Experiences in applying optimization techniques to configurations for the Control of Flexible Structures (COFS) program

Optimization procedures are developed to systematically provide closely-spaced vibration frequencies. A general purpose finite-element program for eigenvalue and sensitivity analyses is combined with formal mathematical programming techniques. Results are presented for three studies. The first study uses a simple model to obtain a design with two pairs of closely-spaced frequencies. Two formulations are developed: an objective function-based formulation and constraint-based formulation for the frequency spacing. It is found that conflicting goals are handled better by a constraint-based formulation. The second study uses a detailed model to obtain a design with one pair of closely-spaced frequencies while satisfying requirements on local member frequencies and manufacturing tolerances. Two formulations are developed. Both the constraint-based and the objective function-based formulations perform reasonably well and converge to the same results. However, no feasible design solution exists which satisfies all design requirements for the choices of design variables and the upper and lower design variable values used. More design freedom is needed to achieve a fully satisfactory design. The third study is part of a redesign activity in which a detailed model is used

Performance optimization of helicopter rotor blades

As part of a center-wide activity at NASA Langley Research Center to develop multidisciplinary design procedures by accounting for discipline interactions, a performance design optimization procedure is developed. The procedure optimizes the aerodynamic performance of rotor blades by selecting the point of taper initiation, root chord, taper ratio, and maximum twist which minimize hover horsepower while not degrading forward flight performance. The procedure uses HOVT (a strip theory momentum analysis) to compute the horse power required for hover and the comprehensive helicopter analysis program CAMRAD to compute the horsepower required for forward flight and maneuver. The optimization algorithm consists of the general purpose optimization program CONMIN and approximate analyses. Sensitivity analyses consisting of derivatives of the objective function and constraints are carried out by forward finite differences. The procedure is applied to a test problem which is an analytical model of a wind tunnel model of a utility rotor blade

Optimization procedure to control the coupling of vibration modes in flexible space structures

As spacecraft structural concepts increase in size and flexibility, the vibration frequencies become more closely-spaced. The identification and control of such closely-spaced frequencies present a significant challenge. To validate system identification and control methods prior to actual flight, simpler space structures will be flown. To challenge the above technologies, it will be necessary to design these structures with closely-spaced or coupled vibration modes. Thus, there exists a need to develop a systematic method to design a structure which has closely-spaced vibration frequencies. This paper describes an optimization procedure which is used to design a large flexible structure to have closely-spaced vibration frequencies. The procedure uses a general-purpose finite element analysis program for the vibration and sensitivity analyses and a general-purpose optimization program. Results are presented from two studies. The first study uses a detailed model of a large flexible structure to design a structure with one pair of closely-spaced frequencies. The second study uses a simple equivalent beam model of a large flexible structure to obtain a design with two pairs of closely-spaced frequencies

Structural optimization of rotor blades with integrated dynamics and aerodynamics

The problem of structural optimization of helicopter rotor blades with integrated dynamic and aerodynamic design considerations is addressed. Results of recent optimization work on rotor blades for minimum weight with constraints on multiple coupled natural flap-lag frequencies, blade autorotational inertia and centrifugal stress has been reviewed. A strategy has been defined for the ongoing activities in the integrated dynamic/aerodynamic optimization of rotor blades. As a first step, the integrated dynamic/airload optimization problem has been formulated. To calculate system sensitivity derivatives necessary for the optimization recently developed, Global Sensitivity Equations (GSE) are being investigated. A need for multiple objective functions for the integrated optimization problem has been demonstrated and various techniques for solving the multiple objective function optimization are being investigated. The method called the Global Criteria Approach has been applied to a test problem with the blade in vacuum and the blade weight and the centrifugal stress as the multiple objectives. The results indicate that the method is quite effective in solving optimization problems with conflicting objective functions

Minimum weight design of rectangular and tapered helicopter rotor blades with frequency constraints

The minimum weight design of a helicopter rotor blade subject to constraints on coupled flap-lag natural frequencies has been studied. A constraint has also been imposed on the minimum value of the autorotational inertia of the blade in order to ensure that it has sufficient inertia to autorotate in the case of engine failure. The program CAMRAD is used for the blade modal analysis and CONMIN is used for the optimization. In addition, a linear approximation analysis involving Taylor series expansion has been used to reduce the analysis effort. The procedure contains a sensitivity analysis which consists of analytical derivatives of the objective function and the autorotational inertia constraint and central finite difference derivatives of the frequency constraints. Optimum designs have been obtained for both rectangular and tapered blades. Design variables include taper ratio, segment weights, and box beam dimensions. It is shown that even when starting with an acceptable baseline design, a significant amount of weight reduction is possible while satisfying all the constraints for both rectangular and tapered blades

Rotor blade aerodynamic design

Aerodynamic performance aspects of rotor blade design are presented. Design considerations, aerodynamic constraints and design variables are described

Stacking-sequence optimization for buckling of laminated plates by integer programming

Integer-programming formulations for the design of symmetric and balanced laminated plates under biaxial compression are presented. Both maximization of buckling load for a given total thickness and the minimization of total thickness subject to a buckling constraint are formulated. The design variables that define the stacking sequence of the laminate are zero-one integers. It is shown that the formulation results in a linear optimization problem that can be solved on readily available software. This is in contrast to the continuous case, where the design variables are the thicknesses of layers with specified ply orientations, and the optimization problem is nonlinear. Constraints on the stacking sequence such as a limit on the number of contiguous plies of the same orientation and limits on in-plane stiffnesses are easily accommodated. Examples are presented for graphite-epoxy plates under uniaxial and biaxial compression using a commercial software package based on the branch-and-bound algorithm

Integrated aerodynamic/dynamic optimization of helicopter rotor blades

An integrated aerodynamic/dynamic optimization procedure is used to minimize blade weight and 4 per rev vertical hub shear for a rotor blade in forward flight. The coupling of aerodynamics and dynamics is accomplished through the inclusion of airloads which vary with the design variables during the optimization process. Both single and multiple objective functions are used in the optimization formulation. The Global Criteria Approach is used to formulate the multiple objective optimization and results are compared with those obtained by using single objective function formulations. Constraints are imposed on natural frequencies, autorotational inertia, and centrifugal stress. The program CAMRAD is used for the blade aerodynamic and dynamic analyses, and the program CONMIN is used for the optimization. Since the spanwise and the azimuthal variations of loading are responsible for most rotor vibration and noise, the vertical airload distributions on the blade, before and after optimization, are compared. The total power required by the rotor to produce the same amount of thrust for a given area is also calculated before and after optimization. Results indicate that integrated optimization can significantly reduce the blade weight, the hub shear and the amplitude of the vertical airload distributions on the blade and the total power required by the rotor

Recent advances in multidisciplinary optimization of rotorcraft

A joint activity involving NASA and Army researchers at NASA LaRC to develop optimization procedures to improve the rotor blade design process by integrating appropriate disciplines and accounting for all of the important interactions among the disciplines is described. The disciplines involved include rotor aerodynamics, rotor dynamics, rotor structures, airframe dynamics, and acoustics. The work is focused on combining these five key disciplines in an optimization procedure capable of designing a rotor system to satisfy multidisciplinary design requirements. Fundamental to the plan is a three-phased approach. In phase 1, the disciplines of blade dynamics, blade aerodynamics, and blade structure are closely coupled while acoustics and airframe dynamics are decoupled and are accounted for as effective constraints on the design for the first three disciplines. In phase 2, acoustics is integrated with the first three disciplines. Finally, in phase 3, airframe dynamics is integrated with the other four disciplines. Representative results from work performed to date are described. These include optimal placement of tuning masses for reduction of blade vibratory shear forces, integrated aerodynamic/dynamic optimization, and integrated aerodynamic/dynamic/structural optimization. Examples of validating procedures are described

Optimization methods applied to the aerodynamic design of helicopter rotor blades

Described is a formal optimization procedure for helicopter rotor blade design which minimizes hover horsepower while assuring satisfactory forward flight performance. The approach is to couple hover and forward flight analysis programs with a general-purpose optimization procedure. The resulting optimization system provides a systematic evaluation of the rotor blade design variables and their interaction, thus reducing the time and cost of designing advanced rotor blades. The paper discusses the basis for and details of the overall procedure, describes the generation of advanced blade designs for representative Army helicopters, and compares design and design effort with those from the conventional approach which is based on parametric studies and extensive cross-plots