{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,3]],"date-time":"2026-08-03T19:32:39Z","timestamp":1785785559880,"version":"3.56.0"},"reference-count":80,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2022,5,10]],"date-time":"2022-05-10T00:00:00Z","timestamp":1652140800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Young Science Foundation CN","award":["11701433"],"award-info":[{"award-number":["11701433"]}]},{"name":"Young Science Foundation CN","award":["2021AAA010"],"award-info":[{"award-number":["2021AAA010"]}]},{"name":"Young Science Foundation CN","award":["12071363"],"award-info":[{"award-number":["12071363"]}]},{"name":"Technology Major Project of Hubei","award":["11701433"],"award-info":[{"award-number":["11701433"]}]},{"name":"Technology Major Project of Hubei","award":["2021AAA010"],"award-info":[{"award-number":["2021AAA010"]}]},{"name":"Technology Major Project of Hubei","award":["12071363"],"award-info":[{"award-number":["12071363"]}]},{"name":"National Natural Science Foundation of China","award":["11701433"],"award-info":[{"award-number":["11701433"]}]},{"name":"National Natural Science Foundation of China","award":["2021AAA010"],"award-info":[{"award-number":["2021AAA010"]}]},{"name":"National Natural Science Foundation of China","award":["12071363"],"award-info":[{"award-number":["12071363"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Micromachines"],"abstract":"<jats:p>Elastic materials include metal plates, rubber, foam, airbags and so on, which have a good buffer effect, toughness and strong recovery ability. In this paper, the deformation and thermal diffusion of 2D and 3D thin plates are studied. Two models are established for the deformation of 2D thin plates. The bending deformation equation of rectangular and circular plates is derived, and the semi-analytical solution of the deflection function w(x,y) is found through the Fourier series approximation in the polar coordinate. The consistencies of the numerical solution and the theoretical solution are verified by numerical method. Then, we find that the factors affecting the deformation are related to the Young\u2019s modulus, load, plate length and deformation factor \u03b1 of the material. In a separate temperature physics field, we establish a heat conduction model of 2D graphene film. Three numerical schemes of the transient heat conduction equation of FDM-FEM are given. In contrast, this paper uses the implicit Euler method to discrete the time term. Furthermore, we compared the difference between the adiabatic condition and the convection condition by the graphical method and the curve trend. The results show that the temperature near the adiabatic boundary is higher. Finally, we proposed a 3D dynamic thermal\u2013mechanical coupling model (3D-DTMCM) that has been established. A laser heating monocrystalline silicon sheet with periodic motion formula is given. The temperature radiation of the laser heat source has Gaussian distribution characteristics. Our proposed model can dynamically determine Young\u2019s modulus with a variable temperature. The numerical results show that the higher the temperature is, the higher the strain energy density of the plate is. In addition, the deformation amplitude of the plates in the coupling field is larger than that in the single mechanical field. Finally, we also discussed the stress field distribution of mixed cracks under high temperature and high load. Our research provides theoretical support for the deformation of different plates, and also reflects the value of the coupled model in practical applications.<\/jats:p>","DOI":"10.3390\/mi13050753","type":"journal-article","created":{"date-parts":[[2022,5,10]],"date-time":"2022-05-10T21:52:11Z","timestamp":1652219531000},"page":"753","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["A Dynamic Thermal-Mechanical Coupling Numerical Model to Solve the Deformation and Thermal Diffusion of Plates"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1126-2423","authenticated-orcid":false,"given":"Wenxing","family":"Chen","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Shuyang","family":"Dai","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China"},{"name":"Hubei Key Laboratory of Computational Science, Wuhan University, Wuhan 430072, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Baojuan","family":"Zheng","sequence":"additional","affiliation":[{"name":"Commerical Vehicle Technology Center, SAIC Motor Group Co., Ltd., Shanghai 200041, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2022,5,10]]},"reference":[{"key":"ref_1","first-page":"e00401","article-title":"Model tests of bending and torsional deformations of thin-walled profiles stiffened with elements made in 3D printing technology","volume":"13","author":"Major","year":"2020","journal-title":"Case Stud. 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