• Research in Mathematical Education
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• v.10 no.3 s.27
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• pp.169-187
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• 2006

Ubiquitous errors in algebra like $(x+y)^2=x^2+y^2$ are a constant reminder that most students' manipulation of algebraic symbols has become detached from structural principles. The U.S. mathematics education community (NCTM, 2000) has responded by shying away from algebra as a structural study, preferring instead to ground meaning in empirical domains of reference. A new analysis of such errors shows that students' detachment from structural meaning stems from an inadequate structural curriculum, not from the inherent difficulty of adopting an abstract perspective on expressions and equations. A structural curriculum is outlined that preserves the possibility of students' engaging fully with algebra as both an empirical and a structural study.

• Earthquakes and Structures
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• v.18 no.5
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• pp.649-665
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• 2020

One of the most important issues in structural systems is evaluation of the margin of safety in low and mid-rise buildings against the progressive collapse mechanism due to the earthquake loads. In this paper, modeling of collapse propagation in structural elements of RC frame buildings is evaluated by tracing down the collapse points in beam and column structural elements, one after another, under earthquake loads and the influence of column removal is investigated on how the collapse expansion in beam and column structural members. For this reason, progressive collapse phenomenon is studied in 3-story and 5-story intermediate moment resisting frame buildings due to the corner and edge column removal in presence of the earthquake loads. In this way, distribution and propagation of the collapse in progressive collapse mechanism is studied, from the first element of the structure to the collapse of a large part of the building with investigating and comparing the results of nonlinear time history analyses (NLTHA) in presence of two-component accelograms proposed by FEMA_P695. Evaluation of the results, including the statistical survey of the number and sequence of the collapsed points in process of the collapse distribution in structural system, show that the progressive collapse distribution are special and similar in low-rise and mid-rise RC buildings due to the simultaneous effects of the column removal and the earthquake loads and various patterns of the progressive collapse distribution are proposed and presented to predict the collapse propagation in structural elements of similar buildings. So, the results of collapse distribution patterns and comparing the values of collapse can be utilized to provide practical methods in codes and guidelines to enhance the structural resistance against the progressive collapse mechanism and eventually, the value of damage can be controlled and minimized in similar buildings.

• Earthquakes and Structures
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• v.18 no.6
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• pp.691-707
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• 2020

One of the most important issues in structural systems is evaluation of the margin of safety in low and mid-rise buildings against the progressive collapse mechanism due to the earthquake loads. In this paper, modeling of collapse propagation in structural elements of RC frame buildings is evaluated by tracing down the collapse points in beam and column structural elements, one after another, under earthquake loads and the influence of column removal is investigated on how the collapse expansion in beam and column structural members. For this reason, progressive collapse phenomenon is studied in 3-story and 5-story intermediate moment resisting frame buildings due to the corner and edge column removal in presence of the earthquake loads. In this way, distribution and propagation of the collapse in progressive collapse mechanism is studied, from the first element of the structure to the collapse of a large part of the building with investigating and comparing the results of nonlinear time history analyses (NLTHA) in presence of two-component accelograms proposed by FEMA_P695. Evaluation of the results, including the statistical survey of the number and sequence of the collapsed points in process of the collapse distribution in structural system, show that the progressive collapse distribution are special and similar in low-rise and mid-rise RC buildings due to the simultaneous effects of the column removal and the earthquake loads and various patterns of the progressive collapse distribution are proposed and presented to predict the collapse propagation in structural elements of similar buildings. So, the results of collapse distribution patterns and comparing the values of collapse can be utilized to provide practical methods in codes and guidelines to enhance the structural resistance against the progressive collapse mechanism and eventually, the value of damage can be controlled and minimized in similar buildings.

• Journal of the Korea institute for structural maintenance and inspection
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• v.12 no.5
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• pp.116-124
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• 2008

In order to evaluate the behavior patterns of the ring beam by excavation at the vertical wall with circular section, the measured field datum were analyzed and evaluated in this study. Additionally, stress patterns of the ring beam with the change of excavation depth were estimated by using FE analysis. As the results, it was shown that the tendency of the measured values for the behavior patterns of the ring beam is similar to the analyzed values in FE analysis. From the tendency, it was confirmed that the behaviors of the ring beam due to change of excavation depth can predict by FE analysis using the suggested method in this study.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2004.04a
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• pp.463-469
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• 2004

This paper discusses 2D lattice models of beams for simulating the fracture of brittle materials. A simulation of an experiment on a connote beam subjected to bending, in which two overlapping cracks occur, is used to study the effect of individual beam characteristics and different arrangements of the beams in the overall lattice. It was found that my regular orientation of the beams influences the resulting crack patterns. Methods to implement a wide range of poisson's ratios are also developed, the use of the lattice to study arbitrary micro-structures is outlined The crack pattern that n obtained with lattice m in good agreement with the experimental results. Also, numerical simulations of the tests were performed by means of a lattice model, and non-integer dimensions were measured on the predicted lattice damage patterns.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2000.04b
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• pp.61-68
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• 2000

In general, the design of membrane structures takes three steps. The first is shape finding analysis which is determination of initial equilibrium geometry with uniform stresses. The second step involve the computation of the stress-deformation to get completed membrane under various load conditions. The third step is to divide the membrane structures into several plan strips from the initial equilibrium states. This procedure is needed because of the initial shape has usually undevelopable curved surface and is called as "cutting patterns generation". By introducing this work, the deformation due to the initial stress is removed and approximate cutting patterns are generated. In this approach, however, material properties is not considered, therefore the error between the design stresses and actual stresses during the fabrication of plan strips should be occurred. In this paper, actual equilibrium shape analysis procedure for HP shape models is presented. The deviations of stresses between the design stresses and actual stresses are estimated.

• Computational Structural Engineering
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• v.9 no.4
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• pp.165-172
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• 1996

For thin elastic structures such as beams, arches, plates and shells, there may exist the boundary layer in the narrow thin region neighborhood of boundaries, where the solution displays the singular behavior exponentially decaying in the normal direction to the boundary. In the finite element analysis of these structures, finite element mesh patterns have a significant role to capture this singularity. This paper introduces the analytic study of this problem and provides a guideline to construct optimal mesh patterns together with numerical experiments.

• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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• 2008.11a
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• pp.229-230
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• 2008

We have studied the structural and optical properties of ZnO thin film deposited on glass by RF magnetron sputtering as functions of working pressures. The grain sizes were decreased as the working pressures were increased. The average optical transmissions over all exceeded 80% for ZnO films deposited in 20, 25 and 300m torr working pressures. And the transmission spectra patterns were almost same. While the transmission spectra pattern of ZnO film deposited in 35nm torr was different with other spectra patterns obtained in 20, 25 and 30nm torr working pressures.

• Computational Structural Engineering : An International Journal
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• v.1 no.1
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• pp.21-29
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• 2001

The general topology optimization can be considered as optimal material distribution. Such an approach can be unstable, unless composite materials are introduced. In this research, a nodal volume fraction method is used to obtain the optimum topology of continuum structures. This method is conducted from a composite material model composed of isotropic matter and spherical void. Because the appearance of the chessboard patterns makes the interpretation of the optimal material layout very difficult, this method contains a chessboard prevention strategy. In this research, several topology optimization problems are presented to demonstrate the validity of the present method and the recursive quadratic programming algorithm is used to solve the topology optimization problems.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.12 no.2
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• pp.215-221
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• 1999

본 연구에서는 구조물의 변위 제약조건을 고려한 위상 최적설계를 체스판무늬 검색 알고리즘과 가상하중을 이용하여 수행하였다. 본 연구에서는 변위 제약조건의 민감도 계산을 위하여 가상 변위장을 도입하였으며, 밀도와 유효강성계수의 상관관계를 정의하기 위하여 가상재료를 도입하였다. 또한, 선형 유한요소를 이용한 위상 최적화 기법에서 일반적으로 나타나는 체스판무늬를 제거하기 위하여 밀도 재분배방법을 이용하였다. 그리고, 변위 제약조건을 고려한 경우와 그렇지 않은 경우의 수치예제를 비교 검토함으로써 본 연구의 타당성을 검증하였다.