The Application of Modal Coordinate Methods to Large Nonlinear Time- Dependent Problems

The research presented in this document demonstrates the application of a modal projection scheme based on inverse Lanczos iteration to a variety of problems in computational mechanics. All the cases considered are nonlinear and time-dependent, and Lanczos vectors are used to achieve coordinate reductions that substantially reduce the sizes of the underlying problems. Varying degrees of success are encountered in these reductions, depending upon numerical characteristics of the original Finite-Element models. A review of the theory of modal projection methods is presented in order to explain the results of the reduced coordinate approximations.