New strategies for some issues of numerical manifold method in simulation of crack propagation

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On generation of lumped mass matrices in partition of unity based methods (2017, methodology): “Such a selection avoids the linear dependence problem [41].”
The MLS-based numerical manifold method with applications to crack analysis (2014, methodology): “In the simulation of crack growth, we utilize two strategies newly developed by Zheng and Xu (2014), to conduct the numerical quadrature of integrands of up to 1/r singularity, and to approximate displacement fields near kinked crack tips.”
Exact imposition of essential boundary condition and material interface continuity in Galerkin‐based meshless methods (2017, methodology): “Different from the standard statements of NMM, such as [22] and [23], d i might contain the number, 1 (one), as its one component, so as to let uhi capture the local feature of solution u over !i .”
Stability analysis of slopes using the vector sum numerical manifold method (2020, unknown): “In this section, the basic concepts in the numerical manifold method (NMM) are introduced, although they have been presented in many literature (Zheng and Xu 2014).”