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The parameterisation of redundancies in repetitive frameworks

The parameterisation of redundancies in repetitive frameworks
The parameterisation of redundancies in repetitive frameworks
The work presented in this thesis concerns the mathematical representation of redundancies within a pin-jointed repetitive structure. The analytical basis for the work is derived from ‘small deflection theory’.
Currently the analysis of redundancy has been restricted to the task of calculating its effect on member forces, and structural performance. While such work is important it does not offer the engineer and great insight into the phenomenon of redundancy. We will construct a representation of redundancy for repetitive structures that is paralleled by the underlying physical framework. In order to do this the mathematical space of redundancies is represented by a non-orthogonal basis set. Such a choice makes poor sense for numerical calculation, but offers the engineer insight into the way that forces due to lack of fit propagate through a lattice structure.
When modelling redundancy we find it desirable to identify localised substructures which contain redundancy. Then, due to the repetitive nature of the truss, similar substructures can be identified by translations. These substructures form the non-orthogonal basis for the redundancy of the truss. It is possible to identify these substructures systematically if we are given a ‘cell’ which is used to generate the truss.
To find the effect upon the members of lack of fit it is necessary to form difference equations involving the redundant substructures. For linear trusses the solution of such equations is straightforward. However for planar trusses we need to employ two difference parameters. Currently the methods of solution for such equations are poorly understood. However we can still use the formulation of these equations to construct measures, of sensitivity to lack of fit, for a truss.
Stinchcombe, D.
219990f9-9b4a-43d9-8ea1-a395b16d84d8
Stinchcombe, D.
219990f9-9b4a-43d9-8ea1-a395b16d84d8

Stinchcombe, D. (2002) The parameterisation of redundancies in repetitive frameworks. University of Southampton, School of Engineering Sciences, Doctoral Thesis.

Record type: Thesis (Doctoral)

Abstract

The work presented in this thesis concerns the mathematical representation of redundancies within a pin-jointed repetitive structure. The analytical basis for the work is derived from ‘small deflection theory’.
Currently the analysis of redundancy has been restricted to the task of calculating its effect on member forces, and structural performance. While such work is important it does not offer the engineer and great insight into the phenomenon of redundancy. We will construct a representation of redundancy for repetitive structures that is paralleled by the underlying physical framework. In order to do this the mathematical space of redundancies is represented by a non-orthogonal basis set. Such a choice makes poor sense for numerical calculation, but offers the engineer insight into the way that forces due to lack of fit propagate through a lattice structure.
When modelling redundancy we find it desirable to identify localised substructures which contain redundancy. Then, due to the repetitive nature of the truss, similar substructures can be identified by translations. These substructures form the non-orthogonal basis for the redundancy of the truss. It is possible to identify these substructures systematically if we are given a ‘cell’ which is used to generate the truss.
To find the effect upon the members of lack of fit it is necessary to form difference equations involving the redundant substructures. For linear trusses the solution of such equations is straightforward. However for planar trusses we need to employ two difference parameters. Currently the methods of solution for such equations are poorly understood. However we can still use the formulation of these equations to construct measures, of sensitivity to lack of fit, for a truss.

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Published date: 2002
Organisations: University of Southampton

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Local EPrints ID: 45908
URI: http://eprints.soton.ac.uk/id/eprint/45908
PURE UUID: befd0820-70b0-4500-a70b-ac149dc6728d

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Date deposited: 25 Apr 2007
Last modified: 13 Mar 2019 21:04

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