Rotation errors in numerical manifold method and a correction based on large deformation theory

2019, Volume 13, Issue 5

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Frontiers of Structural and Civil Engineering >> 2019, Volume 13, Issue 5 doi: 10.1007/s11709-019-0535-5

Rotation errors in numerical manifold method and a correction based on large deformation theory

. School of Civil Engineering, Beijing Jiaotong University, Beijing 100044, China.. Key Laboratory of Urban Underground Engineering of Ministry of Education, Beijing Jiaotong University, Beijing 100044, China.. School of Civil and Architectural Engineering, Wuhan University, Wuhan 430072, China.. State Key Laboratory of Simulation and Regulation of Water Cycle in River Basin, Beijing 100038, China

Accepted: 2019-06-25 Available online: 2019-06-25

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Abstract

Numerical manifold method (NMM) is an effective method for simulating block system, however, significant errors are found in its simulation of rotation problems. Three kinds of errors, as volume expansion, stress vibration, and attenuation of angular velocity, were observed in the original NMM. The first two kind errors are owing to the small deformation assumption and the last one is due to the numerical damping. A large deformation NMM is proposed based on large deformation theory. In this method, the governing equation is derived using Green strain, the large deformation iteration and the open-close iteration are combined, and an updating strategy is proposed. The proposed method is used to analyze block rotation, beam bending, and rock falling problems and the results prove that all three kinds of errors are eliminated in this method.

Keywords

numerical manifold method ; rotation ; large deformation ; Green strain ; open-close iteration

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