Analysis of a crack approaching a circular hole in cross-ply laminates under biaxial loading

The problem of a crack approaching a circular hole in cross-ply laminates under uniaxial and biaxial loading is investigated in this paper. The effects of material orthotropy, geometry [R/d and a/d], and loading conditions on crack lip singularity are investigated. The stress intensity factors are obtained by the modified mapping collocation method. The present results for an isotropic infinite plate show good agreement with existing solutions. The results for cross-ply laminates show that the stress intensity factors strongly depend on material orthotropy, geometry, and loading condition. The stress intensity factors for cross-ply laminates exist between those for theta=0 degrees and those for theta=90 degrees in the whole range of crack length and decrease as the percentage of 0 degrees plies increases. In the range of small crack length the stress intensity factors for biaxial tension are higher than those for uniaxial tension. In the range of large crack length the stress intensity factors for uniaxial tension are higher than those for biaxial tension

Fostering spatial visualization ability through web-based virtual-reality program and paper-based program

This study was conducted to investigate the gender-related effects of two instructional programs on the spatial visualization skills of ninth grade students. Two instructional programs were developed for this study: a web-based virtual reality (VR) graphics program and a paper-based program. 119 ninth graders from two middle schools in Seoul participated in this study. The data analysis indicated that both the web-based and paper-based programs were effective in improving the spatial visualization skills of experimental groups. When deleting the effect of covariance of the pretest, there were no statistically significant differences in the post-test results. This paper demonstrates the promise of virtual reality on the Internet in the context of spatial visualization. © Springer-Verlag Berlin Heidelberg 2003

IB DP 지식론 및 확장형 에세이 교육과정에 나타난 수학 교과의 특성 분석

이 연구는 범교과 교육과정에서 교과의 특성 반영을 위한 시사점을 도출 하기 위해서 IB DP 교육과정의 지식론과 확장형 에세이 교육과정을 분석한 다. IB DP 교육과정에서 지식론 및 확장형 에세이 교육과정은 여러 교과를 아우르면서 학문적 성격을 지닌 핵심 영역이다. 지식론 교육과정은 수학의 본 질과 윤리의 관점, 확장형 에세이 교육과정은 수학적 탐구의 관점으로 분석하 였다. 지식론 교육과정은 학생들이 수학의 본질과 윤리에 관한 다양한 관점을 경험할 수 있도록 수학 관련 지식 질문을 제공하며, 확장형 에세이 교육과정 은 학생들이 수학적 탐구를 경험할 수 있도록 절차와 방법, 사례를 제공하였 다. 이러한 분석은 범교과 교육과정에서 개별 교과의 특성을 반영할 수 있는 교육과정 문서 및 교과서 서술을 위한 기초 자료로 활용될 수 있다