Use of load‐dependent vectors for dynamic analysis of large space structures

Abstract Structural models of large space structures have a substantial number of degrees of freedom (DOF) and possess semi‐positive‐definite stiffness matrices. The paper presents an efficient co‐ordinate reduction procedure for structural dynamic analysis of large space structures. The method is based on the superposition of load‐dependent Ritz vectors, which are computed in block form using a shifted stiffness matrix. Comparative transient dynamic analyses are performed on a 2803 DOF model of the space station Freedom using the load‐dependent method (LDM) and the mode‐displacement method (MDM) based on the superposition of eigenvectors. It is shown that the LDM is able to provide convergence of displacements with a small number of vectors. The acceleration response is found to be more sensitive to vector truncation than the displacement response. Error norms based on the representation of the dynamic load by the vector basis are developed to provide an indication of the effect of vector truncation on the structural response.