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

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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Acknowledgment

This research was supported by the National Natural Science Foundation of China (Grant Nos. 51479001, 41471052) and the IWHR Research & Development Support Program (GE0145B462017, GE0145B692017).

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