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The benefits of structural dynamics modeling methods in aerospace structures are reviewed. Four major issues in structural dynamics modeling are discussed which encompass most of its subdisciplines: reduced order modeling, constraints in problems with large motions, computational strategies, and fundamental methods. Directions for future research in these areas are addressed.
Assessing solution error continues to be a formidable task when numerically solving practical flow problems. Currently, grid refinement is the primary method used for error assessment. The minimum grid spacing requirements to achieve design order accuracy for a structured-grid scheme are determined for several simple examples using truncation error evaluations on a sequence of meshes. For certain methods and classes of problems, obtaining design order may not be sufficient to guarantee low error. Furthermore, some schemes can require much finer meshes to obtain design order than would be needed to reduce the error to acceptable levels. Results are then presented from realistic problems that further demonstrate the challenges associated with using grid refinement studies to assess solution accuracy.
For analysis of large-scale electromagnetic scattering problems, high-frequency asymptotic methods are fast but approximate, whereas low-frequency numerical methods are accurate but slow. Neither can produce an efficient and accurate solution to scattering by large bodies containing small structures. A promising approach is to combine the best features of both types of methods to produce a hybrid technique that is sufficiently fast, reasonably accurate, and applicable to a class of unsolvable problems such as the scatterers mentioned above. There are two extremes for this type of hybridization. One is simply to superimpose solutions from asymptotic and numerical methods. While this approach is most widely used in practical applications, it neglects the interactions between the two solutions, which can be significant in many problems. The other extreme is to combine an asymptotic and a numerical method in an exact manner. In this approach, the effect of a large body is included by incorporating its diffraction into the Green's function in the integral equation for the small structures, which accounts for all interactions. While this approach is accurate, it is difficult to be implemented in a general-purpose computer code because of its complex nature. A more practical approach is to develop a technique that can include all significant interactions and neglect all trivial interactions. The resulting hybrid technique can produce sufficient accuracy and can be implemented in a general-purpose computer code. In this paper, we develop a technique that combines the shooting and- bouncing-ray (SBR) method and the method of moments (MoM) to solve for the scattering by large conducting bodies with small structures mounted on their surfaces.
A method is developed to compute frequency response and acoustic radiation of a complex shell. The axisymmetric geometry of the shell includes cylindrical, conical, and spherical segments stiffened by discrete rings and bulkheads. The shell is coupled to internal masses and elastic frames. Shell segments are treated by transfer matrices. Rings, bulkheads, frames, and concentrated masses are treated by impedances at junctions of segments. The shell is coupled to an external acoustic fluid treated by Green's function and curved surface elements. A major issue facing the method's treatment of the fluid would be lack of existence or uniqueness encountered in the uncoupled, external acoustic problem at characteristic wavenumbers. By using a simple spherical shell, without internal structures, this potential hindrance is shown not to arise. A fuller application of the method awaits subsequent results.
The extended interior penalty function formulation is implemented. A rational method for determining the transition between the interior and extended parts is set forth. The formulation includes a straightforward method for avoiding design points with some negative components, which are physically meaningless in structural analysis. The technique, when extended to problems involving parametric constraints, can facilitate closed form integration of the penalty terms over the most important parts of the parameter interval. The method lends itself well to the use of approximation concepts, such as design variable linking, constraint deletion and Taylor series expansions of response quantities in terms of design variables. Examples demonstrating the algorithm, in the context of planar orthogonal frames subjected to ground motion, are included.
In the investigation, the filtering problem is considered in the continuous time domain. The postulated simple suboptimal nonlinear filter structure closely parallels the structure of the Kalman-Bucy optimal linear filter algorithm. Two filter performance evaluation methods are developed based on the Kolmogorov equations for the transition density of Markov processes. The expansions in the approximations for the nonlinear system and observation functions are in effect carried out up to second-order terms in both methods. The description of the filter's performance is sought in terms of second-order statistics in both methods.
A large deflection analysis was developed for NASTRAN level 16 as an alternative to Rigid Format 4. A progress report is presented for a long term, general nonlinear analysis NASTRAN project, which contains (1) the theory of the structural analysis and numerical analysis methods presently used, and (2) some simple test problems comparing the new analysis with Rigid Format 4.
The general application of finite element methodology and the specific application of NASTRAN to a wide variety of static and dynamic structural problems are described. Topics include: fluids and thermal applications, NASTRAN programming, substructuring methods, unique new applications, general auxiliary programs, specific applications, and new capabilities.
Design considerations were evaluated for general purpose finite element systems to maximize performance when installed on distributed computer hardware/software systems. It is shown how the features of current minicomputers complement those of a modular implementation of the finite element method for increasing the control, speed, and visibility (interactive graphics) in solving structural problems at reduced cost. The approach used is to implement a finite element system in a distributed computer environment to solve structural problems and to explore alternatives in distributing finite element computations.
Aspects of an attitude control system were studied and developed for a large space base that is structurally flexible and whose mass properties change rather dramatically during its orbital lifetime. Topics of discussion include the following: (1) space base orbital pointing and maneuvering; (2) angular momentum sizing of actuators; (3) momentum desaturation selection and sizing; (4) multilevel control technique applied to configuration one; (5) one-dimensional model simulation; (6) N-body discrete coordinate simulation; (7) structural analysis math model formulation; and (8) discussion of control problems and control methods.
The major categories of current ICASE research programs addressed include: numerical methods, with particular emphasis on the development and analysis of basic numerical algorithms; control and parameter identification problems, with emphasis on effective numerical methods; computational problems in engineering and physical sciences, particularly fluid dynamics, acoustics, and structural analysis; and computer systems and software, especially vector and parallel computers.
Theoretical and numerical results are presented for inverse problems involving estimation of spatially varying parameters such as stiffness and damping in distributed models for elastic structures such as Euler-Bernoulli beams. An outline of algorithms used and a summary of computational experiences are presented.
A close link is established between open loop optimal control theory and optimal design by noting certain similarities in the gradient calculations. The resulting benefits include a unified approach, together with physical insights in design sensitivity analysis, and an efficient approach for simultaneous optimal control and design. Both matrix displacement and matrix force methods are considered, and results are presented for dynamic systems, structures, and elasticity problems.
An unconventional framework is described for the design of decentralized controllers for large flexible structures. In contrast to conventional control system design practice which begins with a model of the open loop plant, the controlled plant is assembled from controlled components in which the modeling phase and the control design phase are integrated at the component level. The developed framework is called controlled component synthesis (CCS) to reflect that it is motivated by the well developed Component Mode Synthesis (CMS) methods which were demonstrated to be effective for solving large complex structural analysis problems for almost three decades. The design philosophy behind CCS is also closely related to that of the subsystem decomposition approach in decentralized control.
A complete list of reports from the Institute for Computer Applications in Science and Engineering (ICASE) is presented. The major categories of the current ICASE research program are: numerical methods, with particular emphasis on the development and analysis of basic numerical algorithms; control and parameter identification problems, with emphasis on effectual numerical methods; computational problems in engineering and the physical sciences, particularly fluid dynamics, acoustics, structural analysis, and chemistry; computer systems and software, especially vector and parallel computers, microcomputers, and data management. Since ICASE reports are intended to be preprints of articles that will appear in journals or conference proceedings, the published reference is included when it is available.
There are algorithms for finding zeros or fixed points of nonlinear systems of equations that are globally convergent for almost all starting points, i.e., with probability one. The essence of all such algorithms is the construction of an appropriate homotopy map and then tracking some smooth curve in the zero set of this homotopy map. HOMPACK is a mathematical software package implementing globally convergent homotopy algorithms with three different techniques for tracking a homotopy zero curve, and has separate routines for dense and sparse Jacobian matrices. The HOMPACK algorithms for sparse Jacobian matrices use a preconditioned conjugate gradient algorithm for the computation of the kernel of the homotopy Jacobian matrix, a required linear algebra step for homotopy curve tracking. Here, variants of the conjugate gradient algorithm are implemented in the context of homotopy curve tracking and compared with Craig's preconditioned conjugate gradient method used in HOMPACK. The test problems used include actual large scale, sparse structural mechanics problems.
A set of massively parallel computational procedures are formulated to make finite element method based space frame and truss structural response analyses and stochastic method based structural optimization solution superefficient. Several example frame structural analysis and truss optimization problems are presented for demonstration purposes. All calculations are made on the massively parallel environment of CM-2 computer.
Sounds of Silence. Using a general systems approach, factors and components of the acoustical design process for an isolated, confined space community in a torus space enclosure are considered. These components include the following: organizational structure and its effect on alternatives; problem definition and limits; criteria and priorities; methods of data gathering; modelling and measurement of the whole system and its components; decision methods; and design scenario of the acoustics of the complex, socio-technical space community system with emphasis on the human factors.