Accuracy and implementation of refined second order semi-analytical designsensitivities

Accurate second order design sensitivities of finite element responses play an important role in the optimization process. The semi-analytical (SA) me thod is often used to compute these sensitivities. A disadvantage of the SA method is that severe inaccuracies may be observed for shape design variab les. To improve the accuracy of the SA method a refined second order method has been proposed and implemented The improvement has been based on the co nsistency conditions for rigid body modes and their derivatives. Both analy tical and numerical examples indicate a considerable accuracy improvement o f the refined method over the standard SA method.