不連続面の発生と進展に対するメッシュ依存性を軽減するための数値解析

Abstract

This study is present a numerical method to suppress the mesh dependency in strong discontinuity analysis by the finite cover method (FCM) that is known as a generalized finite element method. To realize fracture process from nucleation to propagation of discontinuity, a seamless crack propagation analysis is combined with the moving least squares method (MLSM), by which standard shape functions are enriched for nodes outside the associated physical cover. Thus, the displacement field is determined by not only the nodes associated but also the non-associated ones. When the integral domain of a finite cover is separated by the discontinuity surface, it sometimes becomes too small to calculate a proper solution. Thus, the displacement field is determined by not the nodes associated with the finite cover but ones around it. In other words, the nodal degrees of freedoms corresponding to the small integral domain of the cover is cut off from the global stiffness matrix. The capabilities of the developed numerical method are demonstrated throughout simple numerical examples.