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Re-analysis method for inversion of block matrix based on change threshold. (English) Zbl 1481.74692

Summary: In the mechanical design industry, it is very time-consuming to convert actual engineering design problems into finite element models, and it is repeatedly modified during the product design process. Each time the structure is modified, computer simulation analysis is repeated, and the product development cycle becomes longer. Therefore, in this paper, a re-analysis theoretical method based on the inversion of the block matrix based on the change threshold is proposed to quickly obtain responses with different accuracy after the structure is modified according to the initial analysis. By modifying the size of the change threshold, the accuracy and calculation time of the reanalysis results are controlled. This reanalysis method shortens a lot of calculation time under the premise of controllable response accuracy. In this paper, numerical calculations are given to show the accuracy of the response under different thresholds, and the efficiency of this method is proved by the finite element model under the same accuracy.

MSC:

74S05 Finite element methods applied to problems in solid mechanics
65F05 Direct numerical methods for linear systems and matrix inversion
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[1] Wang, H.; Zhong, H.; Gao, G. Q., Research progress and prospects of reanalysis methods, Eng. Mech., 34, 5, 1-16 (2017)
[2] Sherman, J.; Morrison, W. J., Adjustment of an inverse matrix corresponding to a change in one element of a given matrix, Ann. Math. Stat., 21, 1, 124-127 (1950) · Zbl 0037.00901
[3] Woodbury, M. A., Inverting Modified Matrices, 42, 106 (1950), Princeton University, Memorandum report
[4] Ma, K.; Li, B., Approximate calculation method of first-order and second-order sensitivity of structure static displacement, J. Jilin Univ., 08, 10, 1-7 (2020), (Engineering Edition)
[5] Deng, L.; Ghosn, M., Pseudoforce method for nonlinear analysis and reanalysis of structural systems, J. Struct. Eng., 127, 5, 570-578 (2001)
[6] Cheikh, M.; Loredo, A., Static reanalysis of discrete elastic structures with reflexive inverse, Appl. Math. Model., 26, 9, 877-891 (2002) · Zbl 1205.74176
[7] Jenkins, W. M., Structural reanalysis using a neural network-based iterative method, J. Struct. Eng., 128, 7, 946-950 (2002)
[8] Yousef, H.; Nasser, T.; Shahin, J., A new structural reanalysis approach based on the polynomial-type extrapolation methods, Struct. Multidiscip. Optim., 58, 3, 1033-1049 (2018)
[9] Wu, B.; Li, Z.; Li, S., The implementation of a vector-valued rational approximate method in structural reanalysis problems, Comput. Methods Appl. Mech. Eng., 192, 13/14, 1773-1784 (2003) · Zbl 1044.74053
[10] Huang, H.; Chen, S. H.; Meng, G., Application of perturbation method combined with Pade approximation in structural topological reanalysis, J. Appl. Mech., 22, 2, 155-158 (2005)
[11] Jun, R.; Qianghao, Z.; Hamid, T., Structural reanalysis based on FRFs using Sherman-Morrison-Woodbury formula, Shock Vib. 2020, 3, 1-12 (2020)
[12] Liu, H.; Wu, B.; Lim, C., An approach for structural static reanalysis with unchanged number of degrees of freedom, Struct. Multidiscip. Optim., 45, 5, 681-692 (2012)
[13] Wu, B.; Li, Z., Static reanalysis of structures with added degrees of freedom, Commun. Numer. Methods Eng., 22, 4, 269―28 (2006) · Zbl 1116.74068
[14] Wu, B.; Li, Z., Reanalysis of structural modifications due to removal of degrees of freedom, Acta Mech., 180, 1, 61―71 (2005) · Zbl 1082.74040
[15] Koohestani, K., Structural reanalysis via force method, Int. Solids Struct. 136-137, 103-111 (2018)
[16] Zuo, W.; Yu, Z.; Zhao, S., A hybrid Fox and Kirsch’s reduced basis method for structural static reanalysis, Struct. Multidiscip. Optim., 46, 2, 261-272 (2012)
[17] Liu, D., Research and Application of Modal Reanalysis Method Based on Lanczos Algorithm (2014), Hunan University: Hunan University Changsha
[18] Zhang, H., Research On the Adaptability of Combined Approximate Reanalysis Algorithm (2011), Jilin University: Jilin University Changchun
[19] Guo, G. K., Research and Application of Structural Dynamic Reanalysis Algorithm (2011), Jilin University: Jilin University Changchun
[20] Fu, H. P., Re-analysis Method For Dynamic Response of Nonlinear Rotor Structure System (2016), Jilin University: Jilin University Changchun
[21] Zhang, M. Y.; Han, P. T., Structural dynamic reanalysis method based on rational approximation and sensitivity analysis, Vib. Shock, 25, 50—52 (2006)
[22] Yong, S.; Chang Eun, H.; Gianmarco de, F., Reanalysis of modified structures by adding or removing substructures, Adv. Civil Eng., 2018, 1-9 (2018)
[23] He, J. J.; Jiang, J. S., Single step perturbation inverse iterative method for dynamic analysis of structural topology modification, J. Northwest. Polytech. Univ., 24, 3, 313-316 (2006)
[24] Hao, J., Research on Local Detail Re-Analysis Method for Structural Dynamic Response Analysis (2010), Nanjing University of Aeronautics and Astronautics: Nanjing University of Aeronautics and Astronautics Nanjing
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