Mixed Finite Element Formulation in Nonlinear Geometrical Analysis of Space Trusses and Application to Trusses With Member Length Imperfection

Space trusses usually have a significant number of elements. As a result, it is inevitable that some elements have imperfections. In this study, the authors proposed a mixed finite element method for nonlinear geometrical analysis of space trusses. The post-buckling behavior of space trusses with length imperfections was predicted using a code list written in the programming software. The numerical results indicate that when the length imperfection approaches zero, the results converge to those obtained in studies on standard trusses. A second approach based on the displacement model is also proposed, in which the Lagrange multiplier method is used to deal with the member length imperfection. The results show that the two approaches proposed by the authors are effective, in which the mix formulation based on the finite element model is superior to that based on the displacement model. These results verify the accuracy of the method. Based on the proposed method, the effects of imperfections in the element layers on the truss were studied. The results show that the imperfections in the top two element layers have the maximum influence on the limit load value, whereas the remaining layers have a negligible influence. The combination of the imperfect lengths of these two layers of elements can produce results in which the limit load value is much larger than in the case of a perfect system. Based on the obtained results, it is possible to provide a solution for improving the overall stability of truss structures by creating reasonable imperfections.