Reanalysis and sensitivity reanalysis by combined approximations

One of the main obstacles in the solution of structural optimization problems is the need to repeat solutions of the analysis and sensitivity analysis equations. In large-scale structures, having complex analysis models, the computational effort may become prohibitive. To alleviate this difficulty a general approach for repeated analysis and repeated sensitivity analysis, called combined approximations, was developed during the last 15 years. The solution is based on the integration of several algorithms and methods. As a result, accurate results can be achieved efficiently. In previous studies, solution procedures for various particular problems were developed. This article summarizes the various formulations and solution procedures for reanalysis and sensitivity reanalysis of linear, nonlinear, static and dynamic systems. It is shown that the various solution procedures are based on applications of similar basic algorithms. Numerical examples demonstrate the efficiency of the calculations and the accuracy of the results.