This paper is intended to summarise the actual work in the area of large deformations of tension systems. The previously conducted research adds significant contributions to the understanding of the response characteristics of pneumatics and suspended membranes with wrinkling allowed. Here the attention will be focused on the applications of the one-dimensional tensioned cable systems. Two- and three-dimensional tensile structures, will be forced to work with compressed members. Since cables can not transmit any compressive forces a verified numerical algorithm, based on the monitoring of the load displacement path is proposed. The special computer code NAFDEM (Nonlinear Analysis by Finite Difference and Element Methods) was adapted to solve undertaken highly nonlinear problems. Calculated results were verified numerically and compared with the solutions obtained by the numerical integration technique.
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