상용 유한요소 프로그램에서 사용하는 보요소와 판요소의 대변형 거동에 관한 연구

Abstract

구조물 해석에 널리 쓰이는 상용 유한요소해석용 소프트웨어인 MSC/NASTRAN 과 NISA-Ⅱ를 사용하여 외팔보와 4변이 고정된 정사각형 평판 문제를 해석하고 그 결과를 각각의 이론해와 비교하였다. 미소변형일 경우 외팔보의 유한요소 해석의 결과는 본 연구에서 해석한 모든 경우에 요소수와 무관하게 이론해와 정확히 일치한다. 대변형일 경우에는 외팔보와 평판 문제 모두에서 요소수가 많을수록 또한 보의 길이나 판의 한 변의 길이가 두께에 비해 클수록 이론해에 근접해 가는 경향이 있다. 특히 길이가 높이에 비해 긴 외팔보의 경우요소수가 5 이상이면 이론해와 0.5% 이내의 오차를 보인다. 평판문제의 대변형 해석결과는 NISA-Ⅱ의 해석결과가 MSC/NASTRAN의 해석결과보다 더 이론해에 근접하다.

The results of FE analysis of a uniform cantilever beam and a uniformly loaded square plate with all edges clamped, using commercial FE software( MSC/NASTRAN and NISA-Ⅱ), are compared with the analytical solutions. For small deformation in cantilever beam, the results of FE analysis for all the cases are identical with the analytic solutions regardless of the number of elements. For large deformation, the results of the FE analysis tends to approach close to the analytic solutions with the increase in the number of elements and the length to thickness ratios in both of two problems. In particular, for the case of the cantilever whose length is much longer than the depth, the errors are within 1% in cases of the number of elements are more than five. Comparing the results of the large deformation analysis of the square plate reveals that the result of the NISA-Ⅱ is closer to the analytical solution than that of the NSC/NASTRAN.

The results of FE analysis of a uniform cantilever beam and a uniformly loaded square plate with all edges clamped, using commercial FE software( MSC/NASTRAN and NISA-Ⅱ), are compared with the analytical solutions. For small deformation in cantilever beam, the results of FE analysis for all the cases are identical with the analytic solutions regardless of the number of elements. For large deformation, the results of the FE analysis tends to approach close to the analytic solutions with the increase in the number of elements and the length to thickness ratios in both of two problems. In particular, for the case of the cantilever whose length is much longer than the depth, the errors are within 1% in cases of the number of elements are more than five. Comparing the results of the large deformation analysis of the square plate reveals that the result of the NISA-Ⅱ is closer to the analytical solution than that of the NSC/NASTRAN.