Efficient dynamic reanalysis of structures

The combined approximations approach developed recently is based on the integration of several concepts and methods, including series expansion, reduced basis, matrix factorization and Gram-Schmidt orthogonalization. The advantage is that efficient local approximations (series expansion) and accurate global approximations (the reduced basis method) are combined to achieve an effective solution procedure. Originally, this approach was developed for linear static reanalysis. This study shows how combined approximations can improve the solution efficiency of dynamic reanalysis problems. Some solution procedures are developed, and typical numerical examples demonstrate the quality of the results. It is shown that high accuracy is achieved efficiently for very large changes in the design.