The moving least squares based numerical manifold method for vibration and impact analysis of cracked bodies

In the numerical manifold method (NMM), the mathematical patches composing the mathematical cover can take on any shape in addition to finite elements. In this study, the influence domains of those scattered nodes in the moving least squares (MLS) approximation serve as the mathematical patches. And accordingly, the MLS based NMM, designated by MLS-NMM, is derived, which owns the advantages of both NMM and MLS. Then, MLS-NMM is applied to analyze cracked bodies under dynamic loading, and a mass lumping scheme fit for MLS-NMM is proposed. The dynamic analyses of some typical cracked bodies are carried out, indicating MLS-NMM equipped with the proposed mass lumping scheme has more excellent numerical properties than that with the consistent mass formulation in the analysis of the time domain as well as the frequency domain.