A Simplified Analytical Model for Strip Buckling in the Pressure-Assisted Milling Process
A simplified column-buckling model is developed to understand the buckling mechanism of thin-walled strips restrained by uniform lateral pressure in the milling process. The strip is simplified as two rigid columns connected by a rotation spring, resting on a smooth surface, restrained by a uniform...
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Published in | Materials Vol. 17; no. 15; p. 3739 |
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Abstract | A simplified column-buckling model is developed to understand the buckling mechanism of thin-walled strips restrained by uniform lateral pressure in the milling process. The strip is simplified as two rigid columns connected by a rotation spring, resting on a smooth surface, restrained by a uniform pressure and loaded by an axial force. Two loading cases are considered, i.e., the dead load and the follower load. Analytical solutions for the post-buckling responses of the two cases are derived based on the energy method. The minimum buckling force, Maxwell force and stability conditions for the two cases are established. It is demonstrated that the application of higher uniform pressure increases the minimum buckling force for the column and thus makes the column less likely to buckle. For the same pressure level, the dead load is found to be more effective than the follower load in suppressing the buckling of the system. The effect of initial geometric imperfection is also investigated, and the imperfection amplitude and critical restraining pressure that prevent buckling are found to be linearly related. The analytical results are validated by finite element simulations. This analytical model reveals the buckling mechanism of strips under lateral pressure restraint, which cannot be explained by the conventional bifurcation buckling theory, and provides a theoretical foundation for buckling-prevention strategies during the milling process of thin-walled strips, plates and shells commonly encountered in aerospace or automotive industries. |
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AbstractList | A simplified column-buckling model is developed to understand the buckling mechanism of thin-walled strips restrained by uniform lateral pressure in the milling process. The strip is simplified as two rigid columns connected by a rotation spring, resting on a smooth surface, restrained by a uniform pressure and loaded by an axial force. Two loading cases are considered, i.e., the dead load and the follower load. Analytical solutions for the post-buckling responses of the two cases are derived based on the energy method. The minimum buckling force, Maxwell force and stability conditions for the two cases are established. It is demonstrated that the application of higher uniform pressure increases the minimum buckling force for the column and thus makes the column less likely to buckle. For the same pressure level, the dead load is found to be more effective than the follower load in suppressing the buckling of the system. The effect of initial geometric imperfection is also investigated, and the imperfection amplitude and critical restraining pressure that prevent buckling are found to be linearly related. The analytical results are validated by finite element simulations. This analytical model reveals the buckling mechanism of strips under lateral pressure restraint, which cannot be explained by the conventional bifurcation buckling theory, and provides a theoretical foundation for buckling-prevention strategies during the milling process of thin-walled strips, plates and shells commonly encountered in aerospace or automotive industries. A simplified column-buckling model is developed to understand the buckling mechanism of thin-walled strips restrained by uniform lateral pressure in the milling process. The strip is simplified as two rigid columns connected by a rotation spring, resting on a smooth surface, restrained by a uniform pressure and loaded by an axial force. Two loading cases are considered, i.e., the dead load and the follower load. Analytical solutions for the post-buckling responses of the two cases are derived based on the energy method. The minimum buckling force, Maxwell force and stability conditions for the two cases are established. It is demonstrated that the application of higher uniform pressure increases the minimum buckling force for the column and thus makes the column less likely to buckle. For the same pressure level, the dead load is found to be more effective than the follower load in suppressing the buckling of the system. The effect of initial geometric imperfection is also investigated, and the imperfection amplitude and critical restraining pressure that prevent buckling are found to be linearly related. The analytical results are validated by finite element simulations. This analytical model reveals the buckling mechanism of strips under lateral pressure restraint, which cannot be explained by the conventional bifurcation buckling theory, and provides a theoretical foundation for buckling-prevention strategies during the milling process of thin-walled strips, plates and shells commonly encountered in aerospace or automotive industries.A simplified column-buckling model is developed to understand the buckling mechanism of thin-walled strips restrained by uniform lateral pressure in the milling process. The strip is simplified as two rigid columns connected by a rotation spring, resting on a smooth surface, restrained by a uniform pressure and loaded by an axial force. Two loading cases are considered, i.e., the dead load and the follower load. Analytical solutions for the post-buckling responses of the two cases are derived based on the energy method. The minimum buckling force, Maxwell force and stability conditions for the two cases are established. It is demonstrated that the application of higher uniform pressure increases the minimum buckling force for the column and thus makes the column less likely to buckle. For the same pressure level, the dead load is found to be more effective than the follower load in suppressing the buckling of the system. The effect of initial geometric imperfection is also investigated, and the imperfection amplitude and critical restraining pressure that prevent buckling are found to be linearly related. The analytical results are validated by finite element simulations. This analytical model reveals the buckling mechanism of strips under lateral pressure restraint, which cannot be explained by the conventional bifurcation buckling theory, and provides a theoretical foundation for buckling-prevention strategies during the milling process of thin-walled strips, plates and shells commonly encountered in aerospace or automotive industries. |
Audience | Academic |
Author | Chen, Kelin He, Zhubin Wang, Xuezhi Lin, Yanli |
Author_xml | – sequence: 1 givenname: Xuezhi surname: Wang fullname: Wang, Xuezhi organization: State Key Laboratory of High-Performance Precision Manufacturing, School of Mechanical Engineering, Dalian University of Technology, Dalian 116024, China – sequence: 2 givenname: Kelin surname: Chen fullname: Chen, Kelin organization: State Key Laboratory of High-Performance Precision Manufacturing, School of Mechanical Engineering, Dalian University of Technology, Dalian 116024, China – sequence: 3 givenname: Yanli surname: Lin fullname: Lin, Yanli organization: State Key Laboratory of High-Performance Precision Manufacturing, School of Mechanical Engineering, Dalian University of Technology, Dalian 116024, China – sequence: 4 givenname: Zhubin surname: He fullname: He, Zhubin organization: State Key Laboratory of High-Performance Precision Manufacturing, School of Mechanical Engineering, Dalian University of Technology, Dalian 116024, China |
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Cites_doi | 10.3390/jmmp6040076 10.1016/j.engstruct.2014.05.006 10.1002/zamm.201600115 10.1007/s00170-023-12647-9 10.1016/j.ijsolstr.2004.03.023 10.1016/j.ijsolstr.2014.02.010 10.1016/j.ijmecsci.2009.10.011 10.1016/j.ijmecsci.2013.01.018 10.1115/1.4064625 10.2118/111511-PA 10.1016/j.ijsolstr.2021.111178 10.1016/j.jmapro.2023.04.074 10.1016/j.mechrescom.2010.07.024 10.2118/99099-PA 10.1016/j.ijmecsci.2016.09.035 10.1007/s00170-024-13934-9 10.1016/j.petrol.2017.03.040 10.1016/j.ijmachtools.2018.01.005 10.1016/j.engstruct.2017.04.033 10.1016/j.jcsr.2020.105988 10.1016/j.compstruct.2020.112732 10.1061/(ASCE)ST.1943-541X.0001508 10.1007/s00158-007-0144-0 10.1590/S1679-78252014001400010 10.1007/s00419-021-01933-1 10.1016/j.jcsr.2012.11.004 10.1016/j.engstruct.2013.07.020 10.1016/j.tws.2023.111396 |
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SubjectTerms | Axial forces Bifurcations characteristic imperfection column buckling Defects energy barrier Energy methods Exact solutions Friction Heat treating Initial geometric imperfections Lateral pressure Manufacturing Mathematical analysis Mathematical models Maxwell force milling post-buckling Postbuckling Pressure effects Static loads Strip |
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Title | A Simplified Analytical Model for Strip Buckling in the Pressure-Assisted Milling Process |
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