본 논문은 에지 기반 평활화 유한요소법(Edge-based smoothed finite element method, ES-FEM)을 도입한 위상 최적화를 간결하고 효 율적인 MATLAB 코드로 구현하였다. 제안한 MATLAB 코드는 교육적 목적을 위해 내부 및 경계 에지를 중심으로 평활화 영역을 체 계적으로 생성하고, 해당 영역에 대한 평활화 강성 행렬을 계산함으로써 ES-FEM을 효과적으로 벡터화하는 방법을 보여준다. 특히 배열 사전 할당을 통해 계산 효율성을 한층 향상시켰다. 아울러, 개선된 밀도 필터를 도입하여 기존 ES-FEM 기반 위상 최적화 기법 보다 수식을 단순화하면서도 계산 성능을 크게 향상시켰다. 이러한 개선으로 전체 MATLAB 코드는 175줄로 구현되어 높은 가독성 과 사용 편의성을 갖춘다. 또한 경계 조건과 하중의 적용은 몇 줄만 수정하면 되어, 연구자가 손쉽게 코드를 유연하게 확장할 수 있 다. MATLAB 코드는 부록에 수록되어 있으며, 이를 통해 위상 최적화와 ES-FEM에 입문하는 연구자들이 보다 쉽게 학습할 수 있도 록 명확하고 직관적인 교육적 자료를 제공하고자 한다.

We performed the quantitative analysis using MATLAB for slice thickness, spatial resolution, and low contrast resolution with the 50 received images which have suitable judgement by scanning AAPM phantom using GE, PHILIPS, SIEMENS, and TOSHIBA. Slice thickness and spatial resolution were measured by using full width at half maximum(below FWHM). Spatial resolution was confirmed that FWHM interval more than 1.0 mm size. Low contrast resolution was measured that how close by using Roundness Index(below RI) until 6.4 mm size. The spatial resolution 9 images and low contrast resolution 10 images which have disapproved judgement were also had the quantitative analysis. The statistic analysis was judged to have statistically significant differences when p-value is less than 0.05 through SPSS statistics 19.0 and T-test (paired t-test). For slice thickness 5 mm, the average qualitative evaluation group shows 4.98 mm and quantitative evaluation group shows 5.02. For slice thickness 10 mm, the average qualitative evaluation group shows 9.98 mm and quantitative evaluation group shows 9.86. No significant differences (p=0.07, p=0.06) with 5 mm and 10 mm. It confirmed the interval for all FWHM until 1.75, 1.50, 1.25, 1.00 mm as approved images on spatial resolution ,and the average distance was 0.102 mm and the minimum distance 0.054 mm. For disapproved images, all interval was not showed under 1.00 mm. For low contrast resolution, spproved image’s RI value shows average 0.81 and minimum 0.77. The disapproved image’s RI average shows 0.70. Statiscally significant differences were presented (all p<0.05) following hole size.

The construction and ability of CAE program are presented. The merit and ability of MATLAB which is widely using in the field of recently engineering and natural science are also introduced. Also, analysis program of frame structure used the MATLAB language which is divide in 4th generation language is presented. In this paper, the proposed program using MATLB language to be based upon the composition of general CAE program is composed to preprocess, solver and post-process procedure. And it is able to carried out the static and eigenvalue analysis of truss structure and two dimensional frame structure. Also, for the sample pre-processing and post-processing, it is used the characteristic of input window and plot window to be made of the various GUI function. Each finite elements to be required for analysis is formulated by the Galerkin's method, as a kind of weighted residual method. For check of the results of calculation for program used in this paper, the results to be calculated using program to be developed by the author was compared with its of ANSYS code for general structural analysis about two dimensional truss and frame structure.