomorphism over (X, A) is a vector bundle morphism ([2], [3]) ${\alpha}:{\xi}_0{\rightarrow}{\xi}_1$ such that the restriction ${\alpha}:{\xi}_0{\mid}A{\longrightarrow}{\xi}_1{\mid}A$ is an isomorphism. Let $S_k(X,A)$ be the set of all difference isomorphism classes over (X, A) of k-dimensional vector bundles over X with fibre $F^k$. Then $S_F(X,A)=\{S_k(X,A)\}_{k=0,1,{\cdots}}$, is a semigroup with Whitney Sum (${\S}2$). In this paper, we shall prove a relation between $Vect_F(X)$ and $S_F(X,A)$ under some conditions (Theorem 2, which is the main theorem of this paper). We shall use the following theorem in the paper. THEOREM 1. Let ${\xi}=(E,P,B)$ be a locally trivial bundle with fibre F, where (B, A) is a relative CW-complex. Then all cross sections S of ${\xi}{\mid}A$ prolong to a cross section $S^*$ of ${\xi}$ under either of the following hypothesis: (H1) The space F is (m-1)-connected for each $m{\leq}dim$ B. (H2) There is a relative CW-complex (Y, X) such that $B=Y{\times}I$ and $A=(X{\times}I)$ ${\cap}(Y{\times}O)$, where I=[0, 1]. (For proof see p.21 [2]).

• Earthquakes and Structures
• /
• v.5 no.2
• /
• pp.161-205
• /
• 2013

We study seismically induced, anti-plane strain wave motion in a non-homogeneous geological region containing tunnels. Two different scenarios are considered: (a) The first models two tunnels in a finite geological region embedded within a laterally inhomogeneous, layered geological profile containing a seismic source. For this case, labelled as the first boundary-value problem (BVP 1), an efficient hybrid technique comprising the finite difference method (FDM) and the boundary element method (BEM) is developed and applied. Since the later method is based on the frequency-dependent fundamental solution of elastodynamics, the hybrid technique is defined in the frequency domain. Then, an inverse fast Fourier transformation (FFT) is used to recover time histories; (b) The second models a finite region with two tunnels, is embedded in a homogeneous half-plane, and is subjected to incident, time-harmonic SH-waves. This case, labelled as the second boundary-value problem (BVP 2), considers complex soil properties such as anisotropy, continuous inhomogeneity and poroelasticity. The computational approach is now the BEM alone, since solution of the surrounding half plane by the FDM is unnecessary. In sum, the hybrid FDM-BEM technique is able to quantify dependence of the signals that develop at the free surface to the following key parameters: seismic source properties and heterogeneous structure of the wave path (the FDM component) and near-surface geological deposits containing discontinuities in the form of tunnels (the BEM component). Finally, the hybrid technique is used for evaluating the seismic wave field that develops within a key geological cross-section of the Metro construction project in Thessaloniki, Greece, which includes the important Roman-era historical monument of Rotunda dating from the 3rd century A.D.

• Steel and Composite Structures
• /
• v.34 no.3
• /
• pp.393-407
• /
• 2020

The braced tube frame system, a combination of perimeter frame and bracing frame, is one of the systems used in tall buildings. Due to the implementation of this system in tall buildings and the high rigidity resulting from the use of general bracing, providing proper ductility while maintaining the strength of the structure when exposing to lateral forces is essential. Also, the high stress at the connection of the beam to the column may cause a sudden failure in the region before reaching the required ductility. The use of Reduced Beam Section connection (RBS connection) by focusing stress in a region away from beam to column connection is a suitable solution to the problem. Because of the fact that RBS connections are usually used in moment frames and not tested in tall buildings with braced tube frames, they should be investigated. Therefore, in this research, three tall buildings in height ranges of 20, 25 and 30 floors were modeled and designed by SAP2000 software, and then a frame in each building was modeled in PERFORM-3D software under two RBS-free system and RBS-based system. Nonlinear time history dynamic analysis is used for each frame under Manjil, Tabas and Northridge excitations. The results of the Comparison between RBS-free and RBS-based systems show that the RBS connections increased the absorbed energy level by reducing the stiffness and increasing the ductility in the beams and structural system. Also, by increasing the involvement of the beams in absorbing energy, the columns and braces absorb less energy.

• Computers and Concrete
• /
• v.20 no.5
• /
• pp.605-616
• /
• 2017

Concrete filled steel tubular (CFST) composite girder is a new type of structures for bridge constructions. The existing design codes cannot be used to predict the thermal stress in the CFST truss girder structures under solar radiation. This study is to develop the temperature gradient curves for predicting thermal stress of the structure based on field and laboratory monitoring data. An in-field testing had been carried out on Ganhaizi Bridge for over two months. Thermal couples were installed at the cross section of the CFST truss girder and the continuous data was collected every 30 minutes. A typical temperature gradient mode was then extracted by comparing temperature distributions at different times. To further verify the temperature gradient mode and investigate the evolution of temperature fields, an outdoor experiment was conducted on a 1:8 scale bridge model, which was installed with both thermal couples and strain gauges. The main factors including solar radiation and ambient temperature on the different positions were studied. Laboratory results were consistent with that from the in-field data and temperature gradient curves were obtained from the in-field and laboratory data. The relationship between the strain difference at top and bottom surfaces of the concrete deck and its corresponding temperature change was also obtained and a method based on curve fitting was proposed to predict the thermal strain under elevated temperature. The thermal stress model for CFST composite girder was derived. By the proposed model, the thermal stress was obtained from the temperature gradient curves. The results using the proposed model were agreed well with that by finite element modelling.

• Journal of the Korean Mathematical Society
• /
• v.50 no.3
• /
• pp.557-578
• /
• 2013

For an ideal $\mathcal{I}$ of a preadditive category $\mathcal{A}$, we study when the canonical functor $\mathcal{C}:\mathcal{A}{\rightarrow}\mathcal{A}/\mathcal{I}$ is local. We prove that there exists a largest full subcategory $\mathcal{C}$ of $\mathcal{A}$, for which the canonical functor $\mathcal{C}:\mathcal{C}{\rightarrow}\mathcal{C}/\mathcal{I}$ is local. Under this condition, the functor $\mathcal{C}$, turns out to be a weak equivalence between $\mathcal{C}$, and $\mathcal{C}/\mathcal{I}$. If $\mathcal{A}$ is additive (with splitting idempotents), then $\mathcal{C}$ is additive (with splitting idempotents). The category $\mathcal{C}$ is ample in several cases, such as the case when $\mathcal{A}$=Mod-R and $\mathcal{I}$ is the ideal ${\Delta}$ of all morphisms with essential kernel. In this case, the category $\mathcal{C}$ contains, for instance, the full subcategory $\mathcal{F}$ of Mod-R whose objects are all the continuous modules. The advantage in passing from the category $\mathcal{F}$ to the category $\mathcal{F}/\mathcal{I}$ lies in the fact that, although the two categories $\mathcal{F}$ and $\mathcal{F}/\mathcal{I}$ are weakly equivalent, every endomorphism has a kernel and a cokernel in $\mathcal{F}/{\Delta}$, which is not true in $\mathcal{F}$. In the final section, we extend our theory from the case of one ideal$\mathcal{I}$ to the case of $n$ ideals $\mathcal{I}_$, ${\ldots}$, $\mathca{l}_n$.

• The Korean Journal of Elementary Counseling
• /
• v.4 no.1
• /
• pp.123-150
• /
• 2005

The purpose of this study was to examine the effects of self-regulated learning program on the underachiever's academic achievement and academic self-concept. To achieve the purpose of study the research hypotheses were as follows : Hypothesis 1 : There will be significant differences in the improvement of academic achievement between the experimental group and the control group. Hypothesis 2 : There will be significant differences in the improvement of academic self-concept between the experimental group and the control group. To verify these hypotheses, 32 underachievers were selected from sixth grade students of 'D' elementary school located in Seoul. 16 students were allocated to the experimental group and 16 students were allocated to the control group. The experimental group trained with self-regulated learning program for 10 times(The length of each section was 60 minutes). The self-regulated learning program in this study was based on program by Kim. Yong-Soo(1998), The measurement instruments of the study were mathematics achievement test paper and academic self-concept test. To find out the difference, Pretest-posttest control design was used. Mean and standard deviations obtained from these tests were analysed with t-test. The major findings obtained through this study are as follows : First, self-regulated learning program was effective in improvement of academic achievement (p<.05). Second, self-regulated learning Program was not effective in improvement of academic self-concept. However, the experimental group showed significant improvement(p<.01) at academic self-concept and sub academic self-concepts (ability, achievement) in the data of pre-post test. it can be suggested that this program had positive influence on underachievers. Although it has some limitations, self-regulated learning program is effective to academic achievement and academic self-concept of underachievers, even though not significant, it has a positive t.