https://scholars.lib.ntu.edu.tw/handle/123456789/636528
標題: | Closed-Form Analytical Solutions for the Deflection of Elastic Beams in a Peridynamic Framework | 作者: | Yang, Zhenghao Naumenko, Konstantin CHIEN-CHING MA Chen, Yang |
關鍵字: | closed-form solution | elastic beam | peridynamics | 公開日期: | 1-九月-2023 | 卷: | 13 | 期: | 18 | 來源出版物: | Applied Sciences (Switzerland) | 摘要: | Peridynamics is a continuum theory that operates with non-local deformation measures as well as long-range internal force/moment interactions. The resulting equations are of the integral type, in contrast to the classical theory, which deals with differential equations. The aim of this paper is to analyze peridynamic governing equations for elastic beams. To this end, the strain energy density is formulated as a function of the non-local curvature. By applying the Lagrange principle, the peridynamic equations of motion are derived. Examples of non-local boundary conditions, including simple support, clamped edge, roller clamped edge, and free edge, are presented by introducing the interaction domain. Novel closed-form analytical solutions to integral equations are presented for beams with various boundary conditions, including clamped—simply supported, clamped–clamped, simply supported–roller-clamped, and clamped–roller-clamped beams. Furthermore, different types of loadings, including uniformly distributed load, concentrated force, and concentrated moment, are considered. The results are validated by comparing the derived solutions against solutions to the classical Bernoulli–Euler beam theory. A very good agreement between the non-local and the classical theories is observed for the case of the small horizon sizes, which shows the capability of the derived equations of motion and proposed boundary conditions. |
URI: | https://scholars.lib.ntu.edu.tw/handle/123456789/636528 | ISSN: | 2076-3417 | DOI: | 10.3390/app131810025 |
顯示於: | 機械工程學系 |
在 IR 系統中的文件,除了特別指名其著作權條款之外,均受到著作權保護,並且保留所有的權利。