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A definition of the multidisciplinary design optimization (MDO) is introduced, and functionality and relationship of the MDO conceptual components are examined. The latter include design-oriented analysis, approximation concepts, mathematical system modeling, design space search, an optimization procedure, and a humane interface.
An algorithm for a general, multilevel structural optimization by substructuring is derived, based on the linear decomposition concept that is rooted in the Bellman's Optimality Criterion enhanced with the optimum sensitivity derivatives used as a means to account for coupling among the subproblems, each of which is limited to optimization of a substructure. The algorithm applies also to those multidisciplinary problems whose subproblems form a hierarchy similar to that of substructures. In systems where the subproblems communicate with each other at the same level, the decomposition becomes non-hierarchic and the system may be optimized as a whole based on the derivatives of the system behavior with respect to the design variables computed by a method that bypasses finite differencing on the system analysis. When a multidisciplinary system includes a structure as its part, a hybrid, hierarchic/non-hierarchic decomposition applies. Numerical examples and references to computational experience accumulated to date illustrate the discussion.
This paper describes a structural and aeroelastic model for wing sizing and weight calculation of a strut-braced wing. The wing weight is calculated using a newly developed structural weight analysis module considering the special nature of strut-braced wings. A specially developed aeroelastic model enables one to consider wing flexibility and spanload redistribution during in-flight maneuvers. The structural model uses a hexagonal wing-box featuring skin panels, stringers, and spar caps, whereas the aerodynamics part employs a linearized transonic vortex lattice method. Thus, the wing weight may be calculated from the rigid or flexible wing spanload. The calculations reveal the significant influence of the strut on the bending material weight of the wing. The use of a strut enables one to design a wing with thin airfoils without weight penalty. The strut also influences wing spanload and deformations. Weight savings are not only possible by calculation and iterative resizing of the wing structure according to the actual design loads. Moreover, as an advantage over the cantilever wing, employment of the strut twist moment for further load alleviation leads to increased savings in structural weight.
The design of supersonic aircraft requires complex analysis in multiple disciplines, posing, a challenge for optimization methods. In this thesis, collaborative optimization, a design architecture developed to solve large-scale multidisciplinary design problems, is applied to the design of supersonic transport concepts. Collaborative optimization takes advantage of natural disciplinary segmentation to facilitate parallel execution of design tasks. Discipline-specific design optimization proceeds while a coordinating mechanism ensures progress toward an optimum and compatibility between disciplinary designs. Two concepts for supersonic aircraft are investigated: a conventional delta-wing design and a natural laminar flow concept that achieves improved performance by exploiting properties of supersonic flow to delay boundary layer transition. The work involves the development of aerodynamics and structural analyses, and integration within a collaborative optimization framework. It represents the most extensive application of the method to date.
An optimization procedure is developed for addressing the design of composite tilt rotor blades. A comprehensive technique, based on a higher-order laminate theory, is developed for the analysis of the thick composite load-carrying sections, modeled as box beams, in the blade. The theory, which is based on a refined displacement field, is a three-dimensional model which approximates the elasticity solution so that the beam cross-sectional properties are not reduced to one-dimensional beam parameters. Both inplane and out-of-plane warping are included automatically in the formulation. The model can accurately capture the transverse shear stresses through the thickness of each wall while satisfying stress free boundary conditions on the inner and outer surfaces of the beam. The aerodynamic loads on the blade are calculated using the classical blade element momentum theory. Analytical expressions for the lift and drag are obtained based on the blade planform with corrections for the high lift capability of rotor blades. The aerodynamic analysis is coupled with the structural model to formulate the complete coupled equations of motion for aeroelastic analyses. Finally, a multidisciplinary optimization procedure is developed to improve the aerodynamic, structural and aeroelastic performance of the tilt rotor aircraft. The objective functions include the figure of merit in hover and the high speed cruise propulsive efficiency. Structural, aerodynamic and aeroelastic stability criteria are imposed as constraints on the problem. The Kreisselmeier-Steinhauser function is used to formulate the multiobjective function problem. The search direction is determined by the Broyden-Fletcher-Goldfarb-Shanno algorithm. The optimum results are compared with the baseline values and show significant improvements in the overall performance of the tilt rotor blade.
Modular prototype software has been designed to implement the method of non-hierarchic decomposition for optimization of coupled, multidisciplinary systems. The modules are intended to be run concurrently on separate processors and to automate all aspects of the method except for the objective function and subspace analysis subroutines, which are inherently problem-dependent. Minimal analysis of problem structure is required, since the software is designed to handle arbitrary system coupling with full generality. The basic feasibility of the approach has been confirmed using six example problems, with varying degrees of lateral coupling among the subspace constraints and dependent variables. Results are given for two of the test problems.
Frameworks or problem solving environments that support application development form an active area of research. The Multidisciplinary Optimization Branch at NASA Langley Research Center is investigating frameworks for supporting multidisciplinary analysis and optimization research. The Branch has generated a list of framework requirements, based on the experience gained from the Framework for Interdisciplinary Design Optimization project and the information acquired during a framework evaluation process. In this study, four existing frameworks are examined against these requirements. The results of this examination suggest several topics for further framework research.
Since the inception of CAS in 1992, NASA Langley has been conducting research into applying multidisciplinary optimization (MDO) and high performance computing toward reducing aircraft design cycle time. The focus of this research has been the development of a series of computational frameworks and associated applications that increased in capability, complexity, and performance over time. The culmination of this effort is an automated high-fidelity analysis capability for a high speed civil transport (HSCT) vehicle installed on a network of heterogeneous computers with a computational framework built using Common Object Request Broker Architecture (CORBA) and Java. The main focus of the research in the early years was the development of the Framework for Interdisciplinary Design Optimization (FIDO) and associated HSCT applications. While the FIDO effort was eventually halted, work continued on HSCT applications of ever increasing complexity. The current application, HSCT4.0, employs high fidelity CFD and FEM analysis codes. For each analysis cycle, the vehicle geometry and computational grids are updated using new values for design variables. Processes for aeroelastic trim, loads convergence, displacement transfer, stress and buckling, and performance have been developed. In all, a total of 70 processes are integrated in the analysis framework. Many of the key processes include automatic differentiation capabilities to provide sensitivity information that can be used in optimization. A software engineering process was developed to manage this large project. Defining the interactions among 70 processes turned out to be an enormous, but essential, task. A formal requirements document was prepared that defined data flow among processes and subprocesses. A design document was then developed that translated the requirements into actual software design. A validation program was defined and implemented to ensure that codes integrated into the framework produced the same results as their standalone counterparts. Finally, a Commercial Off the Shelf (COTS) configuration management system was used to organize the software development. A computational environment, CJOPT, based on the Common Object Request Broker Architecture, CORBA, and the Java programming language has been developed as a framework for multidisciplinary analysis and Optimization. The environment exploits the parallelisms inherent in the application and distributes the constituent disciplines on machines best suited to their needs. In CJOpt, a discipline code is "wrapped" as an object. An interface to the object identifies the functionality (services) provided by the discipline, defined in Interface Definition Language (IDL) and implemented using Java. The results of using the HSCT4.0 capability are described. A summary of lessons learned is also presented. The use of some of the processes, codes, and techniques by industry are highlighted. The application of the methodology developed in this research to other aircraft are described. Finally, we show how the experience gained is being applied to entirely new vehicles, such as the Reusable Space Transportation System. Additional information is contained in the original.
This paper presents a brief overview of some of the more recent advances in steady aerodynamic shape-design sensitivity analysis and optimization, based on advanced computational fluid dynamics (CFD). The focus here is on those methods particularly well-suited to the study of geometrically complex configurations and their potentially complex associated flow physics. When nonlinear state equations are considered in the optimization process, difficulties are found in the application of sensitivity analysis. Some techniques for circumventing such difficulties are currently being explored and are included here. Attention is directed to methods that utilize automatic differentiation to obtain aerodynamic sensitivity derivatives for both complex configurations and complex flow physics. Various examples of shape-design sensitivity analysis for unstructured-grid CFD algorithms are demonstrated for different formulations of the sensitivity equations. Finally, the use of advanced, unstructured-grid CFDs in multidisciplinary analyses and multidisciplinary sensitivity analyses within future optimization processes is recommended and encouraged.
Growing interest in design and optimization of electrified aircraft propulsion concepts prompts the need for accurate, flexible, and efficient methods to model battery systems. Presented in this paper are three battery modeling methods that have been used at NASA’s Glenn Research Center, each representing different mathematical or electrical approaches. Thévenin equivalent circuit, normalization, and curve-fitting methods are compared against battery cell test data for the X-57 Maxwell electric aircraft technology demonstrator. The methods are then applied in a simple multidisciplinary optimization context using NASA’s Six-Passenger Electric Quadrotor concept to determine their applicability and performance. The normalization method achieves the highest accuracy for steady and unsteady discharge rates with a voltage mean error percentage of 0.423% and 1.186%, respectively. Optimal quadrotor mission range between the models varies up to 0.5 nmi, identifying current battery modeling methods as a potentially significant contributor to mission analysis error. A set of relevant tools and techniques for conceptual battery modeling are identified in this paper, with conclusions made on the utility of each modeling approach for various design challenges.
This paper reports the results of initial efforts to apply the System Sensitivity Analysis (SSA) optimization method to the conceptual design of a single-stage-to-orbit (SSTO) launch vehicle. SSA is an efficient, calculus-based MDO technique for generating sensitivity derivatives in a highly multidisciplinary design environment. The method has been successfully applied to conceptual aircraft design and has been proven to have advantages over traditional direct optimization methods. The method is applied to the optimization of an advanced, piloted SSTO design similar to vehicles currently being analyzed by NASA as possible replacements for the Space Shuttle. Powered by a derivative of the Russian RD-701 rocket engine, the vehicle employs a combination of hydrocarbon, hydrogen, and oxygen propellants. Three primary disciplines are included in the design - propulsion, performance, and weights & sizing. A complete, converged vehicle analysis depends on the use of three standalone conceptual analysis computer codes. Efforts to minimize vehicle dry (empty) weight are reported in this paper. The problem consists of six system-level design variables and one system-level constraint. Using SSA in a 'manual' fashion to generate gradient information, six system-level iterations were performed from each of two different starting points. The results showed a good pattern of convergence for both starting points. A discussion of the advantages and disadvantages of the method, possible areas of improvement, and future work is included.
The objective of this paper are to develop a multidisciplinary computational methodology to predict the hot-gas-side and coolant-side heat transfer and to use it in parametric studies to recommend optimized design of the coolant channels for a regeneratively cooled liquid rocket engine combustor. An integrated numerical model which incorporates CFD for the hot-gas thermal environment, and thermal analysis for the liner and coolant channels, was developed. This integrated CFD/thermal model was validated by comparing predicted heat fluxes with those of hot-firing test and industrial design methods for a 40 k calorimeter thrust chamber and the Space Shuttle Main Engine Main Combustion Chamber. Parametric studies were performed for the Advanced Main Combustion Chamber to find a strategy for a proposed combustion chamber coolant channel design.
Consideration is given to the design and status of the Integrated Modeling of Optical Systems (IMOS) tool and to critical design issues. A multidisciplinary spacecraft design and analysis tool with support for structural dynamics, controls, thermal analysis, and optics, IMOS provides rapid and accurate end-to-end performance analysis, simulations, and optimization of advanced space-based optical systems. The requirements for IMOS-supported numerical arrays, user defined data structures, and a hierarchical data base are outlined, and initial experience with the tool is summarized. A simulation of a flexible telescope illustrates the integrated nature of the tools.
This paper presents a brief overview of some of the more recent advances in steady aerodynamic shape-design sensitivity analysis and optimization, based on advanced computational fluid dynamics. The focus here is on those methods particularly well- suited to the study of geometrically complex configurations and their potentially complex associated flow physics. When nonlinear state equations are considered in the optimization process, difficulties are found in the application of sensitivity analysis. Some techniques for circumventing such difficulties are currently being explored and are included here. Attention is directed to methods that utilize automatic differentiation to obtain aerodynamic sensitivity derivatives for both complex configurations and complex flow physics. Various examples of shape-design sensitivity analysis for unstructured-grid computational fluid dynamics algorithms are demonstrated for different formulations of the sensitivity equations. Finally, the use of advanced, unstructured-grid computational fluid dynamics in multidisciplinary analyses and multidisciplinary sensitivity analyses within future optimization processes is recommended and encouraged.
A select overview is provided of ongoing research focusing on the development and verification of integrated structural analysis and optimal design capabilities for advanced aerospace propulsion and power systems. Subjects discussed include the following: (1) Composites - analytical models (composite mechanics), integrated computational methods, and characterization of composite structural response and durability for resin-, metal-, and ceramic-matrix systems; (2) Advanced inelastic analysis - algorithm/numerical methods for more accurate and efficient analysis; (3) Constitutive modeling - theoretical formulation and characterization of thermoviscoplastic material behavior; (4) Computational simulation - engine structures from components to assembly, and up to an entire engine system subjected to simulated test-stand and mission load histories; (5) Probabilistic structural analysis - quantification of the effects of uncertainty in geometry, material, loads, and boundary conditions on structural response for true reliability assessment; and (6) Interdisciplinary optimization - incorporation of mathematical optimization and multidisciplinary analyses to provide streamlined, autonomous optimal design systems.
ASTROS (Automated Structural Optimization System) is a finite-element-based multidisciplinary structural optimization procedure developed under Air Force sponsorship to perform automated preliminary structural design. The design task is the determination of the structural sizes that provide an optimal structure while satisfying numerous constraints from many disciplines. In addition to its automated design features, ASTROS provides a general transient and frequency response capability, as well as a special feature to perform a transient analysis of a vehicle subjected to a nuclear blast. The motivation for the development of a single multidisciplinary design tool is that such a tool can provide improved structural designs in less time than is currently needed. The role of such a tool is even more apparent as modern materials come into widespread use. Balancing conflicting requirements for the structure's strength and stiffness while exploiting the benefits of material anisotropy is perhaps an impossible task without assistance from an automated design tool. Finally, the use of a single tool can bring the design task into better focus among design team members, thereby improving their insight into the overall task.
The development of aircraft gust design techniques is reviewed with emphasis on those techniques applicable to large scale multidisciplinary closed-loop optimization methods. An overall view is presented of the optimization methodology utilized. An analysis is presented wherein the bivariate normal distribution function for a particular loading condition is considered. By use of maximization techniques, functions are derived for stress components along equal probability contours which allow for directionality and auto-correlation effects to be considered. These functions are then applied to the problem being considered and the effects on the structural sizing and weight penalties evaluated against more conventional methods.
Lockheed Martin Skunk Works (LMSW) is currently developing a single-stage-to-orbit reusable launch vehicle called VentureStar(TM) A team at NASA Langley Research Center participated with LMSW in the screening and evaluation of a number of early VentureStar(TM) configurations. The performance analyses that supported these initial studies were conducted to assess the effect of a lifting body shape, linear aerospike engine and metallic thermal protection system (TPS) on the weight and performance of the vehicle. These performance studies were performed in a multidisciplinary fashion that indirectly linked the trajectory optimization with weight estimation and aerothermal analysis tools. This approach was necessary to develop optimized ascent and entry trajectories that met all vehicle design constraints. Significant improvements in ascent performance were achieved when the vehicle flew a lifting trajectory and varied the engine mixture ratio during flight. Also, a considerable reduction in empty weight was possible by adjusting the total oxidizer-to-fuel and liftoff thrust-to-weight ratios. However, the optimal ascent flight profile had to be altered to ensure that the vehicle could be trimmed in pitch using only the flow diverting capability of the aerospike engine. Likewise, the optimal entry trajectory had to be tailored to meet TPS heating rate and transition constraints while satisfying a crossrange requirement.