Characteristic solutions for the statics of repetitive beam-like trusses
Characteristic solutions for the statics of repetitive beam-like trusses
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DOI：
10.1016/s0020-7403(02)00048-6
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发表时间：
2002-07-01
影响因子：
7.3
通讯作者：
Stephen, NG
中科院分区：
文献类型：
--
作者：
Karpov, EG;Dorofeev, DL;Stephen, NG
本文主要研究两个问题：(1)将端部荷载作用下重复铰接梁桁架静力响应的函数解分解为初等函数模态谱；(2)最后进行数学分类。考虑具有代表性的子结构的刚度矩阵，将静力学控制有限差分方程写成单矩阵形式。结果表明，其通解只能由2R个独立模态张成，其中R为桁架内典型节点模式的自由度数。这些模式主要分为两类：转移和本地化。利用传输矩阵的Jordan分解方法，得到了一组唯一的“正则”传输解。同时，提出了一种构造一类桁架传递矩阵的方法。正则模可以进一步细分为指数模、多项式模和拟多项式模。2R正则转移和局域模态的完备集唯一地表示了结构的基本响应行为，并为静力解的特征（非调和）展开提供了基础。考虑了几个说明性的例子。(C) 2002 Elsevier Science Ltd.版权所有。
This paper concerns two major points: (1) decomposition of functional solutions for the static response of repetitive pin-jointed beam trusses under end loadings into spectrum of elementary function modes; and (2) a mathematical classification of the last. The governing finite difference equation of statics is written as a single matrix form by considering the stiffness matrix of a representative substructure. It is shown that its general solution can be spanned by only 2R individual modes, where R is the number of degrees of freedom for a typical nodal pattern inside the truss. These modes are divided into two primary classes: transfer and localised. A unique set of "canonical" transfer solutions is found by a method based on Jordan decomposition of the transfer matrix. Also, a technique of constructing transfer matrices for a wide class of trusses is presented. The canonical modes can be further subclassified as exponential, polynomial and quasi-polynomial. The complete set of 2R canonical transfer and localised modes uniquely represents the basic structural response behaviour, and gives a basis for the characteristic (non-harmonic) expansion of static solutions. Several illustrative examples are considered. (C) 2002 Elsevier Science Ltd. All rights reserved.