A TEMPLATED METHOD FOR PARTITIONING OF SOLID ELEMENTS IN DISCONTINUOUS PROBLEMS1)
Wang Lixiang*,??, Wen Longfei*,??, Xiao Guizhong*,??,**, Tian Rong,*,??,2)*CAEP Software Center for High Performance Numerical Simulation$,$ Beijing $100088$$,$ China ??Institute of Applied Physics and Computational Mathematics$,$ Beijing $100088$$,$ China **Nanjing University of Science and Technology$,$ Nanjing $210094$$,$ China
Abstract The extended finite element method (XFEM) has been one of the privileged tools for crack analysis due to its significant advantages: (1) Independence of crack geometry on the simulation mesh; (2) no necessity of remeshing when a crack grows; and (3) high accuracy. However, the method is hindered in engineering practices by the partitioning difficulty of discontinuous elements, i.e. the geometric interaction between discontinuous interfaces and solid elements. Though current partitioning algorithms are geometrically exact, they are cumbersome to implement, computationally expensive, and insufficiently robust. To overcome these issues, a templated partitioning algorithm is proposed based on element level sets for subdivision and numerical integration of discontinuous elements. Firstly, a templated partitioning library for standard discontinuous elements is established by enumerating all the patterns of element level set values. Secondly, the pattern of a non-standard element to be partitioned is looked up and the sub-coordinates are interpolated based on the element level set values. Lastly, the non-standard element is efficiently partitioned into sub-triangles based on the standard element template. The algorithm is incorporated into the conventional XFEM and the improved XFEM for analysis of discontinuous problems, i.e. the problems with holes, inclusions, cracks and so forth. Numerical examples indicate that the proposed algorithm achieves favorable accuracy. Without cumbersome geometrical operations, the templated partitioning algorithm is also efficient and robust, thereby enabling itself to support the extended finite element methods in practical engineering problems. Keywords:subdivision;level set;discontinuity;crack propagation;conventional XFEM;improved XFEM
PDF (849KB)元数据多维度评价相关文章导出EndNote|Ris|Bibtex收藏本文 本文引用格式 王理想, 文龙飞, 肖桂仲, 田荣. 非连续问题中单元分割的模板方法1). 力学学报[J], 2021, 53(3): 823-836 DOI:10.6052/0459-1879-20-360 Wang Lixiang, Wen Longfei, Xiao Guizhong, Tian Rong. A TEMPLATED METHOD FOR PARTITIONING OF SOLID ELEMENTS IN DISCONTINUOUS PROBLEMS1). Chinese Journal of Theoretical and Applied Mechanics[J], 2021, 53(3): 823-836 DOI:10.6052/0459-1879-20-360
如图15(a)所示, 为一带边裂纹双臂梁模型, 长$l=6$ m, 宽$w=2$ m,裂纹长$a=2.05$ m. 双臂梁弹性模量$E=1000$ Pa, 泊松比$\nu =0.3$.梁右端固支, 左端受非对称集中力载荷$P_{1} =1$ N, $P_{2} =1.01$ N.计算网格如图15(b)所示, 网格数为25$\times$75. 假设裂纹扩展18步,每一步扩展长度为0.1 m.
分别使用高阶高斯积分法和本文切割方法, 并联合XFEM进行求解.计算所得到的$u_{y}$位移场对比, 如图18所示. 使用XFEM$+$高阶高斯积分法,位移最大值为73.92 mm, 最小值为$-$4.978 mm. 使用XFEM$+$本文分割方法,位移最大值为73.91 mm, 最小值为$-$4.976 mm. 两种方法的位移最大值偏差为0.01%, 位移最小值偏差为0.04%. 该算例说明, 对于三维裂纹问题, 本文发展的非连续单元分割方法同样具有有效性.
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