The Vector Form Intrinsic Finite Element method and several other form-finding methods for general networks

Discrete networks is a kind of form-active structural system which actively change its shape under varying load conditions. And for this kind of structural system, form-finding is the initial and essential part in their design process. Before the computer age, people complete the form-finding process using physical models, while with the advances in computational techniques, the research has focused on the numerical form-finding methods since the 1960s. A brief discussion on several numerical formfinding methods is presented in this paper. Firstly, two relatively mature numerical method, Dynamic Relaxation method and Force Density method, are introduced conceptually. And then, a newly developed numerical method, the Vector Form Intrinsic Finite Element method, is presented in more detail. At last, with a replacement of the calculation of the internal force of the element which obeys the Hooke's Law by the product of the force density and the length of the element, two derived methods based on the above three methods are proposed in this paper. Moreover, several numerical examples of hanging networks are shown to illustrate the validity and characteristic of the VFIFE method and the two newly proposed derived methods