Michael Bogomolni

Efficient Finite Difference Design Sensitivities

The problem considered in this study is to evaluate efficiently displacement derivatives using global finite differences. Given the displacements for an initial design, the displacements for various modified designs are evaluated by the recently developed combined approximations method. Calculations of finite difference sensitivity coefficients are demonstrated for static problems and eigenproblems. The presented solution procedure is easy to implement, efficient, and can be used to calculate derivatives for various designs where the exact displacements are not known. Some numerical examples show that the accuracy of the results is similar to the accuracy obtained by finite difference calculations based on exact analysis.

Efficient structural optimization using reanalysis and sensitivity reanalysis

Optimization of large-scale structures using conventional formulations often involves much computational effort. Repeated solutions of the analysis and sensitivity analysis equations usually require most of this effort. The computational cost may become prohibitive in large-scale structures having complex analysis models. To alleviate this difficulty, various procedures are integrated in this study into a general optimization approach. The approach is suitable for different classes of response types and optimization methods, including linear and non-linear response; static and dynamic response; direct and gradient optimization methods. Combined approximations are used for reanalysis and repeated sensitivity analysis. The advantage is that the efficiency of local approximations and the improved quality of global approximations are combined to obtain effective solution procedures. Approximate reanalysis and finite-difference sensitivity reanalysis are considered for each intermediate design during the solution process. Reductions in the computational effort may reach several orders of magnitude. Typical numerical examples show that the results achieved by the approach presented are similar to those obtained by exact reanalysis and sensitivity analysis.

Efficient procedures for repeated calculations of structural sensitivities

Procedures for sensitivity analysis of large-scale structures are presented. Analytical derivatives are evaluated for multiple modified designs where the exact response is unknown. Approximation concepts are used to improve the efficiency and the ease-of-implementation of the calculations. The procedures presented are based on explicit approximations of the response and the combined approximations approach, which is further developed to improve the efficiency of the calculations and the accuracy of the results. Considering sensitivities of static problems and eigenproblems, basis vectors are calculated for a limited number of design points, and then used to evaluate sensitivities for various modified designs. The procedures presented are compared with exact analytical sensitivities. It is shown that accurate results can be achieved with significant reductions in the computational effort.