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유민철(Minchul Yu),노건우(Gunwoo Noh) 대한기계학회 2020 大韓機械學會論文集A Vol.44 No.4
유한구체법은 신뢰성 높은 해석 기법으로, 유한요소법과 다르게 격자를 구성할 필요가 없으므로 매우 쉽고 편리하지만 해석 시간이 오래 걸리기 때문에 상용화에 어려움을 겪고 있다. 이 때문에 유한구체법에 특화된 가우스 구적법의 연구가 진행됐지만 해석 시간 단축에 대한 근본적인 해결책을 제시하지는 못하였다. 이와 관련하여 본 연구에서 인공신경망을 사용하여 가우스 구적법의 가중치를 최적화하는 알고리즘을 제시하고, 이를 통해 얻어낸 가중치를 실제 문제에 적용하였다. 적용한 문제는 총 두 개이며, 정적 문제와 동적 문제를 통해 향상된 가우스 구적법의 성능을 평가하였다. 결과적으로 가우스 구적법에 사용되는 적분 점 개수를 줄일 수 있었으며 해석 시간을 대폭 감소시켰다. The method of finite spheres is a novel and reliable numerical scheme. It is easy to use since it does not require a mesh, in contrast with the finite element method. However, the method of finite spheres uses rational interpolation functions based on the Shepard functions. Thus, it requires more integration points to integrate the element matrices accurately, resulting in poor computational efficiency. In this regard, research on Gaussian quadrature for the method of finite spheres has been conducted, however, it still implies a large computational cost. Therefore, we propose an algorithm for optimizing the weights of Gaussian quadrature using supervised learning. We evaluated the performance of enhanced Gaussian quadrature using the solutions of static and dynamic problems. The results establish that the number of integration points used in the Gaussian quadrature can be reduced, thereby significantly reducing the computational cost.
메타-휴리스틱을 이용한 유한구체법의 직접 질량 역행렬법 개발
정인수(Insu Jeong),유민철(Minchul Yu),노건우(Gunwoo Noh) 대한기계학회 2022 대한기계학회 춘추학술대회 Vol.2022 No.11
The method of finite spheres is a kind of non-element method that overlaps spheres of a certain radius in the analysis area without the need to construct a complex grid. When solving the explicit dynamics equation using this MFS, the inverse of the global mass matrix needs to be found, but since the size of the global mass matrix is very large, high computational cost is required to find the inverse matrix. In this case, there is a method to obtain the inverse matrix in the local area instead of in the global area using the direct mass inverse matrix method. In this regard, we will find the appropriate direct mass inverse matrix method and parameters using a meta-heuristic algorithm. We evaluated the superiority of the solution by comparing the accuracy and operation speed of the solution with the existing method when the improved direct mass inverse matrix method is applied.
메타-휴리스틱을 이용한 유한구체법의 직접 질량 역행렬법 개발
정인수(Insu Jeong),유민철(Minchul Yu),노건우(Gunwoo Noh) 대한기계학회 2022 대한기계학회 춘추학술대회 Vol.2022 No.11
The method of finite spheres is a kind of non-element method that overlaps spheres of a certain radius in the analysis area without the need to construct a complex grid. When solving the explicit dynamics equation using this MFS, the inverse of the global mass matrix needs to be found, but since the size of the global mass matrix is very large, high computational cost is required to find the inverse matrix. In this case, there is a method to obtain the inverse matrix in the local area instead of in the global area using the direct mass inverse matrix method. In this regard, we will find the appropriate direct mass inverse matrix method and parameters using a meta-heuristic algorithm. We evaluated the superiority of the solution by comparing the accuracy and operation speed of the solution with the existing method when the improved direct mass inverse matrix method is applied.