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DOI: 10.1016/j.advengsoft.2018.08.017
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DOI: 10.1016/j.compstruc.2019.01.005
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DOI: 10.1016/j.finel.2018.03.006
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DOI: 10.1299/kikaia.77.1840
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DOI: 10.1016/j.cma.2017.06.021
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DOI: 10.1016/j.cma.2019.112737
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DOI: 10.1016/bs.hna.2020.10.004
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DOI: 10.1007/s10409-018-0807-7
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DOI: 10.2514/6.2018-3720
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DOI: 10.1590/1679-78254991
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DOI: 10.2514/6.2021-1686
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DOI: 10.1016/B978-0-12-821330-8.00007-9
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DOI: 10.1007/s10444-018-9586-8
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DOI: 10.1007/s00366-020-01047-2
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DOI: 10.1007/s00158-004-0436-6
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DOI: 10.1007/s00466-019-01736-w
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DOI: 10.1016/j.cma.2018.04.034
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DOI: 10.1016/j.cma.2019.06.039
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DOI: 10.1007/s00158-017-1846-6
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DOI: 10.3390/app11052112
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DOI: 10.1007/s00158-005-0531-3
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DOI: 10.1007/s40324-018-00185-4
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DOI: 10.1016/j.compstruc.2020.106324
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DOI: 10.1016/j.amc.2018.07.049
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DOI: 10.1007/s10409-018-0827-3
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DOI: 10.1016/j.cma.2020.113335
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DOI: 10.2514/6.2004-4526
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DOI: 10.1007/s42452-020-2947-1
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DOI: 10.1002/adem.201800864
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DOI: 10.1016/j.finel.2017.11.009
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DOI: 10.1002/cnm.3096
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DOI: 10.1016/j.compositesb.2017.12.014
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DOI: 10.1016/j.cma.2018.12.031
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165 231 (2014)
DOI: 10.1007/978-3-319-05083-6_15
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DOI: 10.7735/ksmte.2018.27.4.329
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DOI: 10.1007/s00158-020-02788-w
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DOI: 10.1002/nme.6022
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DOI: 10.2514/6.2019-3559
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DOI: 10.4208/cicp.OA-2017-0003
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DOI: 10.1115/1.4043369
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DOI: 10.1007/s00161-018-0706-y
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DOI: 10.1016/j.advengsoft.2017.09.011
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DOI: 10.1109/TMECH.2019.2943418
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DOI: 10.1007/s12541-017-0166-5
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DOI: 10.1007/s10489-018-1215-1
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DOI: 10.1007/s00158-020-02549-9
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DOI: 10.1007/s11465-019-0534-1
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DOI: 10.1080/25765299.2019.1703493
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DOI: 10.2514/6.2019-3562
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DOI: 10.1016/j.compstruc.2019.106122
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DOI: 10.1098/rspa.2018.0718
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DOI: 10.1016/j.cma.2018.10.004
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DOI: 10.1142/S0218202520500281
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DOI: 10.1051/cocv/2015006
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DOI: 10.1051/m2an/2012014
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DOI: 10.1051/cocv/2010045
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