An efficient iteration procedure for form finding of slack cables under concentrated forces
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Department of Applied Mathematics at National Technical University Kiev Polytechnic Institute, Peremohystr, 37, Kyiv 03056, Ukraine
Department of Structural Engineering at University of Naples “Federico II”, via Claudio, 21-80125 Napoli, Italy
Submission date: 2021-10-11
Final revision date: 2022-02-07
Acceptance date: 2022-02-24
Publication date: 2022-06-30
Archives of Civil Engineering 2022;68(2):645-663
The goal of paper is the development and demonstration of efficiency of algorithm for form finding of a slack cable notwithstanding of the initial position chosen. This algorithm is based on product of two sets of coefficients, which restrict the rate of looking for cable geometry changes at each iteration. The first set restricts the maximum allowable change of absolute values of positions, angles and axial forces. The second set takes into account whether the process is the converging one (the signs of maximal change of parameters remain the same), so that it increases the allowable changes; or it is a diverging one, so that these changes are discarded. The proposed procedure is applied to two different methods of simple slack cable calculation under a number of concentrated forces. The first one is a typical finite element method, with the cable considered as consisting of number of straight elements, with unknown positions of their ends, and it is essentially an absolute coordinate method. The second method is a typical Irvine’s like analytical solution, which presents only two unknowns at the initial point of the cable; due to the peculiarity of implementation it is named here a shooting method. Convergence process is investigated for both solutions for arbitrary chosen, even very illogical initial positions for the ACM, and for angle and force at the left end for SM as well. Even if both methods provide the same correct convergent results, it is found that the ACM requires a much lower number of iterations.
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