The modified force density method for form-finding of cable net structure

Abstract

Form-finding is crucial for the design of typical cable net structures. Based on the original basic force density method, a modified force density method utilizing the concept of relation matrix is proposed in this paper. The modified method realizes the establishment of a clear correspondence between members and nodes of cable net structures. On the basis of the relation matrix, the find function is introduced, and the calculation formula of the modified branch-node matrix is derived. Meanwhile, the corresponding analysis steps and calculation process are given. The modified method is verified by the analysis of representative structural forms. The results show that for the saddle-shaped orthogonal cable net structure, the outcomes obtained from the modified force density method highly agree with the theoretical values, providing preliminary verification of the method's effectiveness. For single-layer spoke cable net structures, the relative error between the results calculated by the modified force density method and the numerical solution is approximately 5 %. The results of both methods are relatively consistent, and the relative error varies in relation to the ratio of inner ring cable force density to radial cable force density. For circular single-layer crossed cable net structure without inner ring, the results of the modified force density method are very close to the numerical solution. The maximum relative error between the two is 6.95 %, and the accuracy is higher than that of the nonlinear finite element method. The outcome of this research demonstrates the accuracy of the modified force density method and its effective application in the form-finding of actual cable net structures.