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Supervised Learning Based Gaussian Quadrature for the Method of Finite Spheres
Min Chul Yu(유민철),Bo-Kyu Choi(최보규),Gunwoo Noh(노건우) 대한기계학회 2019 대한기계학회 춘추학술대회 Vol.2019 No.11
The method of finite spheres is a reliable and novel structural analysis scheme, which is easy to use because of absence of mesh unlike the finite element method. However, it requires more computational cost than the finite element method. In this regard, study on Gaussian quadrature specialized in the method of finite spheres has been conducted, but it cannot provide a fundamental solution. Therefore, we propose an algorithm for optimizing the weights of Gaussian quadrature using supervised learning, which results in improving Gaussian quadrature for the method of finite spheres. Then, we apply the optimal weights to the real problems. There are two problems consisting of static and dynamic problems. The performance of the improved Gaussian quadrature is evaluated using the solution accuracy, the stiffness matrix accuracy and relative solution time. As a result, the number of integration points used in Gaussian quadrature can be reduced and the computational cost is dramatically reduced.