FORCE DENSITY METHOD BASED ON MULTI-COORDINATE-SYSTEM FOR FORM-FINDING OF TENSILE STRUCTURES

The traditional force density method can not be applied to the form-finding analysis of tensile structures with complex oblique boundaries as it is based on a unified global coordinate system. This paper presents a force density method based on multi-coordinate-system, similar to the theory of finite element method. Firstly, the local coordinate system is established for each node according to the boundary condition, and the force density reaction coefficient matrix for each element is derived according to the force vector decomposition. Then, the total force density reaction coefficient matrix is build up through the composition of the element matrixes, and the force equilibrium equation based on multi-coordinate-system is obtained from the force equilibrium between the reaction force and the load. Finally, the equilibrium equation is solved after amended by coordinate equations of the fixed nodes, and the initial equilibrium form for the tensile structure with oblique boundaries is obtained. A computer program of the proposed method is developed using Matlab, and three numerical examples are presented to illustrate the efficiency and robustness of this method.