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.