线性无关高阶数值流形法在断裂力学中的应用

doi:10.13722/j.cnki.jrme.2014.1702

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Abstract The numerical manifold method(NMM) has succeeded in providing a unified solution to continuum and discontinuum problems and therefore it is highly suitable for solving fracture mechanics problems. However，the conventional high-order NMM using the first order polynomial as the local displacement function has the problem of linear dependence，which restricts to a certain degree its further development and application. A new NMM framework was established in this research by introducing a new localized displacement function，as well as a special displacement function for modeling the stress singularity around crack tips. A new paradigm that eliminates the problem of linear dependence is then derived to solve linear elastic fracture mechanics problems. The numerical examples show that：(1) The proposed method successfully eliminates the problem of linear dependence；(2) For classic linear elastic fracture problems，the stress intensity factors at the crack tip can be calculated accurately even if the mesh is relatively sparse；(3) The stress function at interpolation points inside the physical domain is continuous；(4) All the degrees of freedom defined on non-singular physical patches are physically meaningful，with the third to the fifth being the strain components at the interpolation point of the patch. As a result，the stress components at the interpolation point can be directly obtained. Finally，the proposed approach can be easily extended to other methods based on the theory of the partition of unity.

Key words： numerical simulation numerical manifold method mathematical patch mathematical cover physical patch physical cover linear dependence continuous nodal stress

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https://rockmech.whrsm.ac.cn/EN/10.13722/j.cnki.jrme.2014.1702 OR https://rockmech.whrsm.ac.cn/EN/Y2015/V34/I12/2463

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