Nonlinear dynamic reanalysis of structures by combined approximations

A major difficulty in non-linear dynamic reanalysis by mode superposition is the need to repeat the eigenproblem solutions. This study shows how the combined approximations approach can be used to overcome this difficulty. The approach is based on the integration of several concepts and methods, including matrix factorization, series expansion and reduced basis. The advantage is that efficient local approximations and accurate global approximations are combined to achieve an effective solution procedure. In the procedure developed for material non-linearity, improved basis vectors are introduced using the concepts of Gram–Schmidt orthogonalizations and shifts. Numerical examples show that accurate approximations are achieved efficiently for very large changes in the design variables.