## 1 Introduction  
Cable is a general name for structural elements with a high ratio of length per diameter. This special geometry makes cables flexible elements in transverse direction. In other words, a cable has almost zero bending stiffness compared to its tension stiffness. It can be formed by many different materials such as steel wires or fibers or a combination of both. These geometric and structural properties make cable indispensable elements for many structures. Cables are widely used in civil engineering structures (e.g., tele skis, prestressing and post-tensioning process, guyed towers, cable stayed bridges, transmission lines, mooring lines) as the main component of them. Therefore, an accurate analysis of cables is very important for safer civil engineering structures. Analysis of cables has been the interest of many researchers. Different analysis methods have been proposed to simulate highly nonlinear cable elements. The nonlinearity is mostly geometric due to a cable's structural properties. Nonlinearity of the cable was directly considered in various studies by using the finite element method. For example, a method called a method of imaginary reactions, which considers the geometric nonlinearity, developed by [1]. The same method was also used to solve the issue of a cable having different support conditions in [2]. Besides, closed-form solutions were proposed which consider the nonlinearity of the cable by assuming a deflected shape [3]. For an example of closed-form solutions, the nonlinearity was presupposed with an equivalent [PERSON]'s modulus approach [4]. On the other hand, linear shape assumptions were also proposed [5]. This type of solution assumes the cable element is weightless, thus, the cable behaves like a structural bar element. Instead of closed-form solutions and linear approaches, different finite element methods have been proposed. Among the finite element models, a two-node cable element was used in different studies. In [1, 2], an initial reaction was assumed to find the geometry of cable and reaction was changed until the boundary condition of the problem, which is the real form of the catenary cable, was satisfied. The authors in [6] carried out geometric nonlinear analysis of cables by using a two-node element with a displacement control method. In [7], a simple two-node straight line cable element was proposed and compared with a multi-node finite element model, which was also the topic of [8]. Besides finite element models including a catenary cable element were also used for dynamic analysis in [9; 10]. In addition, two different catenary cable elements, named as continuous and discrete, were proposed [11]. In a further research of [PERSON] [12], finite element method combined with contact mechanics was used to model multi-segment cables which are in contact with a truss system. Although studies about cables have been mostly performed by mesh-based methods, meshless methods were also used. A solution technique using the element-free Galerkin (EFG) method was proposed for cable reinforced membrane structures [13]. In that study, a penalty method was used to model the sliding between cable and membrane. In [14], an analysis about overhead power line cables was carried out. In the study, a meshless finite difference method (MFDM) was proposed to simulate cables. In another study, [PERSON] and [PERSON] proposed a meshless method for the model of extensible slender rods which can be regarded as a cable with a small bending stiffness [15]. The method was named as local radial point interpolation method (LRPIM). After the buckling of the column, catenary cable and an entangled cable were solved as validation cases. Among the meshless methods, smoothed particle hydrodynamics (SPH) is one of the most popular ones. SPH was originally introduced by [PERSON] [16] and [PERSON] [17] for astrophysical problems.