{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,18]],"date-time":"2026-08-18T04:53:45Z","timestamp":1787028825276,"version":"build-2736575974"},"reference-count":29,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2022,6,10]],"date-time":"2022-06-10T00:00:00Z","timestamp":1654819200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12172054"],"award-info":[{"award-number":["12172054"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["XSQD-202002005"],"award-info":[{"award-number":["XSQD-202002005"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012236","name":"Beijing Institute of Technology Research Fund Program for Young Scholars","doi-asserted-by":"publisher","award":["12172054"],"award-info":[{"award-number":["12172054"]}],"id":[{"id":"10.13039\/501100012236","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012236","name":"Beijing Institute of Technology Research Fund Program for Young Scholars","doi-asserted-by":"publisher","award":["XSQD-202002005"],"award-info":[{"award-number":["XSQD-202002005"]}],"id":[{"id":"10.13039\/501100012236","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Materials"],"abstract":"<jats:p>Experimental and theoretical studies were carried out on the dynamic deformation and penetration response characteristics of metal ellipsoidal thin curved shells under impact loads. The deformation characteristics of the impacted ellipsoid shell was investigated via the use of a light gas gun to carry out impact loading experiments at different speeds. Ten cases of experiments were conducted with the impact velocities distributed between 25.69 m\/s and 118.97 m\/s. Stereo digital image correlation (3D-DIC) technology was applied to capture the dynamic deformation and penetration process of the impacted shell. The recovered shells were measured, and the deformation characteristics were analyzed, along with the dynamic evolution, as observed through 3D-DIC analysis. Based on the experimental results, the displacement mode was summarized and the displacement distribution of the locally impacted ellipsoid shell was proposed. The governing equations were derived for the dynamic deformation and penetration of the impacted ellipsoid shell by means of the Lagrange equation. The proposed theoretical model was verified based on the experimental results. Finally, the influence of the curvature distribution on the impact resistance of ellipsoidal shells is discussed. The results indicated that the proposed theoretical model was effective in analyzing the large deformation and the penetration speed. Stretching the axial length of the ellipsoid shell in the impact direction improved its resistance to penetration. Stretching the axial length of the ellipsoid shell perpendicular to the impact direction improved its resistance to deformation, but reduced its resistance to penetration. Maintaining the triaxial ratio and appropriately reducing the size of the ellipsoidal shell improved its resistance to both deformation and penetration. The above research provides a reference for the analysis of the impact resistance of thin-walled curved shell structures in engineering.<\/jats:p>","DOI":"10.3390\/ma15124124","type":"journal-article","created":{"date-parts":[[2022,6,12]],"date-time":"2022-06-12T09:26:48Z","timestamp":1655026008000},"page":"4124","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Dynamic Deformation and Perforation of Ellipsoidal Thin Shell Impacted by Flat-Nose Projectile"],"prefix":"10.3390","volume":"15","author":[{"given":"Ling","family":"Liu","sequence":"first","affiliation":[{"name":"State Key Laboratory of Explosion Science and Technology, Beijing Institute of Technology, Beijing 100081, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jianqiao","family":"Li","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Explosion Science and Technology, Beijing Institute of Technology, Beijing 100081, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2022,6,10]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Sobhani, E., Arbabian, A., Civalek, O., and Avcar, M. (2021). The free vibration analysis of hybrid porous nanocomposite joined hemispherical\u2013cylindrical\u2013conical shells. Eng. Comput., 1\u201328.","DOI":"10.1007\/s00366-021-01453-0"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1016\/j.tws.2017.08.009","article-title":"Dynamic response of internally nested hemispherical shell system to impact loading","volume":"120","author":"Hu","year":"2017","journal-title":"Thin-Walled Struct."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1436","DOI":"10.1007\/BF01105292","article-title":"Dynamic reaction of a spherical shell under a local normal load","volume":"65","author":"Sabodash","year":"1993","journal-title":"J. Sov. Math."},{"key":"ref_4","first-page":"620","article-title":"R Numerical and Experimental Investigations on the Buckling of Steel Semi-Spherical Shells under Various Loadings","volume":"48","author":"Shariati","year":"2010","journal-title":"Steel Constr."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1177","DOI":"10.1002\/pc.26446","article-title":"Effect of projectile nose on high-velocity impact behavior of fiber metal laminates","volume":"43","author":"Majzoobi","year":"2022","journal-title":"Polym. Compos."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"144302","DOI":"10.1103\/PhysRevLett.109.144302","article-title":"Indentation of Ellipsoidal and Cylindrical Elastic Shells","volume":"109","author":"Vella","year":"2012","journal-title":"Phys. Rev. Lett."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1016\/S0263-8231(98)00049-4","article-title":"Axial compression of metallic spherical shells between rigid plates","volume":"34","author":"Gupta","year":"1999","journal-title":"Thin-Walled Struct."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"693","DOI":"10.1016\/0020-7403(75)90072-7","article-title":"A theoretical and experimental study of hemispherical shells subjected to axial loads between flat plates","volume":"17","author":"Kitching","year":"1975","journal-title":"Int. J. Mech. Sci."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"949","DOI":"10.1115\/1.3428276","article-title":"On the Large Deformation of a Rigid-Plastic Spherical Shell Compressed by a Rigid Plate","volume":"94","author":"Updike","year":"1972","journal-title":"J. Eng. Ind."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"257","DOI":"10.1590\/1679-78252434","article-title":"Peripheral Deformation and Buckling of Stainless Steel Hemispherical Shells Compressed by a Flat Plate","volume":"13","author":"Yang","year":"2016","journal-title":"Lat. Am. J. Solids Struct."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1225","DOI":"10.1016\/j.ijimpeng.2004.03.009","article-title":"Experimental and numerical studies of dynamic axial compression of thin walled spherical shells","volume":"30","author":"Gupta","year":"2004","journal-title":"Int. J. Impact Eng."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"3136","DOI":"10.1016\/j.ijsolstr.2006.09.014","article-title":"Experimental and numerical investigations into collapse behaviour of thin spherical shells under drop hammer impact","volume":"44","author":"Gupta","year":"2007","journal-title":"Int. J. Solids Struct. Int Solids Struct."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"422","DOI":"10.1016\/j.ijmecsci.2007.10.002","article-title":"Experimental and theoretical studies on buckling of thin spherical shells under axial loads","volume":"50","author":"Gupta","year":"2008","journal-title":"Int. J. Mech. Sci."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Pogorelov, A. (1988). Bendings of Surfaces and Stability of Shells, American Mathematical Society. Translations of mathematical monographs.","DOI":"10.1090\/mmono\/072\/04"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1464","DOI":"10.1016\/j.ijimpeng.2004.11.001","article-title":"Failure analysis of plastic spherical shells impacted by a projectile","volume":"32","author":"Ning","year":"2006","journal-title":"Int. J. Impact Eng."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"107403","DOI":"10.1016\/j.tws.2020.107403","article-title":"Deformation and failure of thin spherical shells under dynamic impact loading: Experiment and analytical model","volume":"161","author":"Li","year":"2021","journal-title":"Thin-Walled Struct."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"92","DOI":"10.1016\/0021-8928(89)90139-1","article-title":"A new approach to the asymptotic integration of the equations of shallow convex shell theory in the post-critical stage","volume":"53","author":"Yevkin","year":"1989","journal-title":"Pmm J. Appl. Math. Mech. Pmm Appl. Math. Mech. Engl."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"111577","DOI":"10.1016\/j.compstruct.2019.111577","article-title":"Composite spherical shells at large deflections. Asymptotic analysis and applications","volume":"233","author":"Yevkin","year":"2019","journal-title":"Compos. Struct."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"8961","DOI":"10.1016\/S0020-7683(01)00184-6","article-title":"Analysis of large deflection equilibrium states of composite shells of revolution. Part 1. General model and singular perturbation analysis","volume":"38","author":"Yevkin","year":"2001","journal-title":"Int. J. Solids Struct."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1016\/j.ijsolstr.2018.06.035","article-title":"Design buckling pressure for thin spherical shells: Development and validation","volume":"156\u2013157","author":"Evkin","year":"2019","journal-title":"Int. J. Solids Struct."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"54","DOI":"10.1115\/1.3454520","article-title":"Nonsymmetric Buckling of Internally Pressurized Ellipsoidal and Torispherical Elastic-Plastic Pressure Vessel Heads","volume":"99","author":"Bushnell","year":"1977","journal-title":"J. Press. Vessel. Technol."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"89","DOI":"10.1016\/0308-0161(85)90042-0","article-title":"Stress analysis of ellipsoidal shell with radial nozzle","volume":"21","author":"Chao","year":"1985","journal-title":"Int. J. Press. Vessel. Pip. Int Press. Vessel. Pip."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"71","DOI":"10.1115\/1.2883670","article-title":"On the Choice of Initial Geometric Imperfections in Externally Pressurized Shells","volume":"121","author":"Jaiswal","year":"1999","journal-title":"J. Press. Vessel. Technol. Trans. Asme Press. Vessel. Technol"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"011210","DOI":"10.1115\/1.2834457","article-title":"Buckling of Externally Pressurized Prolate Ellipsoidal Domes","volume":"130","author":"Smith","year":"2008","journal-title":"J. Press. Vessel. Technol. Trans. Asme Press. Vessel. Technol"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"841","DOI":"10.1016\/S0308-0161(02)00101-1","article-title":"Minimization of stress concentration factor in cylindrical pressure vessels with ellipsoidal heads","volume":"79","author":"Magnucki","year":"2002","journal-title":"Int. J. Press. Vessel. Pip. Int Press. Vessel. Pip."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"514","DOI":"10.1016\/j.tws.2018.01.001","article-title":"Effect of shape imperfection on the buckling of large-scale thin-walled ellipsoidal head in steel nuclear containment","volume":"124","author":"Zheng","year":"2018","journal-title":"Thin-Walled Struct."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"54","DOI":"10.1016\/j.tws.2015.02.021","article-title":"A closed form solution for the impact analysis of elastic ellipsoidal thin shells","volume":"93","author":"Sadegh","year":"2015","journal-title":"Thin-Walled Struct."},{"key":"ref_28","unstructured":"Huang, K. (1987). Theory of Plates and Shells, Tsinghua University Press."},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Willatzen, M., and Voon, L.C.L.Y. (2011). Ellipsoidal Coordinates. Separable Boundary\u2014Value Problems in Physics, WILEY-VCH Verlag GmbH & Co. KGaA. Available online: https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/9783527634927.ch16.","DOI":"10.1002\/9783527634927"}],"container-title":["Materials"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1996-1944\/15\/12\/4124\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T23:27:31Z","timestamp":1760138851000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1996-1944\/15\/12\/4124"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,6,10]]},"references-count":29,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2022,6]]}},"alternative-id":["ma15124124"],"URL":"https:\/\/doi.org\/10.3390\/ma15124124","relation":{},"ISSN":["1996-1944"],"issn-type":[{"value":"1996-1944","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,6,10]]}}}