求解断裂问题的新型无网格数值流形法

doi:10.13722/j.cnki.jrme.2019.0524

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Abstract Combined the moving least squares(MLS) based on the approximation of nodes with numerical manifold method(NMM)，the meshfree-numerical manifold method is developed，abbreviated as MLS-NMM. MLS-NMM owns lower mesh-dependency and higher calculate precision than NMM，and naturally solves the continuous and non-continuous problems in a unified way. To increase the adaptability of MLS-NMM about analyzing the linear elastic fracture problems，a new MLS-NMM is proposed. It makes the mathematical patches containing the same crack tip integrate into a complex patch，in which the finite items of Williams’ displacement series are defined as the local approximation in ordering to reproduce the displacement field of the crack tip. And the method of quadtree′s local refinement is adopted to enhance the calculate precision in the vicinity of the crack tip. This method can directly acquire the stress intensity factors(SIFs) using the relationship between SIFs and items of Williams′ displacement series，avoiding post-processing solution such as the interaction integral method. In this paper，the maximum circumferential stress criterion is applied to decide the direction of crack propagation. At last，two examples of SIF and two examples of crack propagation are simulated，the results reveal that the proposed method can effectively deal with the linear elastic fracture problems，and simultaneously suggest that 2 layer local refinement and 9 items of Williams′ displacement series should be used.

Key words： numerical analysis numerical manifold method moving least squares local refinement stress intensity factor crack propagation

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	LI Wei1
	2
	3
	ZHENG Hong4
	WANG Hailong1
	GUO Hongwei5

Cite this article:

LI Wei1,2,3, et al. A new meshfree-numerical manifold method for solving the fracture problem[J]. , 2020, 39(S1): 2655-2664.

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http://rockmech.whrsm.ac.cn/EN/10.13722/j.cnki.jrme.2019.0524 OR http://rockmech.whrsm.ac.cn/EN/Y2020/V39/IS1/2655

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