{"title":"基于Carrera统一公式的弹性结构大变形分析","authors":"E. Carrera, A. Pagani, Bin Wu, M. Filippi","doi":"10.1115/imece2019-11364","DOIUrl":null,"url":null,"abstract":"Based on the well-known nonlinear hyperelasticity theory and by using the Carrera Unified Formulation (CUF) as well as a total Lagrangian approach, the unified theory of slightly compressible elastomeric structures including geometrical and physical nonlinearities is developed in this work. By exploiting CUF, the principle of virtual work and a finite element approximation, nonlinear governing equations corresponding to the slightly compressible elastomeric structures are straightforwardly formulated in terms of the fundamental nuclei, which are independent of the theory approximation order. Accordingly, the explicit forms of the secant and tangent stiffness matrices of the unified 1D beam and 2D plate elements are derived by using the three-dimensional Cauchy-Green deformation tensor and the nonlinear constitutive equation for slightly incompressible hyperelastic materials. Several numerical assessments are conducted, including uniaxial tension nonlinear response of rectangular elastomeric beams. Our numerical findings demonstrate the capabilities of the CUF model to calculate the large-deformation equilibrium curves as well as the stress distributions with high accuracy.","PeriodicalId":119220,"journal":{"name":"Volume 1: Advances in Aerospace Technology","volume":"63 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2019-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Large-Deformation Analysis of Elastomeric Structures by Carrera Unified Formulation\",\"authors\":\"E. Carrera, A. Pagani, Bin Wu, M. Filippi\",\"doi\":\"10.1115/imece2019-11364\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Based on the well-known nonlinear hyperelasticity theory and by using the Carrera Unified Formulation (CUF) as well as a total Lagrangian approach, the unified theory of slightly compressible elastomeric structures including geometrical and physical nonlinearities is developed in this work. By exploiting CUF, the principle of virtual work and a finite element approximation, nonlinear governing equations corresponding to the slightly compressible elastomeric structures are straightforwardly formulated in terms of the fundamental nuclei, which are independent of the theory approximation order. Accordingly, the explicit forms of the secant and tangent stiffness matrices of the unified 1D beam and 2D plate elements are derived by using the three-dimensional Cauchy-Green deformation tensor and the nonlinear constitutive equation for slightly incompressible hyperelastic materials. Several numerical assessments are conducted, including uniaxial tension nonlinear response of rectangular elastomeric beams. Our numerical findings demonstrate the capabilities of the CUF model to calculate the large-deformation equilibrium curves as well as the stress distributions with high accuracy.\",\"PeriodicalId\":119220,\"journal\":{\"name\":\"Volume 1: Advances in Aerospace Technology\",\"volume\":\"63 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2019-11-11\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Volume 1: Advances in Aerospace Technology\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1115/imece2019-11364\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Volume 1: Advances in Aerospace Technology","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1115/imece2019-11364","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Large-Deformation Analysis of Elastomeric Structures by Carrera Unified Formulation
Based on the well-known nonlinear hyperelasticity theory and by using the Carrera Unified Formulation (CUF) as well as a total Lagrangian approach, the unified theory of slightly compressible elastomeric structures including geometrical and physical nonlinearities is developed in this work. By exploiting CUF, the principle of virtual work and a finite element approximation, nonlinear governing equations corresponding to the slightly compressible elastomeric structures are straightforwardly formulated in terms of the fundamental nuclei, which are independent of the theory approximation order. Accordingly, the explicit forms of the secant and tangent stiffness matrices of the unified 1D beam and 2D plate elements are derived by using the three-dimensional Cauchy-Green deformation tensor and the nonlinear constitutive equation for slightly incompressible hyperelastic materials. Several numerical assessments are conducted, including uniaxial tension nonlinear response of rectangular elastomeric beams. Our numerical findings demonstrate the capabilities of the CUF model to calculate the large-deformation equilibrium curves as well as the stress distributions with high accuracy.