{"title":"复合模型下分数阶欧拉-伯努利梁模型的数值分析","authors":"Shuai Zhu, Yanfei Ma, Yanyun Zhang, Jiaquan Xie, Ning Xue, Haidong Wei","doi":"10.1002/mma.10444","DOIUrl":null,"url":null,"abstract":"The primary objective of this study is to develop a new constitutive model by combining a fractional‐order Kelvin–Voigt model with an Abel dashpot element in parallel. Subsequently, this new model will be incorporated into the Euler–Bernoulli beam's governing equation, utilizing shifted Legendre polynomials as basis functions, a classical orthogonal polynomial system, to solve the fractional‐order partial differential equations. By comparing the numerical solutions with the analytical solutions, we aim to evaluate the applicability of shifted Legendre polynomials in solving such problems and the accuracy of the obtained numerical solutions. Furthermore, we will investigate the performance of viscoelastic HDPE beams under different loading conditions and conduct a comparative analysis of the displacements of HDPE beams under the new constitutive model and the traditional fractional‐order Kelvin–Voigt model. Through this research, we hope to gain a deeper understanding of the characteristics of fractional‐order phenomena and provide more accurate and efficient numerical simulation and analysis methods for the field of structural mechanics, promoting the development of related engineering applications.","PeriodicalId":2,"journal":{"name":"ACS Applied Bio Materials","volume":null,"pages":null},"PeriodicalIF":4.6000,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Numerical analysis of fractional‐order Euler–Bernoulli beam model under composite model\",\"authors\":\"Shuai Zhu, Yanfei Ma, Yanyun Zhang, Jiaquan Xie, Ning Xue, Haidong Wei\",\"doi\":\"10.1002/mma.10444\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The primary objective of this study is to develop a new constitutive model by combining a fractional‐order Kelvin–Voigt model with an Abel dashpot element in parallel. Subsequently, this new model will be incorporated into the Euler–Bernoulli beam's governing equation, utilizing shifted Legendre polynomials as basis functions, a classical orthogonal polynomial system, to solve the fractional‐order partial differential equations. By comparing the numerical solutions with the analytical solutions, we aim to evaluate the applicability of shifted Legendre polynomials in solving such problems and the accuracy of the obtained numerical solutions. Furthermore, we will investigate the performance of viscoelastic HDPE beams under different loading conditions and conduct a comparative analysis of the displacements of HDPE beams under the new constitutive model and the traditional fractional‐order Kelvin–Voigt model. Through this research, we hope to gain a deeper understanding of the characteristics of fractional‐order phenomena and provide more accurate and efficient numerical simulation and analysis methods for the field of structural mechanics, promoting the development of related engineering applications.\",\"PeriodicalId\":2,\"journal\":{\"name\":\"ACS Applied Bio Materials\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":4.6000,\"publicationDate\":\"2024-09-18\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"ACS Applied Bio Materials\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1002/mma.10444\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATERIALS SCIENCE, BIOMATERIALS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"ACS Applied Bio Materials","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1002/mma.10444","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATERIALS SCIENCE, BIOMATERIALS","Score":null,"Total":0}
Numerical analysis of fractional‐order Euler–Bernoulli beam model under composite model
The primary objective of this study is to develop a new constitutive model by combining a fractional‐order Kelvin–Voigt model with an Abel dashpot element in parallel. Subsequently, this new model will be incorporated into the Euler–Bernoulli beam's governing equation, utilizing shifted Legendre polynomials as basis functions, a classical orthogonal polynomial system, to solve the fractional‐order partial differential equations. By comparing the numerical solutions with the analytical solutions, we aim to evaluate the applicability of shifted Legendre polynomials in solving such problems and the accuracy of the obtained numerical solutions. Furthermore, we will investigate the performance of viscoelastic HDPE beams under different loading conditions and conduct a comparative analysis of the displacements of HDPE beams under the new constitutive model and the traditional fractional‐order Kelvin–Voigt model. Through this research, we hope to gain a deeper understanding of the characteristics of fractional‐order phenomena and provide more accurate and efficient numerical simulation and analysis methods for the field of structural mechanics, promoting the development of related engineering applications.