COMMUNICATIONS IN NUMERICAL zyxwvut METHODS IN ENGINEERING, VOl. zyxw 9, 897-908 (1 993) zyx USE OF LOAD-DEPENDENT VECTORS FOR DYNAMIC ANALYSIS OF LARGE SPACE STRUCTURES J. M. RICLES zyxwvu Department of Civil Engineering, Lehigh University I I7 zyxwvu A TLSS Drive, H Building, Bethlehem, Pennsylvania 18015. zyxwvu U. S. A. AND P. LEGER Department of Civil Engineering, k o l e Polytechnique, Montreal University Campus, P.O. Box 6079, Station A, Montreal, Quebec, Canada H3C 3A7 SUMMARY 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. INTRODUCTION Finite-element dynamic analysis of complex structural systems such as the space shuttle and the planned space station Freedom requires detailed structural models with a large number of degrees of freedom (DOF). The standard procedure for performing a transient dynamic analysis of these models utilizes the mode-displacement method (MDM) based on the superposition of eigenvectors. For structural models with large numbers of DOF, the eigenvector basis is generally truncated because of the enormous computational effort and time required to calculate all eigenvectors and eigenvalues of the finite-element model. The constraint of having to use a truncated modal basis, and the fact that the computational effort to calculate vibration characteristics based on an ‘exact’ eigensolution is costly compared to Ritz-based methods gives motivation and justification for considering other procedures for generating an orthogonal vector basis suitable for dynamic response computations. A new method of dynamic analysis for structural systems subjected to fixed spatial distribution of the dynamic load was introduced by Wilson et al. 2*3 as an economic alternative to classical mode-superposition techniques. The ‘load-dependent’ method (LDM) is based on a transformation to a reduced system of generalized Ritz co-ordinates using load-dependent transformation vectors generated from the specified spatial distribution of the dynamic loads. 0748-8025/93/ 110897-12$11 .oO zyxwvut 0 1993 by John Wiley zyxwvut & Sons, Ltd. Received 20 January 1992 Revised I0 January 1993