{"title":"An advanced mixed finite element formulation for flexural analysis of laminated composite plates incorporating HSDT and transverse stretching effect","authors":"Doğan Kanığ, Akif Kutlu","doi":"10.1007/s00419-024-02735-x","DOIUrl":null,"url":null,"abstract":"<div><p>The modeling and analysis of laminated composite plates are performed using a unified Higher Order Shear Deformation Theory (HSDT) that accounts for transverse stretching effect. The adopted unified HSDT formulation allows the implementation of various shear functions. To derive a weak form from the generalized displacement fields of HSDTs, a variational principle is applied within a two-field mixed approach. The stationarity of the functional for laminated plate structures is obtained through the application of the Hellinger–Reissner variational principle. Hence, displacements and stress resultants, namely two independent fields, are included in finite element equations. Four-noded, quadrilateral elements are employed for the discretization of the plate’s domain. While the generated functional initially had <span>\\(C^{1}\\)</span> continuity, benefiting from the two-fields property of the mixed finite element formulation, integration by parts is performed that results with a functional requiring only <span>\\(C^{0}\\)</span> continuity. To effectively capture the nonlinear and parabolic variation of transverse shear stress, it is determined that even with varying functions, the results are theoretically consistent with the elasticity method and the employed HSDT model. Also, when compared to the theories that are already accessible in the literature, for the bending behavior of composite plates, incorporating the stretching effect converges the exact results for laminated composite plates more than the studies where that effect is neglected.</p></div>","PeriodicalId":477,"journal":{"name":"Archive of Applied Mechanics","volume":"95 2","pages":""},"PeriodicalIF":2.2000,"publicationDate":"2025-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Archive of Applied Mechanics","FirstCategoryId":"5","ListUrlMain":"https://link.springer.com/article/10.1007/s00419-024-02735-x","RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MECHANICS","Score":null,"Total":0}
引用次数: 0
Abstract
The modeling and analysis of laminated composite plates are performed using a unified Higher Order Shear Deformation Theory (HSDT) that accounts for transverse stretching effect. The adopted unified HSDT formulation allows the implementation of various shear functions. To derive a weak form from the generalized displacement fields of HSDTs, a variational principle is applied within a two-field mixed approach. The stationarity of the functional for laminated plate structures is obtained through the application of the Hellinger–Reissner variational principle. Hence, displacements and stress resultants, namely two independent fields, are included in finite element equations. Four-noded, quadrilateral elements are employed for the discretization of the plate’s domain. While the generated functional initially had \(C^{1}\) continuity, benefiting from the two-fields property of the mixed finite element formulation, integration by parts is performed that results with a functional requiring only \(C^{0}\) continuity. To effectively capture the nonlinear and parabolic variation of transverse shear stress, it is determined that even with varying functions, the results are theoretically consistent with the elasticity method and the employed HSDT model. Also, when compared to the theories that are already accessible in the literature, for the bending behavior of composite plates, incorporating the stretching effect converges the exact results for laminated composite plates more than the studies where that effect is neglected.
期刊介绍:
Archive of Applied Mechanics serves as a platform to communicate original research of scholarly value in all branches of theoretical and applied mechanics, i.e., in solid and fluid mechanics, dynamics and vibrations. It focuses on continuum mechanics in general, structural mechanics, biomechanics, micro- and nano-mechanics as well as hydrodynamics. In particular, the following topics are emphasised: thermodynamics of materials, material modeling, multi-physics, mechanical properties of materials, homogenisation, phase transitions, fracture and damage mechanics, vibration, wave propagation experimental mechanics as well as machine learning techniques in the context of applied mechanics.