任意阶梁模型的直观推导

IF 12.2 1区 工程技术 Q1 MECHANICS
Hart Honickman
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引用次数: 0

摘要

本文提出了一种新的光束模型,该模型采用递归推导过程,使用户能够将控制微分方程的顺序设置为输入参数,而不需要特别的假设或方法。本文采用了一种新的运动变量、截面常数和截面函数系统,促进了高阶梁模型的发展,这些模型与经典梁模型(如Euler-Bernoulli梁理论和Timoshenko梁理论)保持了明确的哲学联系。目前的梁模型是一种等效单层梁模型,其中截面常数用于模拟梁的整体刚度特性,截面函数用于恢复位移、应变和应力的截面场。对几个实例梁进行了模型求解,并与有限元分析结果进行了比较。结果表明,该模型能较准确地预测每个实例梁的变形形状和应力场。本文还揭示了弹性势能的一个有趣的特性,该特性适用于任何由有限阶微分方程控制的一维梁模型。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
An Intuitive Derivation of Beam Models of Arbitrary Order
This article presents a new beam model that employs a recursive derivation procedure that enables the user to set the order of the governing differential equations as an input parameter, without the need for ad hoc assumptions or methodologies. This article employs a novel system of kinematic variables, section constants, and section functions that facilitate the development of higher-order beam models that retain a clear philosophical link to classical beam models such as Euler–Bernoulli beam theory and Timoshenko beam theory. The present beam model is a type of equivalent single layer beam model, wherein section constants are used to model the global stiffness characteristics of the beam, and section functions are used to recover sectional fields of displacements, strains, and stresses. The present beam model is solved for several example beams, and the results are compared to the results of finite element analyses. It is shown that the present beam model can accurately predict the deformed shapes and stress fields of each of the example beams. This article also reveals an interesting peculiarity of the elastic potential energy that pertains to any unidimensional beam model that is governed by differential equations that are of finite order.
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来源期刊
CiteScore
28.20
自引率
0.70%
发文量
13
审稿时长
>12 weeks
期刊介绍: Applied Mechanics Reviews (AMR) is an international review journal that serves as a premier venue for dissemination of material across all subdisciplines of applied mechanics and engineering science, including fluid and solid mechanics, heat transfer, dynamics and vibration, and applications.AMR provides an archival repository for state-of-the-art and retrospective survey articles and reviews of research areas and curricular developments. The journal invites commentary on research and education policy in different countries. The journal also invites original tutorial and educational material in applied mechanics targeting non-specialist audiences, including undergraduate and K-12 students.
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