{"title":"Constrained Large-Displacement Thermal Analysis","authors":"A. Shabana, Mahmoud Elbakly, Dayu Zhang","doi":"10.1115/1.4056182","DOIUrl":null,"url":null,"abstract":"\n Two different cases are encountered in the thermal analysis of solids. In the first case, continua are not subject to boundary and motion constraints and all material points experience same displacement-gradient changes as the result of application of thermal loads. In this case, referred to as unconstrained thermal expansion, the thermal load produces uniform stress-free motion within the continuum. In the second case, point displacements due to boundary and motion constraints are restricted, and therefore, continuum points do not move freely when thermal loads are applied. This second case, referred to as constrained thermal expansion, leads to thermal stresses and its study requires proper identification of the independent coordinates which represent expansion degrees-of-freedom. To have objective evaluation and comparison between the two cases of constrained and unconstrained thermal expansion, the reference-configuration geometry is accurately described using the absolute nodal coordinate formulation (ANCF) finite elements. ANCF position-gradient vectors have unique geometric meanings as tangent to coordinate lines, allowing systematic description of the two different cases of unconstrained and constrained thermal expansions using multiplicative decomposition of the matrix of position-gradient vectors. Furthermore, generality of the approach for large-displacement thermal analysis requires using the Lagrange–D'Alembert principle for proper treatment of algebraic constraint equations. Numerical results are presented to compare two different expansion cases, demonstrate use of the new approach, and verify its results by comparing with conventional finite element (FE) approaches.","PeriodicalId":54858,"journal":{"name":"Journal of Computational and Nonlinear Dynamics","volume":"64 1","pages":""},"PeriodicalIF":1.9000,"publicationDate":"2022-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Computational and Nonlinear Dynamics","FirstCategoryId":"5","ListUrlMain":"https://doi.org/10.1115/1.4056182","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"ENGINEERING, MECHANICAL","Score":null,"Total":0}
引用次数: 3
Abstract
Two different cases are encountered in the thermal analysis of solids. In the first case, continua are not subject to boundary and motion constraints and all material points experience same displacement-gradient changes as the result of application of thermal loads. In this case, referred to as unconstrained thermal expansion, the thermal load produces uniform stress-free motion within the continuum. In the second case, point displacements due to boundary and motion constraints are restricted, and therefore, continuum points do not move freely when thermal loads are applied. This second case, referred to as constrained thermal expansion, leads to thermal stresses and its study requires proper identification of the independent coordinates which represent expansion degrees-of-freedom. To have objective evaluation and comparison between the two cases of constrained and unconstrained thermal expansion, the reference-configuration geometry is accurately described using the absolute nodal coordinate formulation (ANCF) finite elements. ANCF position-gradient vectors have unique geometric meanings as tangent to coordinate lines, allowing systematic description of the two different cases of unconstrained and constrained thermal expansions using multiplicative decomposition of the matrix of position-gradient vectors. Furthermore, generality of the approach for large-displacement thermal analysis requires using the Lagrange–D'Alembert principle for proper treatment of algebraic constraint equations. Numerical results are presented to compare two different expansion cases, demonstrate use of the new approach, and verify its results by comparing with conventional finite element (FE) approaches.
期刊介绍:
The purpose of the Journal of Computational and Nonlinear Dynamics is to provide a medium for rapid dissemination of original research results in theoretical as well as applied computational and nonlinear dynamics. The journal serves as a forum for the exchange of new ideas and applications in computational, rigid and flexible multi-body system dynamics and all aspects (analytical, numerical, and experimental) of dynamics associated with nonlinear systems. The broad scope of the journal encompasses all computational and nonlinear problems occurring in aeronautical, biological, electrical, mechanical, physical, and structural systems.