Adaptive subdomain integration method for representing complex localized geometry in ANCF
doi: 10.1007/s10409-021-09032-x
-
摘要: 论文将有限胞元法与绝对节点坐标法相结合, 提出高效稳定的含有复杂局部结构特征的ANCF单元分析方法; 并基于三角划分原理设计了自适应子域积分算法, 避免了过度的子域细分, 大大减少了计算成本. 论文用数值实例验证了所提出方法在大变形、大转动的动力学问题分析中的有效性.Abstract: In this work, we propose incorporating the finite cell method (FCM) into the absolute nodal coordinate formulation (ANCF) to improve the efficiency and robustness of ANCF elements in simulating structures with complex local features. In addition, an adaptive subdomain integration method based on a triangulation technique is devised to avoid excessive subdivisions, largely reducing the computational cost. Numerical examples demonstrate the effectiveness of the proposed method in large deformation, large rotation and dynamics simulation.
-
3. Basic principle of FCM: a physical domain, b fictitious domain, c extended domain, d structured mesh.
8. Numbering of subdividing cell: a cells to be subdivided, b cells after subdivision.
13. Partition and distribution of integration points of the plate under different subdomain size constraints: a size unconstrained, b size of subdomains less than 0.5, c size less than 0.25.
14. Geometric model of the plate with circular through-hole: a the geometric model of the plate, b the definition of hole.
15. Adaptive subdomain refining of the plate with circular through-hole: a adaptive subdomain partitioning, b integration point distribution.
19. Comparison of common cell subdivision and adaptive cell subdivision: a degree freedom and integration point, b running time of simulation.
21. The plate with groove: a geometric model (top surface), b geometric model (bottom surface), c groove defined in the straight configuration.
22. Adaptively subdomain subdivision of the plate with groove: a adaptive subdomain partitioning, b integration point distribution.
25. Contact force of plate with groove: a t = 0.178 s, b t = 0.195 s, c t=0.852 s, d t = 1.956 s.
26. Comparison of common cell subdivision and adaptive cell subdivision: a degree freedom and integration point, b running time of simulation.
Table 1. Material parameters of the model
Linear elastic material value Density (kg/m3) 2000 Elastic modulus (MPa) 2 Shear modulus (MPa) 1 
下载: 导出CSV
Table 2. Material parameters of soft plate
Linear elastic material value Elastic modulus (MPa) 0.5 Shear modulus (MPa) 0.25
下载: 导出CSV
Table 3. The material parameters of plate for contact analysis
Linear elastic material Value Density (kg/m3) 7000 Elastic modulus (MPa) 1.2 Shear modulus (MPa) 0.6
下载: 导出CSV
Table 4. The parameters of contact model
Parameters Value Ground stiffness (N/m) 9000 Ground damping coefficient (N·s/m) 20.0 Friction coefficient μ 0.75
下载: 导出CSV
-
[1] A. A. Shabana, and D. Zhang, ANCF curvature continuity: Application to soft and fluid materials, Nonlin. Dyn. 100, 1497 (2020). [2] A. A. Shabana, C. J. Desai, E. Grossi, and M. Patel, Generalization of the strain-split method and evaluation of the nonlinear ANCF finite elements, Acta Mech. 231, 1365 (2020). [3] P. Lan, Q. Tian, and Z. Yu, A new absolute nodal coordinate formulation beam element with multilayer circular cross section, Acta Mech. Sin. 36, 82 (2020). [4] H. Hu, Q. Tian, and C. Liu, Computational dynamics of soft machines, Acta Mech. Sin. 33, 516 (2017). [5] S. Zhang, A. L. Gain, and J. A. Norato, Adaptive mesh refinement for topology optimization with discrete geometric components, Comput. Methods Appl. Mech. Eng. 364, 112930 (2020). [6] R. Bouclier, J. C. Passieux, and M. Salaün, Local enrichment of NURBS patches using a non-intrusive coupling strategy: Geometric details, local refinement, inclusion, fracture, Comput. Methods Appl. Mech. Eng. 300, 1 (2016). [7] J. Xu, N. Sun, L. Shu, T. Rabczuk, and G. Xu, An improved integration for trimmed geometries in isogeometric analysis, Comput. Mater. Continua 60, 615 (2019). [8] B. Marussig, and T. J. R. Hughes, A review of trimming in isogeometric analysis: Challenges, data exchange and simulation aspects, Arch. Computat. Methods Eng. 25, 1131 31186608(2018). [9] A. Chemin, T. Elguedj, and A. Gravouil, Isogeometric local h-refinement strategy based on multigrids, Finite Elem. Anal. Des. 100, 77 (2015). [10] Y. L. Kuo, W. L. Cleghorn, K. Behdinan, and R. G. Fenton, The h-p-r-refinement finite element analysis of a planar high-speed four-bar mechanism, Mechanism Machine Theor. 41, 505 (2006). [11] A. I. Valkeapää, M. K. Matikainen, and A. M. Mikkola, Meshing strategies in the absolute nodal coordinate formulation-based Euler-Bernoulli beam elements, Proc. Institut. Mech. Engineers Part K-J. Multi-Body Dyn. 230, 606 (2016). [12] Y. Zhang, C. Wei, Y. Zhao, C. Tan, and Y. Liu, Adaptive ANCF method and its application in planar flexible cables, Acta Mech. Sin. 34, 199 (2018). [13] N. A. Dodgson, and J. Kosinka, Can local NURBS refinement be achieved by modifying only the user interface?, Comput.-Aided Des. 71, 28 (2016). [14] L. Coradello, D. D’Angella, M. Carraturo, J. Kiendl, S. Kollmannsberger, E. Rank, and A. Reali, Hierarchically refined isogeometric analysis of trimmed shells, Comput. Mech. 66, 431 (2020). [15] G. Zhao, J. Yang, W. Wang, Y. Zhang, X. Du, and M. Guo, T-splines based isogeometric topology optimization with arbitrarily shaped design domains, Comput. Modeling Eng. Sci. 123, 1033 (2020). [16] J. Videla, F. Contreras, H. X. Nguyen, and E. Atroshchenko, Application of PHT-splines in bending and vibration analysis of cracked Kirchhoff-Love plates, Comput. Methods Appl. Mech. Eng. 361, 112754 (2020). [17] D. Miao, Z. Zou, M. A. Scott, M. J. Borden, and D. C. Thomas, Isogeometric Bézier dual mortaring: The enriched Bézier dual basis with application to second- and fourth-order problems, Comput. Methods Appl. Mech. Eng. 363, 112900 (2020). [18] Z. Zou, M. A. Scott, M. J. Borden, D. C. Thomas, W. Dornisch, and E. Brivadis, Isogeometric Bézier dual mortaring: Refineable higher-order spline dual bases and weakly continuous geometry, Comput. Methods Appl. Mech. Eng. 333, 497 (2018). [19] R. R. Hiemstra, K. M. Shepherd, M. J. Johnson, L. Quan, and T. J. R. Hughes, Towards untrimmed NURBS: CAD embedded reparameterization of trimmed B-rep geometry using frame-field guided global parameterization, Comput. Methods Appl. Mech. Eng. 369, 113227 (2020). [20] R. Schmidt, R. Wüchner, and K. U. Bletzinger, Isogeometric analysis of trimmed NURBS geometries, Comput. Methods Appl. Mech. Eng. 241-244, 93 (2012). [21] J. Xu, L. Gao, M. Xiao, J. Gao, and H. Li, Isogeometric topology optimization for rational design of ultra-lightweight architected materials, Int. J. Mech. Sci. 166, 105103 (2020). [22] P. Kang, and S. K. Youn, Isogeometric topology optimization of shell structures using trimmed NURBS surfaces, Finite Elem. Anal. Des. 120, 18 (2016). [23] G. He, M. Patel, and A. Shabana, Integration of localized surface geometry in fully parameterized ANCF finite elements, Comput. Methods Appl. Mech. Eng. 313, 966 (2017). [24] J. Parvizian, A. Düster, and E. Rank, Finite cell method, Comput. Mech. 41, 121 (2007). [25] M. Ranjbar, M. Mashayekhi, J. Parvizian, A. Düster, and E. Rank, Finite cell method implementation and validation of a nonlocal integral damage model, Int. J. Mech. Sci. 128-129, 401 (2017). [26] K. Khadra, P. Angot, S. Parneix, and J. P. Caltagirone, Fictitious domain approach for numerical modelling of Navier-Stokes equations, Int. J. Numer. Meth. Fluids 34, 651 (2000). [27] E. Rank, S. Kollmannsberger, C. Sorger, and A. Düster, Shell finite cell method: A high order fictitious domain approach for thin-walled structures, Comput. Methods Appl. Mech. Eng. 200, 3200 (2011). [28] L. Kudela, N. Zander, T. Bog, S. Kollmannsberger, and E. Rank, Efficient and accurate numerical quadrature for immersed boundary methods, Adv. Model. Simul. Eng. Sci. 2, 10 (2015). [29] M. Patel, G. Orzechowski, Q. Tian, and A. A. Shabana, A new multibody system approach for tire modeling using ANCF finite elements, Proc. Instit. Mech. Engineers Part K-J. Multi-body Dyn. 230, 69 (2016). [30] L. Piegl, W. Tiller, The NURBS Book. (Springer, Berlin, 1995) [31] W. J. Gordon, and C. A. Hall, Transfinite element methods: Blending-function interpolation over arbitrary curved element domains, Numer. Math. 21, 109 (1973). -
下载:
点击查看大图
计量
- 文章访问数: 31
- HTML全文浏览量: 63
- PDF下载量: 0
- 被引次数: 0
京公网安备 11010502036328号 京ICP备17033152号