Local Continuum Sensitivity Method for Shape Design Derivatives Using Spatial Gradient Reconstruction
Novel aircraft configurations tend to be sized by physical phenomena that are largely neglected during conventional fixed wing aircraft design. High-fidelity fluid-structure interaction that accurately models geometric nonlinerity during a transient aeroelastic gust response is critical for sizing the aircraft configuration early in the design process. The primary motivation of this research is to develop a continuum shape sensitivity method that can support gradient-based design optimization of practical and multidisciplinary high-fidelity analyses. A local continuum sensitivity analysis (CSA) that utilizes spatial gradient reconstruction (SGR) and avoids mesh sensitivities is presented for shape design derivative calculations. Current design sensitivity analysis (DSA) methods have shortcomings regarding accuracy, efficiency, and ease of implementation. The local CSA method with SGR is a nonintrusive and element agnostic method that can be used with black box analysis tools, making it relatively easy to implement. Furthermore, it overcomes many of the accuracy issues documented in the current literature. The method is developed to compute design derivatives for a variety of applications, including linear and nonlinear static beam bending, linear and nonlinear transient gust analysis of a 2-D beam structure, linear and nonlinear static bending of rectangular plates, linear and nonlinear static bending of a beam-stiffened plate, and two-dimensional potential flow. The analyses are conducted using general purpose codes. For each example the design derivatives are validated with either analytic or finite difference solutions and practical numerical and modeling considerations are discussed. The local continuum shape sensitivity method with spatial gradient reconstruction is an accurate analytic design sensitivity method that is amenable to general purpose codes and black box tools.