This paper is a continuation of part I – Theory and verification and presents some examples of application of the Extended Force Density Method. This method allows for form-finding of cable nets under self-weight and is based on the catenary cable element which assures high accuracy of the results and enables solving wide range of problems. Some essentials of the method are highlighted in this article. A computer program UC-Form was developed in order to perform the calculations and graphically present the results. Main advantages and features of the program are presented in this paper. Subsequently the program is used to perform calculations for a few practical examples with taut and slack cables. Input data is provided in order to enable reproducing calculations by other researchers. The outcomes are shown in the paper and prove that EFDM is an efficient tool for analysis of behaviour of cable nets under self-weight in different configurations.

Tensile structures in general, achieve their load-carrying capability only after the process of initial form-finding. From the mechanical point of view, this process can be considered as a problem in statics. As cable systems are close siblings of trusses (cables, however, can carry tensile forces only), in our study we refer to equilibrium equation similar to those known from the theory of the latter. In particular, the paper regards designing pre-tensioned cable systems, with a goal to make them kinematically stable and such that the weight of so designed system is lowest possible. Unlike in typical topology optimization problems, our goal is not to optimize the structural layout against a particular applied load. However, our method uses much the same pattern. First, we formulate the variational problem of form-finding and next we describe the corresponding iterative numerical procedure for determining the optimum location of nodes of the cable system mesh. We base our study on the concept of force density which is a ratio of an axial force in cable segment to its length.

This paper presents the Extended Force Density Method which allows for form-finding of cable nets under self-weight. Formulation of the method is based on the curved catenary cable element which assures high accuracy of the results and enables solving wide range of problems. Essential rules of the Force Density Method (FDM) are summarized in the paper. Some well-known formula describing behaviour of a catenary cable element under self-weight are given.Next the improved variant ofFDMwith all the theoretical and numerical details is introduced. Iterative procedure for solving nonlinear equations is described. Finally a simple verification example proves correctness of methods assumptions. Two further analyses of parameters crucial for correct use of Extended Force Density Method (EFDM) are presented in order to indicate their initial values for other numerical examples. Accuracy of the results are also investigated. A computer program UC-Form was developed in order to perform the calculations and graphically present the results. Some examples of use of EFDM are presented in details in Part II – Examples of application.