Evolutionary Multicriteria Design Optimization of Integrally Stiffened Airframe Structures

Abstract

In industrial practice, innovative structural aircraft design is, on the one hand, driven by several design criteria like static stress, damage tolerance, and stability, and, on the other hand, by new manufacturing methods and materials, which promise beneficial effects on manufacturing costs and weight. Published optimization approaches are mostly based on pure static stress criteria, albeit the important influence of stability and damage tolerance is neglected. This assumption is perilous but significantly simplifies the investigation. The investigation of unconventional designs under consideration of the preceding criteria is challenging because no analytical or handbook solutions are available. This paper introduces an optimization approach based on an evolution strategy, which incorporates multiple criteria by using nonlinear finite-element analyses for stability and a set of linear analyses for damage-tolerance evaluation. To demonstrate the approach, one design investigation is presented for the window area of a generic aircraft fuselage. The definition of dimensions and the choice of an ideal topology define the optimization problem. The chosen fuselage structure uses an integral design with an innovative combination of window and circumferential frame and is investigated with regard to three load cases that represent relevant in-flight conditions derived from global finite-element analyses. NomenclatureA, B, k, C f , n f , K c = Forman coefficients a = crack length a m , b m , m = shape coefficients of the mass mapping function a u , b u = shape coefficients of the deflection mapping function a SIF , b SIF = shape coefficients of the fatigue-response mapping function C feas , D feas = coefficients of the failure mapping function, feasible state C limit , D limit = coefficients of the failure mapping function, limit state d i = design response i E = Young's modulus G I = energy release rate, mode I G II = energy release rate, mode II g = gravitational acceleration K = stress intensity factor K th = stress intensity factor, threshold value N = load cycle n = load factor p = pressure R = stress ratio t = thickness u = longitudinal displacements at the crack surface v = normal displacements at the crack surface w i = weight factor i X i = longitudinal force at the crack tip Y i = normal force at the crack tip d = exponent of the deflection mapping function SIF = exponent of the fatigue-response mapping function = life span = offspring per generation = population size = Poisson's ratio = density

Stochastic analysis and optimum design of structures subjected to fracture

“…Bureerat and Limtragool (2008) presented the application of simulated annealing for solving structural topology optimization, while a numerical technique termed as multiresolution design variables was proposed as a numerical tool to enhance the searching performance. Hansen et al (2008) introduced an optimization approach based on an evolution strategy that incorporates multiple criteria by using nonlinear finite-element analyses for stability and a set of linear analyses for damage-tolerance evaluation, the applicability of the approach was presented for the window area of a generic aircraft fuselage. Kaveh and Shahrouzi (2008) proposed a hybrid strategy combining indirect information share in ant systems with direct constructive genetic search, for this purpose some proper coding techniques were employed to enable testing the method with various sets of control parameters.…”