Continuum Sensitivity Analysis
Motivation
Multidisciplinary design analysis and optimization (MDAO) has become increasingly popular in recent decades. Some reasons for this are the current transition from metals to composites and the growing demand for unmanned flight capabilities. The result is a very large design space of novel aircraft configurations. Modeling the physics of many of these novel configurations requires multidisciplinary analysis. For instance, high aspect ratio wings, which are flexible, require aeroelastic analysis to account for the fluid-structure interaction on the surface of the wing.
There is high demand for development of computational design environments capable of MDAO. Such an environment may provide the ability to design an aircraft that can perform unique missions very efficiently. Gradient based optimization methods are commonly used to explore such large design spaces. Sensitivity analysis is the algorithmic step which provides the required design gradients. In short, the design gradients point the optimization algorithm in the direction of optimality.
The most common way to calculate design sensitivities is through approximate or numerical methods, such as the finite difference and complex step methods. These methods can be computationally expensive, inaccurate, and/or infeasible to implement. Although, analytic (continuum) sensitivity methods can be more difficult to formulate and implement, they are typically more accurate and computationally efficient.
Objectives
The current body of literature contains very few implementations of continuum sensitivity methods with multidisciplinary analysis. Of particular interest is to develop a continuum sensitivity capability for nonlinear transient gust analysis of an aircraft with rigid body motion.
Most commercial codes that are used by industry leaders either provide no means or very limited means to calculate analytic sensitivities. Therefore, another research objective is to develop a general continuum sensitivity approach that is easy to formulate and implement for 'black box' analysis tools. Such an approach would enable the inclusion of commercial codes in an MDAO environment and drastically simplify the formulation and calculation of analytic design sensitivities.
Progress
To date a general formulation of the local continuum sensitivity method has been developed that can be implemented for displacement based finite element analysis. The approach makes use of spatial gradient reconstruction (SGR) in order to accurately formulate the sensitivity boundary conditions. The method has been successfully demonstrated on 1-D and 2-D nonlinear transient beam models, as well as linear static bending of rectangular plates and a beam-stiffened rectangular plates. For these rather simple models, using this local continuum shape sensitivity method with SGR is an accurate and efficient way to calculate design sensitivities. Future work will require further development of the method and evaluating its performance for more complex structures. In addition, the method will be extended to sensitivity analysis of aerodynamic forces. For more details regarding derivation and implementation, please see the following publications.
There is high demand for development of computational design environments capable of MDAO. Such an environment may provide the ability to design an aircraft that can perform unique missions very efficiently. Gradient based optimization methods are commonly used to explore such large design spaces. Sensitivity analysis is the algorithmic step which provides the required design gradients. In short, the design gradients point the optimization algorithm in the direction of optimality.
The most common way to calculate design sensitivities is through approximate or numerical methods, such as the finite difference and complex step methods. These methods can be computationally expensive, inaccurate, and/or infeasible to implement. Although, analytic (continuum) sensitivity methods can be more difficult to formulate and implement, they are typically more accurate and computationally efficient.
Objectives
The current body of literature contains very few implementations of continuum sensitivity methods with multidisciplinary analysis. Of particular interest is to develop a continuum sensitivity capability for nonlinear transient gust analysis of an aircraft with rigid body motion.
Most commercial codes that are used by industry leaders either provide no means or very limited means to calculate analytic sensitivities. Therefore, another research objective is to develop a general continuum sensitivity approach that is easy to formulate and implement for 'black box' analysis tools. Such an approach would enable the inclusion of commercial codes in an MDAO environment and drastically simplify the formulation and calculation of analytic design sensitivities.
Progress
To date a general formulation of the local continuum sensitivity method has been developed that can be implemented for displacement based finite element analysis. The approach makes use of spatial gradient reconstruction (SGR) in order to accurately formulate the sensitivity boundary conditions. The method has been successfully demonstrated on 1-D and 2-D nonlinear transient beam models, as well as linear static bending of rectangular plates and a beam-stiffened rectangular plates. For these rather simple models, using this local continuum shape sensitivity method with SGR is an accurate and efficient way to calculate design sensitivities. Future work will require further development of the method and evaluating its performance for more complex structures. In addition, the method will be extended to sensitivity analysis of aerodynamic forces. For more details regarding derivation and implementation, please see the following publications.