1 A NATURAL SET OF EIGENVECTORS FOR THE DYNAMIC ANALYSIS OF STRUCTURAL SYSTEMS

A general numerical algorithm is presented that produces a complete set of orthogonal vectors that can be used to reduce the number of unknown displacements required to produce an accurate analysis of structures subjected to both static and dynamic loads. For any specified type of loading error indicators are calculated and the generation of the vectors can be terminated automatically; hence, the engineer/program-user need only to specify the error tolerance and not the number of vectors requested. Therefore, an optimum number of vectors are calculated and there is no need to add approximate static load corrections to the solution or to be concerned about missing mass in a dynamic response analysis. The new algorithm generates a different set of vectors for different types of spatial loading acting on the structure. Thus, the vectors generated are a set of Natural Load Dependent, NLD, vectors for the problem to be solved. A special application of the NLD vector algorithm, using random load vectors and iteration, produces exacts dynamic eigenvectors, rigid-body modes and static elastic modes for any structural system. However, the use of these exact eigenvectors in a dynamic response analysis may require a very large number of vectors to produce the same accuracy as obtained by the use of a small number of NLD vectors. The NLD vectors are always a linear combination of the exact eigenvectors; however, eigenvectors are not calculated unless they are required to obtain an accurate solution. The algorithm has been applied to the dynamic analysis of many large structural systems with over 50,000 degrees-of-freedom. The method has proven to be very robust, numerically efficient and accurate