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A finite element for 3‐D prestressed cablenets
Author(s) -
Gambhir M. L.,
de V. Batchelor Barrington
Publication year - 1977
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620111106
Subject(s) - finite element method , displacement (psychology) , displacement field , mathematics , mathematical analysis , boundary value problem , stiffness , geometry , basis (linear algebra) , structural engineering , engineering , psychology , psychotherapist
A finite element method is presented for the analysis of prestressed cablenets. The method is based on representing the prestressed cablenet as a series of finite length curved elements. The large displacement formulation used, enables the evaluation of the static and dynamic response of 3‐D cablenets. The development is general and the mathematical basis is explained at length. It is shown by means of comparison functions that for absolute continuity at nodes, a cubic displacement field is sufficient for the prediction of the first frequency of shallow nets. For globally deep networks the accuracy can be increased by employing a quintic displacement field for the normal component of displacement. The application of the proposed model to cable structures of shallow and also of deep global geometry, is presented. A variety of edge boundary shapes are employed in order to illustrate the versatility of the large displacement formulation. In all the example problems studied, gravity load has been taken as the initial load condition in calculating the equilibrium configuration. The stiffness and consistent mass matrices associated with the equation of motion are derived using Hamilton's variational principle.