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DOI: 10.1016/j.amc.2018.10.018
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DOI: 10.1007/978-3-642-11842-5_81
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International Journal for Numerical Methods in Engineering 63 (6) 859 (2005)
DOI: 10.1002/nme.1302
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Structural and Multidisciplinary Optimization 37 (3) 255 (2009)
DOI: 10.1007/s00158-008-0228-5
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DOI: 10.1007/s10444-009-9122-y
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DOI: 10.1016/j.amc.2019.02.012
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DOI: 10.1007/s10596-005-2848-9
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DOI: 10.1002/num.20131
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DOI: 10.1016/j.cam.2015.06.021
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DOI: 10.1016/j.cam.2016.07.028
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DOI: 10.4208/aamm.12-m12126
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DOI: 10.1016/j.aml.2015.09.016
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DOI: 10.1016/j.cam.2015.11.004
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DOI: 10.1007/s10255-020-0931-6
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DOI: 10.1007/s10915-018-0865-9
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DOI: 10.1016/j.cam.2020.113021
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DOI: 10.1002/mma.2849
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