A decomposed subspace reduction for fracture mechanics based on the meshfree integrated singular basis function method

Abstract

In this work, we propose a new decomposed subspace reduction (DSR) method for reduced-order modeling of fracture mechanics based on the integrated singular basis function method (ISBFM) with reproducing kernel approximation enriched by crack-tip basis functions. It is shown that the standard MOR approach based on modal analysis (ISBFM-MA) with a direct employment of the crack-tip enrichment functions yields an inappropriate scaling effect to the stiffness matrix, and results in the loss of essential crack features and the erroneous representation of inhomogeneous Dirichlet boundary conditions in the reduced subspace. On the other hand, the solution of ISBFM-DSR is not affected by the arbitrary scaling of the enrichment functions, and it properly captures the singularity and discontinuity properties of fracture problems in its low-dimensional reduced-order approximation. It is also shown that the inhomogeneous boundary conditions can be accurately represented in the ISBFM-DSR solution. Validations are given in the numerical examples.