Stability of Heterogeneous Beams with Three Supports—Solutions Using Integral Equations

IF 12.2 1区 工程技术 Q1 MECHANICS
L. Kiss, A. Messaoudi, G. Szeidl
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引用次数: 0

Abstract

It is our main objective to find the critical load for three beams with cross sectional heterogeneity. Each beam has three supports, of which the intermediate one is a spring support. Determination of the critical load for these beams leads to three point boundary value problems (BVPs) associated with homogeneous boundary conditions—the mentioned BVPs constitute three eigenvalue problems. They are solved by using a novel solution strategy based on the Green functions that belong to these BVPs: the eigenvalue problems established for the critical load are transformed into eigenvalue problems governed by homogeneous Fredholm integral equations with kernels that can be given in closed forms provided that the Green function of each BVP is known. Then the eigenvalue problems governed by the Fredholm integral equations can be manipulated into algebraic eigenvalue problems solved numerically by using effective algorithms. It is an advantage of the way we attack these problems that the formalism established and the results obtained remain valid for homogeneous beams as well. The numerical results for the critical forces can be applied to solve some stability problems in the engineering practice.
三支承非均质梁的稳定性——用积分方程求解
我们的主要目标是找出具有截面非均匀性的三梁的临界载荷。每根梁有三个支撑物,中间的是弹簧支撑物。这些梁的临界载荷的确定导致了与齐次边界条件相关的三点边值问题(BVPs)——上述BVPs构成了三个特征值问题。通过使用一种基于属于这些BVP的Green函数的新颖解决策略来解决这些问题:为临界负荷建立的特征值问题被转换为由具有核的齐次Fredholm积分方程控制的特征值问题,该方程可以以封闭形式给出,只要每个BVP的Green函数是已知的。然后利用有效的算法将Fredholm积分方程控制的特征值问题转化为数值求解的代数特征值问题。我们处理这些问题的方法的一个优点是,所建立的形式主义和所得到的结果对均质梁也是有效的。临界力的数值计算结果可用于解决工程实践中的一些稳定性问题。
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
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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