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Characteristic solutions for the statics of repetitive beam-like trusses

Characteristic solutions for the statics of repetitive beam-like trusses
Characteristic solutions for the statics of repetitive beam-like trusses
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.
repetitive truss, static solution, transfer matrix
0020-7403
1363-1379
Karpov, E.G.
5479efe4-a7fa-49c0-9730-c1e6f0cc0d4f
Dorofeev, D.L.
049aefe5-d084-439b-b4c7-86c18b869005
Stephen, N.G.
af39d0e9-b190-421d-86fe-28b793d5bca3
Karpov, E.G.
5479efe4-a7fa-49c0-9730-c1e6f0cc0d4f
Dorofeev, D.L.
049aefe5-d084-439b-b4c7-86c18b869005
Stephen, N.G.
af39d0e9-b190-421d-86fe-28b793d5bca3

Karpov, E.G., Dorofeev, D.L. and Stephen, N.G. (2002) Characteristic solutions for the statics of repetitive beam-like trusses. International Journal of Mechanical Sciences, 44 (7), 1363-1379. (doi:10.1016/S0020-7403(02)00048-6).

Record type: Article

Abstract

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.

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Published date: 2002
Keywords: repetitive truss, static solution, transfer matrix

Identifiers

Local EPrints ID: 22071
URI: http://eprints.soton.ac.uk/id/eprint/22071
ISSN: 0020-7403
PURE UUID: 89cbc5cc-e91b-4b2f-9238-75e0067593b2

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Date deposited: 21 Mar 2006
Last modified: 25 Nov 2019 19:29

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