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A stable one-point quadrature rule for three-dimensional numerical manifold method

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We present a numerically stable one-point quadrature rule for the stiffness matrix and mass matrix of the three-dimensional numerical manifold method(3D NMM).The rule simplifies the integration over irregularly shaped manifold elements and overcomes locking issues,and it does not cause spurious modes in modal analysis.The essential idea is to transfer the integral over a manifold element to a few moments to the element center,thereby deriving a one-point integration rule by the moments and making modifications to avoid locking issues.For the stiffness matrix,after the virtual work is decomposed into moments,higher-order moments are modified to overcome locking issues in nearly incompressible and bending-dominated conditions.For the mass matrix,the consistent and lumped types are derived by moments.In particular,the lumped type has the clear advantage of simplicity.The proposed method is naturally suitable for 3D NMM meshes automatically generated from a regular grid.Numerical tests justify the accuracy improvements and the stability of the proposed procedure.

three-dimensional numerical manifold methodquadrature rulelockingmass lumping

ZHANG Ning、ZHENG Hong、YANG Liang、WU WenAn、YUAN Chi

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School of Civil Engineering,Qinghai University,Qinghai 810016,China

Key Laboratory of Urban Security and Disaster Engineering,Ministry of Education,Beijing University of Technology,Beijing 100124,China

Faculty of Engineering,China University of Geoscience,Wuhan 430074,China

National Natural Science Foundation of ChinaNational Natural Science Foundation of ChinaNational Natural Science Foundation of China

423023315213090552079002

2024

10.1007/s11431-022-2353-4

中国科学:技术科学(英文版)
中国科学院

中国科学:技术科学(英文版)

CSTPCDEI
影响因子：1.056
ISSN：1674-7321
年,卷(期)：2024.67(5)