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An exact and efficient X-FEM-based reanalysis algorithm for quasi-static crack propagation

APPLIED MATHEMATICAL MODELLING 2019年 72卷 601-622页

作者： Cheng, Zhenxing Wang, Hu Hunan Univ State Key Lab Adv Design & Mfg Vehicle Body Changsha 410082 Hunan Peoples R China

This study suggests a specific reanalysis algorithm termed decomposed updating reanalysis (DUR) for quasi-static linear crack propagation based on the extended finite element method (X-FEM). It is well known that the number of iterative steps is usually very large during X-FEM simulation procedures because a small crack increment is required to improve the accuracy of the simulation. However, according to the features of the X-FEM, the small crack increment only influences the nearby elements and only leads the local change of the stiffness matrix at each iterative step. Therefore, the OUR method is proposed to accelerate the X-FEM solving process by only calculating the changed part of the equilibrium equations. Moreover, the local updating strategy can efficiently update the modified stiffness matrix and the Cholesky factorization. Compared with other reanalysis algorithms, such as combined approximations (CA), the DUR method is more accurate. Numerical examples demonstrate that the DUR method improves the efficiency of the X-FEM significantly with a high accuracy. (C) 2019 Elsevier Inc. All rights reserved.

关键词： Crack propagation reanalysis algorithm Decomposed updating reanalysis Extended finite element method

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Optimization algorithm of Crack Initial Angle Using the Extended Finite Element Method

Optimization Algorithm of Crack Initial Angle Using the Exte...

引用

2nd International Conference on Advances in Computational Modeling and Simulation (ACMS 2013)

作者： Su, Yi Wang, Shengnan Du, Yong'en Northwestern Polytech Univ Sch Aeronaut Xian 710072 Peoples R China

ISBN: (纸本)9783037859063

The extended finite element method (XFEM) allows the entire crack to be represented independently from the mesh, which means re-mesh is unnecessary in model crack growth, reduces the computational time drastically. However, fatigue crack growth simulation has been computationally challenged by lots of analog computations in crack growth. Therefore, a new reanalysis algorithm based on incremental Cholesky factorization is derived. In this paper, we consider a variant of XFEM in which an exponent discontinuous function is used to simulate the crack through unit. Then the corresponding formula of XFEM with inclusion and crack problem with a new reanalysis algorithm is derived. In the end, we use the new reanalysis algorithm and an optimization algorithm to predict the angle of crack initiation from a hole in a plate with inclusion. It shows that the algorithm is effective.

关键词： The extended finite element method(XFEM) Cholesky factorization reanalysis algorithm optimization algorithm

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