Development and Application of a Flexibility-Based Method for Multi-Scale Design Sergio Carlos, 1 Kaarthic Madhavan, 1 Gaurav Gupta, 1 Darren Keese, 1 Uma Maheshwaraa, 1 and Carolyn Conner Seepersad. 2 Mechanical Engineering Department, The University of Texas at Austin, Austin, TX 78712 A flexibility-based approach is presented for the solution of multiscale engineering design problems. The methodology is aimed at enhancing distribution of design activities and reducing the number of costly iterations between multiple engineering teams operating on different scales. This goal is achieved by exchanging flexible families of solutions rather than single point solutions, thereby reducing the need for iteration between scales. The effectiveness of the approach is illustrated by a two-level problem involving the system-level design of a gas turbine engine and the mesoscale design of cellular material for the combustor liner. A multi-objective design problem formulation is used to obtain families of prismatic cellular materials that embody a range of tradeoffs between conflicting thermal and structural performance objectives. The results are communicated to the system level and a solution is chosen to meet system-level goals as closely as possible. The effectiveness of the method is evaluated by comparison with a benchmark integrated design method. The approach facilitates identification of satisfactory or nearly optimal solutions quickly and with minimal iterations between scales. Nomenclature c p = Air specific heat (J/kgK) CPR = Compressor pressure ratio D i = Inner combustor liner diameter (m) D o = Outer combustor liner diameter (m) F thrust = Engine net thrust (N) γ = Air specific heat ratio h PR = Enthalpy of reaction (J/kgK) LHV = Lower heating value of fuel (J/kg) L min = Minimum combustor length m = Total mass m  = Air mass flow rate (kg/s) m fuel = Fuel mass flow rate (kg/s) η D = Diffuser efficiency η C = Compressor efficiency η T = Turbine efficiency η N = Nozzle efficiency η th = Thermal efficiency η p = Propulsive efficiency η o = Overall efficiency P i = Pressure at state i (Pa) T i = Temperature at state i (Pa) T lo = Liner exit temperature (K) T a = Ambient air temperature (K) υ = Total volume V in = Air speed (m/s) V liner = Volume of material in liner (m 3 ) C W  = Power in shaft (W) I. Introduction ULTISCALE design is a field of simulation-based design in which computational models and simulations, coupled with systems-based design methods, are used to solve design problems that incorporate a number of scales, from material microstructures to overall system configuration. Materials design—the simultaneous design of M American Institute of Aeronautics and Astronautics 1 1 Graduate Research Assistant, Mechanical Engineering Department. 2 Assistant Professor, Mechanical Engineering Department, AIAA Member. Email: ccseepersad@mail.utexas.edu . Phone: 512-471-1985.