有限要素法に基づく時間積分法について

抄録

There are three kinds of numerical integrations to solve the equation of motion for systems with a large number of freedom ; Solutions by the finite difference method, the Pade approximation and the finite element method. So far, various methods based on the finite element method have been examined. Two years ago, the authors proposed a new algorithm based on the finite element method and showed its usefulness. In this paper, first, the accuracy of the authors' algorithm is studied mathematically and compared with other algorithms. Then, in order to confirm the above-mentioned results, the numerical calculation of responses of the linear system with a single degree of freedom is carried out. The features of the authors' algorithm are summarized as follows : 1) The algorithm derived from 2-nodes element is equivalent to the one of β method for β=1/6 2) In the case of 3-nodes element, the algorithm is as accurate as the one of the Argyris method. 3) The algorithm derived from 4-nodes element has very high accuracy and takes less time in computation than other algorithms.