Arch Appl Mech https://doi.org/10.1007/s00419-018-1489-0 ORIGINAL Damir Sedlar · Zeljan Lozina · Andjela Bartulovic Nonlinear static isogeometric analysis of cable structures Received: 5 February 2018 / Accepted: 5 November 2018 © Springer-Verlag GmbH Germany, part of Springer Nature 2018 Abstract The purpose of this paper is to develop and evaluate the efficiency of the cable element based on the Lagrangian formulation using the Isogeometric analysis (IGA) approach. Two Lagrangian formulations (Total Lagrangian and Updated Lagrangian) have been adopted in the static analysis of nonlinear behaviour of the cable structures. The same basis functions are used to represent the geometry of the cable as well as the cable displacement field. These two formulations are tested on benchmark examples and compared to each other and to the existing analysis methods. The influence of a different number of elements, the order of polynomials and the number of numerical integration points was examined. Compared to the other method, the obtained results in benchmark examples indicate the capability and accuracy of the presented approach. This paper demonstrates successful IGA implementation of the Lagrangian formulation for the nonlinear analysis of cable structures. Keywords Cable element · Lagrangian formulation · Nonlinear isogeometric analysis · Static analysis 1 Introduction Cable structures have been extensively used, and still are, in numerous civil and mechanical structures. Main reasons for their widespread use are simplicity, elasticity, economy and the ability to cover large distances. However, due to their nonlinear behaviour, extra caution is required when performing the structural analysis of cable structures. Their nonlinearity is primarily geometrical, and occurs as a result of large displacements. Numerous researchers have analysed the behaviour of the cable structures, and the research can be divided into two main approaches: analytical approach [1, 6, 14, 16, 26] and finite element approach [5, 8, 9, 17]. The analytical approach is based on the elastic catenary expressions. Most commonly, a single two-node element is used to model the cable. This element is suitable to model the cable with a small sag and a large sag. In this way, the nonlinear equations system was obtained and is solved by the iterative incremental scheme. The solving of this nonlinear system shows numerical instability and may yield unreliable results. The finite element approach is based on the interpolation functions which are used to describe displacements. The truss elements [9, 17] and the multi-node curved elements [5, 8] are commonly used. For the cable with a large sag, it is necessary to use a large number of elements which represent computational costs and may cause a numerical and convergence problem. Recently, the isogeometric analysis has been introduced into the solving of the structural tasks [7]. Com- pared to the finite element analysis, the isogeometric analysis has several advantages, of which the most D. Sedlar (B ) · Z. Lozina · A. Bartulovic University of Split, Faculty of Electrical Engineering, Mechanical Engineering and Naval Architecture, R. boskovica 32, 21000 Split, Croatia E-mail: dsedlar@fesb.hr Tel.: +385-21-305967 Fax: +385-21-305776