{"title":"石墨烯平板强化功能梯度电介质板的电致非线性稳定性","authors":"Jinghua Zhang, Haorui Ren","doi":"10.1007/s00161-025-01381-0","DOIUrl":null,"url":null,"abstract":"<div><p>The stability of composite structures are fundamental problems in continuum mechanics. In present study, considering piezoelectric and electrostrictive effects simultaneously, electro-induced nonlinear buckling and post-buckling characteristics of graphene platelets (GPL) reinforced functionally graded dielectric circular plates are examined. Firstly, equivalent dielectric constant and Young’s modulus of the intelligent composites with different GPL distribution patterns are calculated according to effective medium theory, in which the gradient characteristics, the imperfect combination between reinforcements and matrix, the interface electron tunnel and the Maxwell–Wagner–Silla polarization are considered. Then, the nonlinear displacement governing differential equations are derived according to von Kármán nonlinear plate theory and virtual work principle and solved by shooting method for different boundary conditions. The buckling critical voltage and post-buckling deflection-voltage path under various conditions are obtained. Finally, the effects of distribution pattern, gradient slope and geometrical dimension parameters of GPL, as well as interface phase size on the critical electrical parameters and post-buckling characteristics are examined by cross-scale analysis between micro and macro in detail. This research may offer theoretical guidance value for the engineering design of the intelligent structures.</p></div>","PeriodicalId":525,"journal":{"name":"Continuum Mechanics and Thermodynamics","volume":"37 3","pages":""},"PeriodicalIF":1.9000,"publicationDate":"2025-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Electro-induced nonlinear stability of graphene platelets reinforced functionally graded dielectric plate\",\"authors\":\"Jinghua Zhang, Haorui Ren\",\"doi\":\"10.1007/s00161-025-01381-0\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>The stability of composite structures are fundamental problems in continuum mechanics. In present study, considering piezoelectric and electrostrictive effects simultaneously, electro-induced nonlinear buckling and post-buckling characteristics of graphene platelets (GPL) reinforced functionally graded dielectric circular plates are examined. Firstly, equivalent dielectric constant and Young’s modulus of the intelligent composites with different GPL distribution patterns are calculated according to effective medium theory, in which the gradient characteristics, the imperfect combination between reinforcements and matrix, the interface electron tunnel and the Maxwell–Wagner–Silla polarization are considered. Then, the nonlinear displacement governing differential equations are derived according to von Kármán nonlinear plate theory and virtual work principle and solved by shooting method for different boundary conditions. The buckling critical voltage and post-buckling deflection-voltage path under various conditions are obtained. Finally, the effects of distribution pattern, gradient slope and geometrical dimension parameters of GPL, as well as interface phase size on the critical electrical parameters and post-buckling characteristics are examined by cross-scale analysis between micro and macro in detail. This research may offer theoretical guidance value for the engineering design of the intelligent structures.</p></div>\",\"PeriodicalId\":525,\"journal\":{\"name\":\"Continuum Mechanics and Thermodynamics\",\"volume\":\"37 3\",\"pages\":\"\"},\"PeriodicalIF\":1.9000,\"publicationDate\":\"2025-04-23\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Continuum Mechanics and Thermodynamics\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s00161-025-01381-0\",\"RegionNum\":4,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MECHANICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Continuum Mechanics and Thermodynamics","FirstCategoryId":"5","ListUrlMain":"https://link.springer.com/article/10.1007/s00161-025-01381-0","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MECHANICS","Score":null,"Total":0}
The stability of composite structures are fundamental problems in continuum mechanics. In present study, considering piezoelectric and electrostrictive effects simultaneously, electro-induced nonlinear buckling and post-buckling characteristics of graphene platelets (GPL) reinforced functionally graded dielectric circular plates are examined. Firstly, equivalent dielectric constant and Young’s modulus of the intelligent composites with different GPL distribution patterns are calculated according to effective medium theory, in which the gradient characteristics, the imperfect combination between reinforcements and matrix, the interface electron tunnel and the Maxwell–Wagner–Silla polarization are considered. Then, the nonlinear displacement governing differential equations are derived according to von Kármán nonlinear plate theory and virtual work principle and solved by shooting method for different boundary conditions. The buckling critical voltage and post-buckling deflection-voltage path under various conditions are obtained. Finally, the effects of distribution pattern, gradient slope and geometrical dimension parameters of GPL, as well as interface phase size on the critical electrical parameters and post-buckling characteristics are examined by cross-scale analysis between micro and macro in detail. This research may offer theoretical guidance value for the engineering design of the intelligent structures.
期刊介绍：
This interdisciplinary journal provides a forum for presenting new ideas in continuum and quasi-continuum modeling of systems with a large number of degrees of freedom and sufficient complexity to require thermodynamic closure. Major emphasis is placed on papers attempting to bridge the gap between discrete and continuum approaches as well as micro- and macro-scales, by means of homogenization, statistical averaging and other mathematical tools aimed at the judicial elimination of small time and length scales. The journal is particularly interested in contributions focusing on a simultaneous description of complex systems at several disparate scales. Papers presenting and explaining new experimental findings are highly encouraged. The journal welcomes numerical studies aimed at understanding the physical nature of the phenomena.
Potential subjects range from boiling and turbulence to plasticity and earthquakes. Studies of fluids and solids with nonlinear and non-local interactions, multiple fields and multi-scale responses, nontrivial dissipative properties and complex dynamics are expected to have a strong presence in the pages of the journal. An incomplete list of featured topics includes: active solids and liquids, nano-scale effects and molecular structure of materials, singularities in fluid and solid mechanics, polymers, elastomers and liquid crystals, rheology, cavitation and fracture, hysteresis and friction, mechanics of solid and liquid phase transformations, composite, porous and granular media, scaling in statics and dynamics, large scale processes and geomechanics, stochastic aspects of mechanics. The journal would also like to attract papers addressing the very foundations of thermodynamics and kinetics of continuum processes. Of special interest are contributions to the emerging areas of biophysics and biomechanics of cells, bones and tissues leading to new continuum and thermodynamical models.
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