有限要素法による逆解析法とパーソナルコンピュータ利用 : ペナルティ法による未知境界条件の能率的な同定法

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This paper presents an efficient inverse analysis technique for the identification of an unknown boundary condition in a finite element method (FEM) on a small memory capacity machine such as a personal computer. The author has previously presented the FEM of inverse analysis introducing an inverse compliance matrix that uses an influence function into the stiffness matrix for the unknown boundary. Since the stiffness matrix of the FEM becomes singular, following two calculation processes are adopted: (1) a calculation process which obtains an approximate solution by decreasing the effect of the inverse compliance in the stiffness, and (2) an iterative calculation process computing a correct solution from the approximation using (1). First, a penalty function method is used to decrease the rank of a singular stiffness matrix in (1). Then, the number for computing LDU decomposed matrix becomes twice in comparison with fourth times in the previous paper. Next, an efficient calculation method is presented using an attack technique based on both accelerative moving lower and upper bounds in (2). Moreover, a zooming identification method is developed, owing to an improvement of node displacements on and near the edges. Therefore, this technique makes it possible to establish an efficient inverse analysis for the identification of the unknown boundary. Finally, the validity of the inverse analysis technique is confirmed from the numerical solution of a three-dimensional inverse finite element analysis model, as an example of an elastic structure with reinforced members under tension, carried out on a small memory capacity machine.
一般社団法人日本機械学会の論文
1996-01-25

有限要素法による逆解析法とパーソナルコンピュータ利用 : ペナルティ法による未知境界条件の能率的な同定法

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