Application Of A Two-Point Exponential Approximation Method In Optimizing Rotorcraft Airframe Structures

Rotorcraft Structures have to be designed for minimum weight while maintaining low vibration levels and high degree of structural integrity. In optimizing rotorcraft airframe structures with constraints on forced response and airframe natural frequencies, the cost of running the analyses and the reduction in the number of iterations become important considerations. Therefore, approximation methods are invariably employed to transform objective and constraint functions to an explicit, easier to evaluate form, using first order Taylor Series. This paper examines the application of a Two-Point Exponential approximation technique introduced by Fadel [Fadel, 1990] in comparison with the commonly used linear and hybrid first order methods in optimizing rotorcraft airframe structures. Adapting the first order approximation method using an exponent adjusted to better fit the functions, the Two-Point Exponential approxirnauon method uses previous analytical results to reduce the overall number of iterations needed to attain the optimum. This application is demonstrated through a structural optimization methodology applied to both the elastic-line model as well as the built up finite element model of a Bell AH-1G airframe structure. In this methodology, the NASTRAN based Direct Matrix Abstraction Programming language is used to compute sensitivity derivatives and motivate the optimizer, CONMIN, to produce the design change. By using this novel first-order approximation method, a reduction in total number of iterations and finite eleinent analyses needed to converge on the optimum is obtained.