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Analysis of cable structures by Newton's method Miller, Ronald Ian Spencer

Abstract

The analysis of structures which contain catenary cables is made difficult by the non-linear force-deformation relationships of the cables. For all but the smallest deflections it is not possible to linearize these relationships without causing significant inaccuracies. Newton's Method solves non-linear equations by solving a succession of linearized problems, the answer converging to the solution of the non-linear problem. Newton's Method so used to analyze cable-containing structures results in a succession of linear stiffness analysis problems. As a result, conventional stiffness analysis computer programs may be modified without great difficulty to solve cable structures by Newton's Method. The use of Newton's Method to solve cable structures forms the body of this thesis. The two basic innovations necessary, which are the provision of methods for calculating the end-forces of a cable in an arbitrary position, and for evaluating the stiffness matrix of a cable, are presented. Also discussed are the co-ordinate transformations necessary to describe the cable stiffness matrix and cable end forces in a Global Co-ordinate System. The virtues of the method are demonstrated in two example problems, and the theoretical basis for Newton's Method is examined. Finally, the value of the method presented is briefly discussed.

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