An exact reanalysis algorithm for local non-topological high-rank structural modifications in finite element analysis

Abstract

This paper proposes a novel direct reanalysis algorithm based on finding updated triangular factorization in sparse matrix solution. The key concept lies on the binary tree characteristics of the global stiffness matrix derived by a graph partitioner as fill-ins’ reducer. Accommodating a local modification, the update of the triangular factor happens only through a particular path of the binary tree, which traces back from modified nodes to the root node. Numerical examples show that the proposed algorithm improves reanalysis efficiency significantly, especially for high-rank structural modification. In terms of implementation, little additional storage is needed to perform the proposed algorithm. This method can be applied to a wide range of engineering problems and can be the foundation of a lot of subsequent analyses.