• Steel and Composite Structures
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• 제41권6호
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• pp.787-803
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• 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.

• 한국초등수학교육학회지
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• 제20권1호
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• pp.105-129
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• 2016

2009 개정 교육과정에서 수학적 과정은 수학적 추론, 수학적 문제 해결, 수학적 의사소통의 형태로 강조되고 있으며, 수학적 추론의 한 형태인 비례 추론은 비와 비율 개념과 관련된 추론이다. 비례 추론은 초등학교 수학에서 규칙성 영역의 핵심이면서 중등수학에서 학습하는 함수 개념의 기본이 된다. 본 연구는 2007 개정과 2009 개정 교육과정 사이에 놓인 초등학교 6학년 학생들을 대상으로 비례와 관련된 형식적인 알고리즘을 배우기 전 단계에서 비례 추론의 특징과 유형을 분석해봄으로써 비례 추론을 사용하는 학생들의 문제해결전략과 오류를 살펴본다. 이를 위해 먼저 비례 추론 문항을 개발하고, 초등학교 6학년 학생들이 비와 비율을 학습하기 전후에 비례 추론 관련 문제를 어떻게 해결하고 또 어떠한 오류가 나타나는지를 분석한다. 그 결과 초등학교 6학년 학생들은 문제의 조건과 유형에 따라 다양한 비례 추론 전략을 활용한다. 대부분의 학생들은 곱셈적 추론 수준에 있으며, 비례 추론 검사에서 가장 많이 나타난 전략으로는 분수 전략과 간비교, 내비교 전략 등이었다. 그러나 학생들은 상대적인 비교를 필요로 하는 문제의 경우 문제의 이해 단계에서부터 어려움을 나타냈다. 따라서 절대적 상대적 변화를 비교하는 수준에 이를 수 있도록 다양한 형태의 비례 추론 문항 개발이 요구되며, 이와 함께 비례 추론 상황을 포함하여 지도할 수 있는 교수 방안의 개발이 요구된다.

• 한국수학교육학회지시리즈C:초등수학교육
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• 제25권1호
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• pp.57-79
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• 2022

본 연구에서 초등 교과서의 비와 비율 단원 및 비례식과 비례배분 단원에서 비와 비례 개념과 관련하여 제시된 활동을 분석하여 교과서에 제시된 비례추론 과제가 교육과정별로 어떠한지 알아보았다. 비와 비율 단원에 제시된 비례추론 과제가 2009 개정 때에는 비와 비율의 곱셈 구조 유형과 비례추론 활동이 모두 늘어 내용이 다양해졌지만, 백분율의 곱셈 구조 유형과 비례추론 활동은 모두 약화되었다. 2015 개정 때에도 둘 다 약화되었고, 백분율의 곱셈 구조 유형과 비례 추론 활동은 모두 늘어 내용이 다양해졌다. 비례식과 비례배분 단원에 제시된 비례추론 과제가 2009 개정 시기에는 비의 성질의 곱셈 구조 유형과 비례추론 활동이 모두 증가하여 내용이 다양해졌지만, 비례식과 비례배분은 곱셈 구조 유형만 늘고 비례추론 활동에는 큰 변화가 없어 이전과 내용이 비슷했다. 그리고 2015 개정 시기에 비례식의 곱셈 구조 유형과 비례추론 활동이 모두 늘어 내용이 다양해졌지만, 비의 성질과 비례배분은 곱셈 구조의 유형과 비례추론 활동에 큰 변화가 없어 이전 내용과 비슷하였다. 비와 비율 단원과 비례식과 비례배분 단원에서 모두 다중 묶음 관점에 따라 측정 공간 내의 분석으로 해석하려는 시도가 주로 있었다.

• 한국수학교육학회지시리즈E:수학교육논문집
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• 제29권3호
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• pp.553-571
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• 2015

본 연구는 공간능력이 수학 성취도 및 STEM 분야의 성공에서 중요한 역할을 한다는 사실에 기초하여, 공과 대학생들의 공간능력, 수학 성취도, 그리고 언어 성취도 사이의 관계와 각 영역에서 성별 차이를 파악하는데 목적을 두었다. 그와 함께 수학 성취도에서의 성별 차이가 공간능력에서의 차이에 의해서 매개되는 지도 확인하고자 하였다. 이를 위하여 서울 소재 공과대학 신입생들에게 공간 시각화-회전(PSVT-R)검사를 실시한 후에 대학수학능력 시험의 수학 및 언어 영역과의 상관관계를 성별로 조사하였다. 연구 결과, 성별 차이는 공간 시각화 능력에서 가장 크게 나타났고, 다음이 언어 성취도, 그리고 수학 성취도의 순서로 낮아졌다. 남학생의 공간 시각화 능력이 여학생보다 0.8d(effect size) 정도 우수하였으며 남학생의 67%가 도달한 수준에 여학생은 34%가 속해있었다. 영역별 상관계수를 살펴보면 수학과 언어 성취도 사이에는 음의 상관관계가 존재하였다, 그러나 예측과는 다르게 수학 성취도와 공간 시각화 능력 사이의 상관관계는 작았다. 공간 시각화 능력과 언어 성취도 사이에도 상관관계는 존재하지 않았다. 그렇지만 공간 시각화 능력은 남학생보다는 여학생의 수학 성취도에 좀 더 강한 영향을 주는 것으로 나타났다. 그 이유는 남학생에서는 공간능력이 보편적인 현상이기 때문에 남학생 내에서는 공간능력이 수학 성취도에 별다른 영향을 미치지 않았던 것으로 파악된다. 그 외에도 공간능력이 낮은 집단에서도 수학 성취도에서는 성별차이가 나타나는 것을 확인하였다. 이것은 현 연구 집단에서는 공간능력이 수학 성취도를 결정하는 주된 요인은 아니라는 점을 보여준다. 언어 성취도가 수학 성취도와 음의 상관관계를 갖는 이유는 입시전형에 합격하기 위해서는 한 영역에서 낮은 점수를 받은 경우에 다른 영역의 점수는 상위권인 학생들이 지원한 결과로 해석된다. 마지막으로 공간 시각화와 언어 능력이 결합하여 수학 성취도에 미치는 영향을 살펴보았다. 언어 성취도와 공간 시각화 점수를 상위권과 하위권으로 구분한 다음 네 그룹으로 나누어서 수학 성취도를 비교하였다. 이 때 수학 성취도는 남학생, 여학생 모두에서 (1) 공간 상위권- 언어 하위권인 그룹, (2) 공간 하위권 - 언어 하위권인 그룹, (3) 공간 상위권 - 언어 상위권 그룹, (4) 공간 하위권 - 언어 상위권 그룹의 순서로 낮아졌다.

• Kyungpook Mathematical Journal
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• 제13권2호
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• pp.235-240
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• 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
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• 제5권2호
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• pp.161-205
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• 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
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• 제34권3호
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• pp.393-407
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• 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
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• 제20권5호
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• pp.605-616
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• 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.

• 대한수학회지
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• 제50권3호
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• pp.557-578
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• 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 $\mathcal{I}_$, ${\ldots}$, $\mathca{l}_n$.

• 초등상담연구
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• 제4권1호
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• pp.123-150
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• 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.