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THE NUMERICAL MANIFOLD METHOD: A REVIEW

GUOWEI MA

School of Civil and Environmental Engineering, Nanyang Technological University, Singapore 639798, Singapore

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XINMEI AN

School of Civil and Environmental Engineering, Nanyang Technological University, Singapore 639798, Singapore

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, and

LEI HE

School of Civil and Environmental Engineering, Nanyang Technological University, Singapore 639798, Singapore

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https://doi.org/10.1142/S0219876210002040Cited by:204 (Source: Crossref)

Abstract

This paper presents a review on the numerical manifold method (NMM), which covers the basic theories of the NMM, such as NMM components, NMM displacement approximation, formulations of the discrete system of equations, integration scheme, imposition of the boundary conditions, treatment of contact problems involved in the NMM, and also the recent developments and applications of the NMM. Modeling the strong discontinuities within the framework of the NMM is specially emphasized. Several examples demonstrating the capability of the NMM in modeling discrete block system, strong discontinuities, as well as weak discontinuities are given. The similarities and distinctions of the NMM with various other numerical methods such as the finite element method (FEM), the extended finite element method (XFEM), the generalized finite element method (GFEM), the discontinuous deformation analysis (DDA), and the distinct element method (DEM) are investigated. Further developments on the NMM are suggested.

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