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Optimal Design of General Stiffened Composite Circular Cylinders for Global Buckling with Strength Constraints

A design strategy for optimal design of composite grid-stiffened cylinders subjected to global and local buckling constraints and strength constraints was developed using a discrete optimizer based on a genetic algorithm. An improved smeared stiffener theory was used for the global analysis. Local buckling of skin segments were assessed using a Rayleigh-Ritz method that accounts for material anisotropy. The local buckling of stiffener segments were also assessed. Constraints on the axial membrane strain in the skin and stiffener segments were imposed to include strength criteria in the grid-stiffened cylinder design. Design variables used in this study were the axial and transverse stiffener spacings, stiffener height and thickness, skin laminate stacking sequence and stiffening configuration, where stiffening configuration is a design variable that indicates the combination of axial, transverse and diagonal stiffener in the grid-stiffened cylinder. The design optimization process was adapted to identify the best suited stiffening configurations and stiffener spacings for grid-stiffened composite cylinder with the length and radius of the cylinder, the design in-plane loads and material properties as inputs. The effect of having axial membrane strain constraints in the skin and stiffener segments in the optimization process is also studied for selected stiffening configurations.

Jaunky, N.

Optimal Design of Grid-Stiffened Panels and Shells With Variable Curvature

A design strategy for optimal design of composite grid-stiffened structures with variable curvature subjected to global and local buckling constraints is developed using a discrete optimizer. An improved smeared stiffener theory is used for the global buckling analysis. Local buckling of skin segments is assessed using a Rayleigh-Ritz method that accounts for material anisotropy and transverse shear flexibility. The local buckling of stiffener segments is also assessed. Design variables are the axial and transverse stiffener spacing, stiffener height and thickness, skin laminate, and stiffening configuration. Stiffening configuration is herein defined as a design variable that indicates the combination of axial, transverse and diagonal stiffeners in the stiffened panel. The design optimization process is adapted to identify the lightest-weight stiffening configuration and stiffener spacing for grid-stiffened composite panels given the overall panel dimensions. in-plane design loads, material properties. and boundary conditions of the grid-stiffened panel or shell.

Ambur, Damodar R.

Precision of Sensitivity in the Design Optimization of Indeterminate Structures

Design sensitivity is central to most optimization methods. The analytical sensitivity expression for an indeterminate structural design optimization problem can be factored into a simple determinate term and a complicated indeterminate component. Sensitivity can be approximated by retaining only the determinate term and setting the indeterminate factor to zero. The optimum solution is reached with the approximate sensitivity. The central processing unit (CPU) time to solution is substantially reduced. The benefit that accrues from using the approximate sensitivity is quantified by solving a set of problems in a controlled environment. Each problem is solved twice: first using the closed-form sensitivity expression, then using the approximation. The problem solutions use the CometBoards testbed as the optimization tool with the integrated force method as the analyzer. The modification that may be required, to use the stiffener method as the analysis tool in optimization, is discussed. The design optimization problem of an indeterminate structure contains many dependent constraints because of the implicit relationship between stresses, as well as the relationship between the stresses and displacements. The design optimization process can become problematic because the implicit relationship reduces the rank of the sensitivity matrix. The proposed approximation restores the full rank and enhances the robustness of the design optimization method.

Patnaik, Surya N.

Neural Network and Regression Approximations in High Speed Civil Transport Aircraft Design Optimization

Nonlinear mathematical-programming-based design optimization can be an elegant method. However, the calculations required to generate the merit function, constraints, and their gradients, which are frequently required, can make the process computational intensive. The computational burden can be greatly reduced by using approximating analyzers derived from an original analyzer utilizing neural networks and linear regression methods. The experience gained from using both of these approximation methods in the design optimization of a high speed civil transport aircraft is the subject of this paper. The Langley Research Center's Flight Optimization System was selected for the aircraft analysis. This software was exercised to generate a set of training data with which a neural network and a regression method were trained, thereby producing the two approximating analyzers. The derived analyzers were coupled to the Lewis Research Center's CometBoards test bed to provide the optimization capability. With the combined software, both approximation methods were examined for use in aircraft design optimization, and both performed satisfactorily. The CPU time for solution of the problem, which had been measured in hours, was reduced to minutes with the neural network approximation and to seconds with the regression method. Instability encountered in the aircraft analysis software at certain design points was also eliminated. On the other hand, there were costs and difficulties associated with training the approximating analyzers. The CPU time required to generate the input-output pairs and to train the approximating analyzers was seven times that required for solution of the problem.

Patniak, Surya N.

Robust Acoustic Objective Functions and Sensitivities in Adjoint-Based Design Optimizations

The multidisciplinary design of aircraft typically includes considerations of performance, weight, fuel burn, and noise, among other factors. An objective function is applied to each of these considerations in order to weight the influence of trade-offs between different designs. Higher-order optimization exercises have utilized an adjoint approach to reach an optimal set of objective functions, such as maximum lift and reduced drag. Taking advantage of the adjoint approach significantly reduces the computational time required to find an optimal configuration. Including acoustics in the set of objective functions during an adjoint-based design optimization requires the sensitivity of the acoustic objective function. This document will present an approach for defining the sensitivity of several acoustic metrics and operations that can fill the role of the acoustic objective function. This includes time-integrated metrics such as effective perceived noise level (EPNL) and frequency-integrated metrics such as overall sound pressure level (OASPL). A demonstration case, validation, and details on the implementation in the second generation Aircraft NOise Prediction Program (ANOPP2) are also shown.

Lopes, Leonard V.

Analysis-Driven Design Optimization of a SMA-Based Slat-Cove Filler for Aeroacoustic Noise Reduction

Airframe noise is a significant component of environmental noise in the vicinity of airports. The noise associated with the leading-edge slat of typical transport aircraft is a prominent source of airframe noise. Previous work suggests that a slat-cove filler (SCF) may be an effective noise treatment. Hence, development and optimization of a practical slat-cove-filler structure is a priority. The objectives of this work are to optimize the design of a functioning SCF which incorporates superelastic shape memory alloy (SMA) materials as flexures that permit the deformations involved in the configuration change. The goal of the optimization is to minimize the actuation force needed to retract the slat-SCF assembly while satisfying constraints on the maximum SMA stress and on the SCF deflection under static aerodynamic pressure loads, while also satisfying the condition that the SCF self-deploy during slat extension. A finite element analysis model based on a physical bench-top model is created in Abaqus such that automated iterative analysis of the design could be performed. In order to achieve an optimized design, several design variables associated with the current SCF configuration are considered, such as the thicknesses of SMA flexures and the dimensions of various components, SMA and conventional. Designs of experiment (DOE) are performed to investigate structural response to an aerodynamic pressure load and to slat retraction and deployment. DOE results are then used to inform the optimization process, which determines a design minimizing actuator forces while satisfying the required constraints.

Scholten, William

An expert system for integrated structural analysis and design optimization for aerospace structures

The results of a research study on the development of an expert system for integrated structural analysis and design optimization is presented. An Object Representation Language (ORL) was developed first in conjunction with a rule-based system. This ORL/AI shell was then used to develop expert systems to provide assistance with a variety of structural analysis and design optimization tasks, in conjunction with procedural modules for finite element structural analysis and design optimization. The main goal of the research study was to provide expertise, judgment, and reasoning capabilities in the aerospace structural design process. This will allow engineers performing structural analysis and design, even without extensive experience in the field, to develop error-free, efficient and reliable structural designs very rapidly and cost-effectively. This would not only improve the productivity of design engineers and analysts, but also significantly reduce time to completion of structural design. An extensive literature survey in the field of structural analysis, design optimization, artificial intelligence, and database management systems and their application to the structural design process was first performed. A feasibility study was then performed, and the architecture and the conceptual design for the integrated 'intelligent' structural analysis and design optimization software was then developed. An Object Representation Language (ORL), in conjunction with a rule-based system, was then developed using C++. Such an approach would improve the expressiveness for knowledge representation (especially for structural analysis and design applications), provide ability to build very large and practical expert systems, and provide an efficient way for storing knowledge. Functional specifications for the expert systems were then developed. The ORL/AI shell was then used to develop a variety of modules of expert systems for a variety of modeling, finite element analysis, and design optimization tasks in the integrated aerospace structural design process. These expert systems were developed to work in conjunction with procedural finite element structural analysis and design optimization modules (developed in-house at SAT, Inc.). The complete software, AutoDesign, so developed, can be used for integrated 'intelligent' structural analysis and design optimization. The software was beta-tested at a variety of companies, used by a range of engineers with different levels of background and expertise. Based on the feedback obtained by such users, conclusions were developed and are provided.

Source record

A hybrid nonlinear programming method for design optimization

Solutions to engineering design problems formulated as nonlinear programming (NLP) problems usually require the use of more than one optimization technique. Moreover, the interaction between the user (analysis/synthesis) program and the NLP system can lead to interface, scaling, or convergence problems. An NLP solution system is presented that seeks to solve these problems by providing a programming system to ease the user-system interface. A simple set of rules is used to select an optimization technique or to switch from one technique to another in an attempt to detect, diagnose, and solve some potential problems. Numerical examples involving finite element based optimal design of space trusses and rotor bearing systems are used to illustrate the applicability of the proposed methodology.

Rajan, S. D.

Coupled Aeropropulsive Design Optimization of a Podded Electric Propulsor

New aircraft concepts are increasingly relying on non-traditional propulsion systems to achieve lower energy consumption. These non-traditional technologies, such as boundary layer ingestion or distributed electric propulsion, require a tight integration of the propulsion sys- tem to the airframe, and therefore, a traditional design approach where the aerodynamics and propulsion disciplines are considered separately is likely to result in sub-optimal designs. As a result, we have to rely on coupled aeropropulsive design optimization, in which fully coupled aeropropulsive models are optimized to maximize the advantages of these tightly integrated propulsion systems. Despite its advantages, aeropropulsive design optimization is a relatively new field, and significant advancements are required for wide adoption of this approach, especially in the context of robustness. In this work, we introduce two fully coupled aeropropulsive design optimization approaches that are compatible with CFD models with body-force terms and boundary conditions to model the effects of the propulsion system in the flow field. To test these new approaches, we developed a podded electric fan model based on the aft-propulsor of NASA’s STARC-ABL concept. This simple design problem enables us to rapidly develop and test different aeropropulsive coupling approaches, while including the challenging physical interactions that arise from coupling CFD and propulsion models. The coupled aeropropulsive model is implemented using the MPhys library, which is built with NASA’s OpenMDAO frame- work. Using this benchmark design problem, we demonstrate the robustness of the approaches and our aeropropulsive design optimization framework by performing a sweep of optimizations for a total of 50 CFD-based aeropropulsive design optimizations. Furthermore, the new aero- propulsive coupling approaches enable multi-point design optimizations. We demonstrate this capability in a multi-point design optimization problem where we optimize cruise performance subject to a fan-face distortion constraint at rolling take-off conditions. The aeropropulsive modeling approaches we present in this work represent a significant milestone in the field of aeropropulsive design optimization. The framework we developed is extremely robust and flexible, and these developments will be crucial for future aeropropulsive design optimizations of complete turbofan engines.

Optimization propulsion aerodynamics

Progress in multidisciplinary design optimization at NASA Langley

Multidisciplinary Design Optimization refers to some combination of disciplinary analyses, sensitivity analysis, and optimization techniques used to design complex engineering systems. The ultimate objective of this research at NASA Langley Research Center is to help the US industry reduce the costs associated with development, manufacturing, and maintenance of aerospace vehicles while improving system performance. This report reviews progress towards this objective and highlights topics for future research. Aerospace design problems selected from the author's research illustrate strengths and weaknesses in existing multidisciplinary optimization techniques. The techniques discussed include multiobjective optimization, global sensitivity equations and sequential linear programming.

Padula, Sharon L.

Rapid Modeling, Assembly and Simulation in Design Optimization

A new capability for design is reviewed. This capability provides for rapid assembly of detail finite element models early in the design process where costs are most effectively impacted. This creates an engineering environment which enables comprehensive analysis and design optimization early in the design process. Graphical interactive computing makes it possible for the engineer to interact with the design while performing comprehensive design studies. This rapid assembly capability is enabled by the use of Interface Technology, to couple independently created models which can be archived and made accessible to the designer. Results are presented to demonstrate the capability.

Housner, Jerry

Multidisciplinary Design Optimization of Low-Boom Supersonic Aircraft with Mission Constraints

Conceptual design of low-boom supersonic aircraft is heavily dictated by aircraft volume and lift distributions. These unique design characteristics make it a challenge to enforce mission requirements (such as static margins and trim requirements) during design optimization. This low-boom design challenge is resolved by using reversed equivalent area targets for low-fidelity low-boom inverse design and a block coordinate optimization (BCO) method for multidisciplinary design optimization (MDO). The corresponding low-boom MDO problem includes aircraft mission constraints on ranges, cruise speeds, trim for low-boom cruise, static margins for takeoff/cruise/landing, takeoff/landing field lengths, approach velocity, and tail rotation angles for trim at takeoff/landing, as well as fuselage volume constraints for passengers and main gear storage. The BCO method is developed to optimally resolve the conflicts between the low-boom inverse design objective and other design constraints. This method is successfully applied to design a low-boom supersonic configuration that carries 40 passengers, flies a low-boom mission with cruise Mach of 1.6 and range of 2,500 nm, and cruises overwater at Mach 1.8 with range of 3,600 nm. The generated configuration satisfies all specified mission constraints and has the potential to match a reversed equivalent area target with ground noise level below 70 PLdB.

Multidisciplinary design optimization

An assessment of separable fluid connector system parameters to perform a connector system design optimization study

The key to optimization of design where there are a large number of variables, all of which may not be known precisely, lies in the mathematical tool of dynamic programming developed by Bellman. This methodology can lead to optimized solutions to the design of critical systems in a minimum amount of time, even when there are a great number of acceptable configurations to be considered. To demonstrate the usefulness of dynamic programming, an analytical method is developed for evaluating the relationship among existing numerous connector designs to find the optimum configuration. The data utilized in the study were generated from 900 flanges designed for six subsystems of the S-1B stage of the Saturn 1B space carrier vehicle.

Prasthofer, W. P.

Optimal design of compact spur gear reductions

The optimal design of compact spur gear reductions includes the selection of bearing and shaft proportions in addition to gear mesh parameters. Designs for single mesh spur gear reductions are based on optimization of system life, system volume, and system weight including gears, support shafts, and the four bearings. The overall optimization allows component properties to interact, yielding the best composite design. A modified feasible directions search algorithm directs the optimization through a continuous design space. Interpolated polynomials expand the discrete bearing properties and proportions into continuous variables for optimization. After finding the continuous optimum, the designer can analyze near optimal designs for comparison and selection. Design examples show the influence of the bearings on the optimal configurations.

Savage, M.

Multidisciplinary Design Optimization of Low-Boom Supersonic Aircraft with Mission Constraints

Design of low-boom supersonic aircraft is heavily dictated by aircraft volume and lift distributions. These unique design characteristics make it a challenge to enforce mission requirements (such as static margins and trim requirements) during design optimization. This low-boom design challenge is resolved by using reversed equivalent area targets for low-fidelity low-boom design and a decomposition method for multidisciplinary design optimization(MDO).The corresponding low-boom MDO problem includes aircraft mission constraints for cruise ranges, cruise speeds, trim margin for low-boom cruise, static margins for takeoff/cruise/landing, tail rotation angles for trim at takeoff/landing, takeoff/landing field lengths, and approach velocity, as well as volume constraints for cabin and main landing gear packaging. The decomposition method is developed to optimally resolve the conflicts between the low-boom design objective and other design constraints. The decomposition method is successfully applied to design a low-boom supersonic configuration that carries 40 passengers, has low-boom cruise of Mach 1.6 with range ≥ 2,500 nm, and can also cruise at Mach 1.8 with range ≥ 3,600 nm. The generated configuration satisfies all specified mission constraints and has the potential to achieve a low-boom ground noise level below 75 PLdB.

Wu Li

Formulation for Simultaneous Aerodynamic Analysis and Design Optimization

An efficient approach for simultaneous aerodynamic analysis and design optimization is presented. This approach does not require the performance of many flow analyses at each design optimization step, which can be an expensive procedure. Thus, this approach brings us one step closer to meeting the challenge of incorporating computational fluid dynamic codes into gradient-based optimization techniques for aerodynamic design. An adjoint-variable method is introduced to nullify the effect of the increased number of design variables in the problem formulation. The method has been successfully tested on one-dimensional nozzle flow problems, including a sample problem with a normal shock. Implementations of the above algorithm are also presented that incorporate Newton iterations to secure a high-quality flow solution at the end of the design process. Implementations with iterative flow solvers are possible and will be required for large, multidimensional flow problems.

Hou, G. W.

A decomposition-based design optimization method with applications

A two-level design optimization metholology is described. A progress report of its application to Printed Wiring Board (PWB) assembly examples is given. The design of PWB assemblies is a complex task which is generally conducted as a sequential process. Individual PWBs are usually designed first, followed by the composition of the PWBs into an assembly. As a result, optimizing design considerations such as assembly reliability cannot be accomplished. This study showed that a two-level decomposition method can be employed to optimize for reliability at both the PWB- and the assembly-level in a coupled manner. The two-level decomposition method also resolved the mixed-integer nonlinear programming nature of the problem rather easily.

Azarm, Shapour