Exact Element Method For Analysis Of Cable Structures

This dissertation presents a new type of exact element method for analysis ofcable structures by new constructing exact element models and meticulously analyzesprimary problems of cable structures. In the method, all equations have accurateforms, calculation results with high accuracy can be checked and their speed ofconvergence is high by application of Newton's method. The study consists of fourmajor parts as follows.1. New exact element models are constructed. In these elements the basicunknowns are horizontal forces, distributed load densities and joint coordinates. Allexact elements ensure that equilibrium differential equations are satisfied exactlyeverywhere on the element, and can be classified as five groups based oncommonly-used load types.2. The proposed method solves the problems of form-finding, length calculation,load-analysis and displacement calculation related to load increment in elements.Numerical examples are presented to demonstrate the exactness, efficiency andapplicability of this method.3. General problems of cable structures are analyzed in the proposed method.The general exact elements are constructed by ordinary differential equation solversCOLSYS;A discrete approximation solution for simple membrane structures isproposed;Three typical form-solution problems defined under different knownconditions are analyzed and the exact algorithms are obtained;Problems of singularmatrixes are resolved when element tension forces vanish.4. A group of computation program PEECS is completed. The softwarepackages are convenient to operate and give accurate outcomes. Theoretical analysis and numerical results have shown some remarkableadvantages in the method, such as results with highly accurate results, steadily rapidconvergence, etc. In summary, the proposed method is worth further study andapplication.