Solving Large-Deflection Problem of Spatial Beam with Circular Cross-Section Using an Optimization-Based Runge–Kutta Method

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2016-02-01 DOI:10.1515/ijnsns-2015-0053

Geng Li, J. Jia, Guimin Chen

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引用次数: 3

Abstract

Abstract Based on the Bernoulli–Euler beam theory, the nonlinear governing differential equations (GDEs) for a spatially deflected beam with circular cross-section are formulated, which are then reduced to first-order differential equations to be compatible with Runge–Kutta method. With the boundary conditions of a spatial beam, the governing equations are treated as an initial value problem (IVP) of ordinary differential equations. A Runge–Kutta method combined with an unconstrained optimization algorithm (RKUO) is presented to solve the IVP. The approach for determining the orientation of the cross-section plane at any position on the deflected beam is also provided. Finally, the comparison between the RKUO results and those achieved using nonlinear finite element (NFE) analysis and spatial pseudo-rigid-body model validate the accuracy and effectiveness of RKUO. The results also demonstrated the unique capabilities of RKUO to solve large spatial deflection problems that are outside the range of nonlinear finite element model.

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基于优化的龙格-库塔法求解圆形截面空间梁大挠度问题

摘要基于Bernoulli-Euler梁理论，建立了具有圆形截面的空间偏转梁的非线性控制微分方程，并将其简化为与龙格-库塔方法兼容的一阶微分方程。在空间梁的边界条件下，将控制方程视为常微分方程的初值问题。提出了一种结合无约束优化算法(RKUO)的龙格-库塔法求解IVP问题。还提供了用于确定在偏转梁上任何位置的横截面平面方向的方法。最后，将RKUO计算结果与非线性有限元分析和空间拟刚体模型计算结果进行了比较，验证了RKUO计算结果的准确性和有效性。结果还证明了RKUO解决非线性有限元模型范围之外的大空间挠度问题的独特能力。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.