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Multidimensional Space Method for Geometrically Nonlinear Problems under Total Lagrangian Formulation Based on the Extended Finite-Element Method
AbstractFor the standard extended finite-element method (XFEM), the degrees of freedom (DOFs) at nodes around the surfaces and tips of cracks are enriched to represent the discontinuity and the singularity of cracks. However, for the incremental approach, the XFEM encounters some troubles as the total number of DOFs increases with the crack growth. This leads to difficulties of the matrix algorithm. In this paper, a multidimensional space method for geometrically nonlinear problems under the total Lagrangian formulation is presented to simulate the crack growth and coalescence. The multidimensional space method is developed from the XFEM. The core concept is that the two-dimensional domain containing cracks is placed into the 12-dimensional space. Each node has 12n DOFs in the domain containing n cracks. The total Lagrangian formulation is applied to analyze the two-dimensional (2D) geometrically nonlinear problems, especially for large deformation. Moreover, three numerical experiments are presented to verify the efficiency and robustness of the proposed method.
Multidimensional Space Method for Geometrically Nonlinear Problems under Total Lagrangian Formulation Based on the Extended Finite-Element Method
AbstractFor the standard extended finite-element method (XFEM), the degrees of freedom (DOFs) at nodes around the surfaces and tips of cracks are enriched to represent the discontinuity and the singularity of cracks. However, for the incremental approach, the XFEM encounters some troubles as the total number of DOFs increases with the crack growth. This leads to difficulties of the matrix algorithm. In this paper, a multidimensional space method for geometrically nonlinear problems under the total Lagrangian formulation is presented to simulate the crack growth and coalescence. The multidimensional space method is developed from the XFEM. The core concept is that the two-dimensional domain containing cracks is placed into the 12-dimensional space. Each node has 12n DOFs in the domain containing n cracks. The total Lagrangian formulation is applied to analyze the two-dimensional (2D) geometrically nonlinear problems, especially for large deformation. Moreover, three numerical experiments are presented to verify the efficiency and robustness of the proposed method.
Multidimensional Space Method for Geometrically Nonlinear Problems under Total Lagrangian Formulation Based on the Extended Finite-Element Method
Cheng, Hao (author) / Zhou, Xiaoping
2017
Article (Journal)
English
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