Optimal placement of active/passive members in truss structures using simulated annealing
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Chen, Gun-Shing↗
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Multidisciplinary Design Optimization and Cruise Mach Number Study of Truss-Braced Wing Aircraft
The Subsonic Ultra Green Aircraft Research (SUGAR) Phase III was led by Dr. Rakesh K. Kapania and Dr. Joseph A. Schetz at the Multidisciplinary Analysis and Design Center for Advanced Vehicles, Department of Aerospace and Ocean Engineering, Virginia Tech, Blacksburg VA. The research was performed from December 2014 to December 2015. Three major areas were investigated: Multidisciplinary Design Optimization (MDO) studies of truss braced wing (TBW) and strut braced wing (SBW) vehicles at cruise Mach numbers of 0.7 and 0.8 for a flight mission similar to current market single aisle configurations. The performance and the characteristics of the optimized vehicles were compared to the SUGAR Phase II TBW vehicle. These results were obtained without applying any of the extended transonic aerodynamic and aeroelastic tools that will be discussed later. It was found that the cruise Mach number has a large effect on the best “truss” configuration. At Mach 0.7, an SBW has a better fuel consumption and better take-off gross weight (TOGW). However, at Mach 0.8, the TBW is superior because the jury strut aids in satisfying the flutter constraint; Two-dimensional, steady, transonic aerodynamic analysis of the Boeing Airfoil J (BACJ) airfoil was performed for a range of thickness ratios, Mach numbers and lift coefficients. Reynolds-averaged Navier-Stokes (RANS) equations were solved to obtain the lift-curve slope, wave drag coefficient, the location of the center of pressure and to predict the separation at the trailing edge, which may lead to buffeting. One of the goals was to develop a database of lift-curve slope and the location of center of pressure, which could be used in a transonic aeroelastic analysis. Another goal was to compare the wave drag coefficients to those predicted by Lock’s fourth-power law and also to compare the transonic effects obtained from RANS simulations to those predicted by the Korn equations. A third goal was to develop a buffet boundary, which can be integrated into the MDO framework to prevent the optimized designs from probable buffeting; A state-space transonic aeroelastic analysis tool was developed, which can incorporate the nonlinear transonic effects in the unsteady aerodynamics but is yet computationally cheap when used within the VT MDO framework. The aeroelastic analysis uses Leishman- Beddoes (LB) indicial functions, which generated a state-space representation of the aeroelastic system. The indicial functions allow the incorporation of data for steady lift-curve slope and location of the center of pressure. Thus, the steady transonic effects are included, and the unsteady aerodynamic responses are a linearization about the steady results. The aeroelastic approach discretizes the wing into numerous strips, which results in a large eigenvalue problem as each strip has eight augmented aerodynamic states as per the LB theory. Thus, to reduce the computation expense, a reduced order model (ROM) was developed. The approach was validated using a few examples.
Kapania, Rakesh K.↗
Integrated topology and shape optimization in structural design
Structural optimization procedures usually start from a given design topology and vary its proportions or boundary shapes to achieve optimality under various constraints. Two different categories of structural optimization are distinguished in the literature, namely sizing and shape optimization. A major restriction in both cases is that the design topology is considered fixed and given. Questions concerning the general layout of a design (such as whether a truss or a solid structure should be used) as well as more detailed topology features (e.g., the number and connectivities of bars in a truss or the number of holes in a solid) have to be resolved by design experience before formulating the structural optimization model. Design quality of an optimized structure still depends strongly on engineering intuition. This article presents a novel approach for initiating formal structural optimization at an earlier stage, where the design topology is rigorously generated in addition to selecting shape and size dimensions. A three-phase design process is discussed: an optimal initial topology is created by a homogenization method as a gray level image, which is then transformed to a realizable design using computer vision techniques; this design is then parameterized and treated in detail by sizing and shape optimization. A fully automated process is described for trusses. Optimization of two dimensional solid structures is also discussed. Several application-oriented examples illustrate the usefulness of the proposed methodology.
Bremicker, M.↗
Optimal placement of excitations and sensors by simulated annealing
The optimal placement of discrete actuators and sensors is posed as a combinatorial optimization problem. Two examples for truss structures were used for illustration; the first dealt with the optimal placement of passive dampers along existing truss members, and the second dealt with the optimal placement of a combination of a set of actuators and a set of sensors. Except for the simplest problems, an exact solution by enumeration involves a very large number of function evaluations, and is therefore computationally intractable. By contrast, the simulated annealing heuristic involves far fewer evaluations and is best suited for the class of problems considered. As an optimization tool, the effectiveness of the algorithm is enhanced by introducing a number of rules that incorporate knowledge about the physical behavior of the problem. Some of the suggested rules are necessarily problem dependent.
Salama, Moktar↗
Design optimization studies using COSMIC NASTRAN
The purpose of this study is to create, test and document a procedure to integrate mathematical optimization algorithms with COSMIC NASTRAN. This procedure is very important to structural design engineers who wish to capitalize on optimization methods to ensure that their design is optimized for its intended application. The OPTNAST computer program was created to link NASTRAN and design optimization codes into one package. This implementation was tested using two truss structure models and optimizing their designs for minimum weight, subject to multiple loading conditions and displacement and stress constraints. However, the process is generalized so that an engineer could design other types of elements by adding to or modifying some parts of the code.
Pitrof, Stephen M.↗
Design considerations for large space antennas
Performance requirements and costs for transportation, fabrication, and orbital assembly are the drivers in the design of large space antennas will range in size from approximately 30 m to 1 km in diameter and include radiometers, multibeam lens antennas, and microwave power transmission systems. Research and development is required to define comprehensive structural criteria for specific missions, to determine optimized geometries for truss elements and truss configurations and to establish requirements for joint design with consideration of tolerances, load transfer, thermal compatibility, and assembly and disassembly. Candidate structural elements, materials systems for the low pressure rapid cure of advanced composite materials, and various on orbit assembly and fabrication techniques must also be developed.
Johnson, R., Jr.↗
Optimal design of a passive vibration absorber for a truss beam
The selection of the design parameters of passive vibration absorbers attached to a long cantilevered beam is studied. This study was motivated by the need for conducting parametric analysis of dynamics and control for Space-Shuttle-attached long beams. An optimization scheme using a quadratic cost function is introduced yielding the optimal sizing of the tip vibration absorber. Analytical solutions for an optimal absorber are presented for the case of one beam vibrational mode coupled with the absorber dynamics, and results are extended to cover the multiple mode case. An algorithm is developed to make an initial estimate of optimal tuning parameters which minimize the quadratic error cost function. Examples are given to illustrate the design concept.
Juang, J.-N.↗
Optimal design of a passive vibration absorber for a truss beam
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Juang, J.-N.↗
Optimal location of actuators for correcting distortions in large truss structures
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Burdisso, Ricardo A.↗
Selection of active member locations in adaptive structures
The effective use of multiple passive and active members in adaptive structures necessitates that these members be optimally distributed throughout the structure. In truss structures, the problem falls into the class of combinatorial optimization for which the solution becomes exceedingly intractable as the problem size increases. This is overcome by using the simulated annealing algorithm to obtain near optimal locations for passive and/or active members. The maximization of the rate of energy dissipation over a finite time period as the measure of optimality is adopted. The selection of optimal locations for both passive and active members is consistently treated through the use of the energy dissipation rate criterion within the simulated annealing algorithm. Numerical examples are used to illustrate the effectiveness of the methodology for large truss structures.
Chen, G.-S.↗
Actuator placement in prestressed adaptive trusses for vibration control
This paper describes the optimal location selection of actuators for vibration control in prestressed adaptive trusses. Since prestressed adaptive trusses are statically indeterminate, the actuators to be used for vibration control purposes must work against (1) existing static axial prestressing forces, (2) static axial forces caused by the actuation, and (3) dynamic axial forces caused by the motion of the mass. In statically determinate adaptive trusses (1) and (2) are non - existing. The actuator placement problem in statically indeterminate trusses is therefore governed by the actuation energy and the actuator strength requirements. Assuming output feedback type control of selected vibration modes in autonomous systems, a procedure is given for the placement of vibration controlling actuators in prestressed adaptive trusses.
Jalihal, P.↗
Control of a flexible planar truss using proof mass actuators
A flexible structure was modeled and actively controlled by using a single space realizable linear proof mass actuator. The NASA/UVA/UB actuator was attached to a flexible planar truss structure at an optimal location and it was considered as both passive and active device. The placement of the actuator was specified by examining the eigenvalues of the modified model that included the actuator dynamics, and the frequency response functions of the modified system. The electronic stiffness of the actuator was specified, such that the proof mass actuator system was tuned to the fourth structural mode of the truss by using traditional vibration absorber design. The active control law was limited to velocity feedback by integrating of the signals of two accelerometers attached to the structure. The two lower modes of the closed-loop structure were placed further in the LHS of the complex plane. The theoretically predicted passive and active control law was experimentally verified.
Minas, Constantinos↗
On the placement of active members in adaptive truss structures for vibration control
The problem of optimal placement of active members which are used for vibration control in adaptive truss structures is investigated. The control scheme is based on the method of eigenvalue assignment as a means of shaping the transient response of the controlled adaptive structures, and the minimization of required control action is considered as the optimization criterion. To this end, a performance index which measures the control strokes of active members is formulated in an efficient way. In order to reduce the computation burden, particularly for the case where the locations of active members have to be selected from a large set of available sites, several heuristic searching schemes are proposed for obtaining the near-optimal locations. The proposed schemes significantly reduce the computational complexity of placing multiple active members to the order of that when a single active member is placed.
Lu, L.-Y.↗
Structural optimization with probability of failure constraint
Probability of failure constraint concept for optimization of general structural system under simultaneous and alternative load systems - truss example
LOADING↗
The damper placement problem for large flexible space structures
The damper placement problem for large flexible space truss structures is formulated as a combinatorial optimization problem. The objective is to determine the p truss members of the structure to replace with active (or passive) dampers so that the modal damping ratio is as large as possible for all significant modes of vibration. Equivalently, given a strain energy matrix with rows indexed on the modes and the columns indexed on the truss members, we seek to find the set of p columns such that the smallest row sum, over the p columns, is maximized. We develop a tabu search heuristic for the damper placement problems on the Controls Structures Interaction (CSI) Phase 1 Evolutionary Model (10 modes and 1507 truss members). The resulting solutions are shown to be of high quality.
Kincaid, Rex K.↗
The multi-disciplinary design study. A life cycle cost algorithm
Life-cycle cost (LCC) is investigated as a comprehensive design criterion for two major interrelated spacecraft subsystems, Controls and Structures. A Multi-Disciplinary Design Tool (MDDT) is developed to evaluate the sensitivity of LCC to subsystem design parameters. Major costs addressed are: non-recurring; launch; ground support; maintenance; expendables; and software. Examples and results from the MDDT are described, including a structural optimization study between different truss designs; a solar array feathering trade for a minimal drag configuration during umbra; and the cost of active control of a flexible structure is compared against the cost of passive damping using visco-elastic material.
Harding, R. R.↗
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.↗
Displacement based multilevel structural optimization
Multidisciplinary design optimization (MDO) is expected to play a major role in the competitive transportation industries of tomorrow, i.e., in the design of aircraft and spacecraft, of high speed trains, boats, and automobiles. All of these vehicles require maximum performance at minimum weight to keep fuel consumption low and conserve resources. Here, MDO can deliver mathematically based design tools to create systems with optimum performance subject to the constraints of disciplines such as structures, aerodynamics, controls, etc. Although some applications of MDO are beginning to surface, the key to a widespread use of this technology lies in the improvement of its efficiency. This aspect is investigated here for the MDO subset of structural optimization, i.e., for the weight minimization of a given structure under size, strength, and displacement constraints. Specifically, finite element based multilevel optimization of structures (here, statically indeterminate trusses and beams for proof of concept) is performed. In the system level optimization, the design variables are the coefficients of assumed displacement functions, and the load unbalance resulting from the solution of the stiffness equations is minimized. Constraints are placed on the deflection amplitudes and the weight of the structure. In the subsystems level optimizations, the weight of each element is minimized under the action of stress constraints, with the cross sectional dimensions as design variables. This approach is expected to prove very efficient, especially for complex structures, since the design task is broken down into a large number of small and efficiently handled subtasks, each with only a small number of variables. This partitioning will also allow for the use of parallel computing, first, by sending the system and subsystems level computations to two different processors, ultimately, by performing all subsystems level optimizations in a massively parallel manner on separate processors. It is expected that the subsystems level optimizations can be further improved through the use of controlled growth, a method which reduces an optimization to a more efficient analysis with only a slight degradation in accuracy. The efficiency of all proposed techniques is being evaluated relative to the performance of the standard single level optimization approach where the complete structure is weight minimized under the action of all given constraints by one processor and to the performance of simultaneous analysis and design which combines analysis and optimization into a single step. It is expected that the present approach can be expanded to include additional structural constraints (buckling, free and forced vibration, etc.) or other disciplines (passive and active controls, aerodynamics, etc.) for true MDO.
Striz, Alfred G.↗