复合模型下分数阶欧拉-伯努利梁模型的数值分析

IF 4.6 Q2 MATERIALS SCIENCE, BIOMATERIALS
Shuai Zhu, Yanfei Ma, Yanyun Zhang, Jiaquan Xie, Ning Xue, Haidong Wei
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引用次数: 0

摘要

本研究的主要目的是通过将分数阶 Kelvin-Voigt 模型与 Abel dashpot 元素并行结合,开发一种新的结构模型。随后,这个新模型将被纳入欧拉-伯努利梁的控制方程,利用移位 Legendre 多项式作为基函数,即经典的正交多项式系统,来求解分数阶偏微分方程。通过比较数值解与分析解,我们旨在评估移位 Legendre 多项式在解决此类问题中的适用性以及所获数值解的准确性。此外,我们还将研究粘弹性高密度聚乙烯梁在不同加载条件下的性能,并对新构造模型和传统分数阶 Kelvin-Voigt 模型下高密度聚乙烯梁的位移进行比较分析。我们希望通过这项研究,更深入地了解分数阶现象的特点,为结构力学领域提供更准确、更高效的数值模拟和分析方法,促进相关工程应用的发展。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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.
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来源期刊
ACS Applied Bio Materials
ACS Applied Bio Materials Chemistry-Chemistry (all)
CiteScore
9.40
自引率
2.10%
发文量
464
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