Static Reanalysis

It has been noted that the overall effectiveness of reanalysis depends to a large extent on the numerical procedures used for the solution of the equilibrium equations. The accuracy of the analysis can, in general, be improved if a more refined model is used. Because of the tendency to employ more and more refined models to approximate the actual structure, the cost of an analysis and its practical feasibility depend to a considerable degree on the algorithms available for the solution of the resulting equations. The time required for solving the equilibrium equations of large-scale systems can be a high percentage of the total solution time, particularly in nonlinear analysis, when the solution must be repeated many times. An analysis may not be possible if the solution procedures are too costly or unstable.

In this section approximate solution procedures, for static analysis and reanalysis by the CA approach, are developed. The solution is based on results of a single exact analysis and the integration of several concepts and methods, most of them presented in previous chapters. These include matrix factorization, series expansion, reduced basis, and Gram-Schmidt orthogonalization. In the approach presented, the terms of the binomial series are used as high quality basis vectors in a reduced basis expression. 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. Due to the nature of the selected basis vectors, high accuracy can be achieved by considering only a few vectors. Yet, the accuracy of the results can be improved at the expense of more computational effort, by considering additional vectors.