{"title":"Elasticity solutions for functionally graded beams with arbitrary distributed loads","authors":"","doi":"10.1016/j.compstruct.2024.118578","DOIUrl":null,"url":null,"abstract":"<div><p>This paper derives the exact general elasticity solution for functionally graded rectangular beams subjected to arbitrary normal and tangential loads and with arbitrary end constraints. The general solution consists of bending moments and their integrals and derivatives, along with load-independent function sequences of the longitudinal coordinate. The method for determining function sequences has been established based on the stress function method. General solution formulas for stresses, strains and displacements have been derived and used to solve explicit special solutions for six cases involving concentrated forces, uniformly loads, and quadratically distributed loads with different displacement constraints scenarios. The results obtained are compared with existing exact solutions and those of Euler–Bernoulli and Timoshenko beams, and the errors of the latter two are analysed.</p></div>","PeriodicalId":281,"journal":{"name":"Composite Structures","volume":null,"pages":null},"PeriodicalIF":6.3000,"publicationDate":"2024-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0263822324007062/pdfft?md5=a10b3530982041672b9a56fc582a4fd6&pid=1-s2.0-S0263822324007062-main.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Composite Structures","FirstCategoryId":"5","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0263822324007062","RegionNum":2,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATERIALS SCIENCE, COMPOSITES","Score":null,"Total":0}
引用次数: 0
Abstract
This paper derives the exact general elasticity solution for functionally graded rectangular beams subjected to arbitrary normal and tangential loads and with arbitrary end constraints. The general solution consists of bending moments and their integrals and derivatives, along with load-independent function sequences of the longitudinal coordinate. The method for determining function sequences has been established based on the stress function method. General solution formulas for stresses, strains and displacements have been derived and used to solve explicit special solutions for six cases involving concentrated forces, uniformly loads, and quadratically distributed loads with different displacement constraints scenarios. The results obtained are compared with existing exact solutions and those of Euler–Bernoulli and Timoshenko beams, and the errors of the latter two are analysed.
期刊介绍：
The past few decades have seen outstanding advances in the use of composite materials in structural applications. There can be little doubt that, within engineering circles, composites have revolutionised traditional design concepts and made possible an unparalleled range of new and exciting possibilities as viable materials for construction. Composite Structures, an International Journal, disseminates knowledge between users, manufacturers, designers and researchers involved in structures or structural components manufactured using composite materials.
The journal publishes papers which contribute to knowledge in the use of composite materials in engineering structures. Papers deal with design, research and development studies, experimental investigations, theoretical analysis and fabrication techniques relevant to the application of composites in load-bearing components for assemblies, ranging from individual components such as plates and shells to complete composite structures.
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