Coupled finite element-moving least squares technique for stochastic structural response of cracked structures

In recent years, a class of Galerkin-based meshfree or meshless methods have been developed that do not require a structured mesh to discretize the problem, such as the element-free Galerkin method, and the reproducing kernel particle method. These methods employ a moving leastsquares (MLS) approximation method that allows resultant shape functions to be constructed entirely in terms of arbitrarily placed nodes. These methods employ a moving least-squares approximation method that allows resultant shape functions to be constructed entirely in terms of arbitrarily placed nodes. Meshless discretization presents significant advantages for modeling fracture propagation. By sidestepping remeshing requirements, crack-propagation analysis can be dramatically simplified. Since no element connectivity data are needed, the burdensome remeshing required by the FEM is avoided. A growing crack can be modeled by simply extending the free surfaces, which correspond to the crack. In addition, stochastic meshless method (SMM) facilitates to have different discretizations for capturing the spatial variability of the material properties and the structural response, without much difficulty in mapping between the two discretizations. However, the computational cost of a SMM typically exceeds the cost of a SFEM. Hence, it is advantageous to adopt MLS approximation for material property discretization and FEM for structural response computation. This paper presents a new coupled finite element-moving least squares technique for predicting probabilistic structural response and reliability of cracked structures. Copyright © 2006 by ASME.