×

Model order reduction of linear peridynamic systems using static condensation. (English) Zbl 07357416

Summary: Static condensation is widely used as a model order reduction technique to reduce the computational effort and complexity of classical continuum-based computational models, such as finite-element models. Peridynamic theory is a nonlocal theory developed primarily to overcome the shortcoming of classical continuum-based models in handling discontinuous system responses. In this study, a model order reduction algorithm is developed based on the static condensation technique to reduce the order of peridynamic models. Numerical examples are considered to demonstrate the robustness of the proposed reduction algorithm in reproducing the static and dynamic response and the eigenresponse of the full peridynamic models.

MSC:

74-XX Mechanics of deformable solids

References:

[1] Wagih, AM, Hegaze, MM, Kamel, MA. Satellite FE model validation for coupled load analysis using conventional and enhanced correlation criteria. In: AIAA SPACE and Astronautics Forum and Exposition, 2017. · doi:10.2514/6.2017-5319
[2] Guyan, RJ. Reduction of stiffness and mass matrices. AIAA J 1965; 3(2): 380-380. · doi:10.2514/3.2874
[3] Kidder, RL. Reduction of structural frequency equations. AIAA J 1984; 11(6): 892-892. · doi:10.2514/3.6852
[4] Bourquin, F. Component mode synthesis and eigenvalues of second order operators: discretization and algorithm. ESAIM Math Model Numer Anal 1992; 26(3): 385-423. · Zbl 0765.65100 · doi:10.1051/m2an/1992260303851
[5] Bouhaddi, N, Fillod, R. Substructuring by a two level dynamic condensation method. Comput Struct 1996; 60(3): 403-409. · Zbl 0918.73355 · doi:10.1016/0045-7949(95)00400-9
[6] Pazs, M. Dynamic condensation. AIAA J 1984; 22(5): 724-727. · doi:10.2514/3.48498
[7] Lin, R, Xia, Y. A new eigensolution of structures via dynamic condensation. J Sound Vib 2003; 266(1): 93-106. · doi:10.1016/S0022-460X(02)01278-6
[8] Silling, SA. Reformulation of elasticity theory for discontinuities and long-range forces. J Mech Phys Solids 2000; 48(1): 175-209. · Zbl 0970.74030 · doi:10.1016/S0022-5096(99)00029-0
[9] Xia, W, Galadima, YK, Oterkus, E, et al. Representative volume element homogenization of a composite material by using bond-based peridynamics. J Compos Biodegrad Polym 2019; 7: 51-56. · doi:10.12974/2311-8717.2019.07.7
[10] Kefal, A, Oterkus, E. Displacement and stress monitoring of a chemical tanker based on inverse finite element method. Ocean Eng 2016; 112: 33-46. · doi:10.1016/j.oceaneng.2015.11.032
[11] Huang, Y, Oterkus, S, Hou, H, et al. Peridynamic model for visco-hyperelastic material deformation in different strain rates. Continuum Mech Thermodyn Epub ahead of print 20 November 2019. DOI: 10.1007/s00161-019-00849-0. · doi:10.1007/s00161-019-00849-0.
[12] Nguyen, CT, Oterkus, S. Peridynamics formulation for beam structures to predict damage in offshore structures. Ocean Eng 2019; 173: 244-267. · doi:10.1016/j.oceaneng.2018.12.047
[13] Silling, SA, Askari, E. A meshfree method based on the peridynamic model of solid mechanics. Comput Struct 2005; 83(17): 1526-1535. · doi:10.1016/j.compstruc.2004.11.026
[14] Yang, Z, Vazic, B, Diyaroglu, C, et al. A Kirchhoff plate formulation in a state-based peridynamic framework. Math Mech Solids 2020; 25(3): 727-738. · Zbl 1446.74161
[15] Agwai, A, Guven, I, Madenci, E. Predicting crack propagation with peridynamics: a comparative study. Int J Fract 2011; 171(1): 65. · Zbl 1283.74052 · doi:10.1007/s10704-011-9628-4
[16] Bobaru, F, Ha, YD. Adaptive refinement and multiscale modeling in 2-D peridynamics. Int J Multiscale Comput Eng 2011; 9(6): 635-660. · doi:10.1615/IntJMultCompEng.2011002793
[17] Rahman, R, Haque, A. A peridynamics formulation based hierarchical multiscale modeling approach between continuum scale and atomistic scale. Int J Comput Mater Sci Eng 2012; 01(03): 1250029.
[18] Silling, SA. A coarsening method for linear peridynamics. Int J Multiscale Comput Eng 2011; 9(6): 609-622. · doi:10.1615/IntJMultCompEng.2011002674
[19] Galadima, Y, Oterkus, E, Oterkus, S. Two-dimensional implementation of the coarsening method for linear peridynamics. AIMS Mater Sci 2019; 6(2): 252-275. · doi:10.3934/matersci.2019.2.252
[20] Paz, M. Practical reduction of structural eigenproblems. J Struct Eng 1983; 109(11): 2591-2599. · doi:10.1061/(ASCE)0733-9445(1983)109:11(2591)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.