Local continuum shape sensitivity with spatial gradient reconstruction

Utilizing gradient-based optimization for large scale, multidisciplinary design problems requires accurate and efficient sensitivity or design derivative analysis. In general, numerical sensitivity methods, such as the finite difference method, are easy to implement but can be computationally expensive and inaccurate. In contrast, analytic sensitivity methods, such as the discrete and continuum methods, are highly accurate but can be very difficult, if not infeasible, to implement. A popular compromise is the semi-analytic method, but it too can be highly inaccurate when computing shape design derivatives. Presented here is an alternative method, which is easy to implement and can be as accurate as conventional analytic sensitivity methods. In this paper a general local continuum shape sensitivity method with spatial gradient reconstruction (SGR) is formulated. It is demonstrated that SGR, a numerical technique, can be used to solve the continuous sensitivity equations (CSEs) in a non-intrusive manner. The method is used to compute design derivatives for a variety of applications, including linear static beam bending, linear transient gust analysis of a 2-D beam structure, linear static bending of rectangular plates, and linear static bending of a beam-stiffened plate. Analysis is conducted with Nastran, and both displacement and stress design derivative solutions are presented. For each example the design derivatives are validated with either analytic or finite difference solutions.