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NASTRAN contains two techniques to solve the differential stiffness problems. One is incorporated in a new static analysis rigid format and the other is contained in a new normal modes analysis rigid format. The two techniques relative to computational accuracy and time of execution are compared.
A technique utilizing the finite element displacement method is developed for the static analysis of structures subjected to non-deterministic thermal loading in which the material properties, assumed isotropic, are temperature dependent. Matrix equations are developed for the first two statistical moments of the displacements using a third order series expansion for the displacements in terms of the random temperatures. Sample problems are included to demonstrate the range of applicability of the third order series solutions. These solutions are compared with results from Monte Carlo analyses and also, for some problems, with solutions obtained by numerically integrating equations for the statistical properties of the displacements. In general, it is shown that the effect of temperature dependent material properties can have a significant effect on the covariances of the displacements.
Structural dynamic environmental test levels were developed for the thematic mapper instrument, components of the Tandberg-Hanssen instrument, and components of the International Ultraviolet Explorer spacecraft using NASTRAN structural models and test data. Both static and dynamic NASTRAN analyses were used. The model size required could be as small as 300 degrees of freedom for the static analysis and as large as 4000 degrees of freedom or more for the high frequency dynamic analysis. An important step in the development of the levels is model verification by test. The launch environments that generally dictate many important features of the design of an instrument or component are steady state acceleration, sinusoidal vibration, and random vibration.
Methodologies are discussed on four of the major approaches to program upgrading -- namely dynamic testing, symbolic execution, formal verification and static analysis. The different patterns of strengths, weaknesses and applications of these approaches are shown. It is demonstrated that these patterns are in many ways complementary, offering the hope that they can be coordinated and unified into a single comprehensive program testing and verification system capable of performing a diverse and useful variety of error detection, verification and documentation functions.
The current versions of NASTRAN, i.e., NASA, MSC, and MAC support nonzero boundary displacements only in the static analysis. Forcing functions in the dynamic analysis formats allow only forces and pressures to exercise the mathematical model. A DMAP alter sequence to circumvent this limitation is described. For the direct harmonic problem, a simple change to module FRRD is incorporated to effect a more efficient use of the code.
Status and some recent developments in the application of reduction methods to nonlinear structural mechanics problems are summarized. The aspects of reduction methods discussed herein include: (1) selection of basis vectors in nonlinear static and dynamic problems, (2) application of reduction methods in nonlinear static analysis of structures subjected to prescribed edge displacements, and (3) use of reduction methods in conjunction with mixed finite element models. Numerical examples are presented to demonstrate the effectiveness of reduction methods in nonlinear problems. Also, a number of research areas which have high potential for application of reduction methods are identified.
(Automated Verification of Flight Software), a collection of tools for analyzing source programs written in FORTRAN and AED is documented. The quality and the reliability of flight software are improved by: (1) indented listings of source programs, (2) static analysis to detect inconsistencies in the use of variables and parameters, (3) automated documentation, (4) instrumentation of source code, (5) retesting guidance, (6) analysis of assertions, (7) symbolic execution, (8) generation of verification conditions, and (9) simplification of verification conditions. Use of AVFS in the verification of flight software is described.
A finite element model that is suitable for the static analysis of shells of revolution with arbitrary local deviations is presented. The model employs three types of elements: rotational, general, and transitional shell elements. The rotational shell elements are used in the region where the shell is axisymmetric. The general shell element are used in the local region of the deviation. The transitional shell elements connect these two distinctively different types of elements and make it possible to combine them in a single analysis. The form of the global stiffness matrix resulting when different forms of nodal degrees of freedom are combined is illustrated. The coupling of harmonic degrees of freedom due to the locally nonaxisymmetric geometry was studied. The use of a substructuring technique and separate partial harmonic analysis is recommended.
Static analysis, dynamic analysis, and computer programs are discussed. Spur gear formulae and involute profile development and deflection are also discussed.
Static analysis and a computer structural model for the large 64-m antenna pedestal are developed using the MSC version of the NASTRAN program. This model was necessary to conduct a variety of hydrostatic bearing rehabilitation studies. The results obtained from the model show that the top surface deflections due to pad loads are in good agreement with the results previously obtained from a simplified "shortcut' analytical model, and also in agreement with field measurements. In addition, the displacement and force distributions as well as the state of stress and strain are obtained.
Static analysis and a computer structural model for the large 64-m antenna pedestal are developed using the MSC version of the NASTRAN program. This improved pedestal model includes the launch areas and the actual pressure pattern of the oil under the hydrostatic bearing pad. The results obtained from the new improved model have indicated that the deflections due to pad loads are in good agreement with field measurements. The top surface deflection of the pedestal obtained from the NASTRAN model is used as an input to the oil film computer program to determine the minimum oil film thickness under the pad.
A static analysis is given of the problem of an elastic layer perfectly bonded, except for a frictionless interface crack, to a dissimilar elastic half-plane. The free surface of the layer is loaded by a finite pressure distribution directly over the crack. The problem is formulated using the two dimensional linear elasticity equations. Using Fourier transforms, the governing equations are converted to a pair of coupled singular integral equations. The integral equations are reduced to a set of simultaneous algebraic equations by expanding the unknown functions in a series of Jacobi polynomials and then evaluating the singular Cauchy-type integrals. The resulting equations are found to be ill-conditioned and, consequently, are solved in the least-squares sense. Results from the analysis show that, under a normal pressure distribution on the free surface of the layer and depending on the combination of geometric and material parameters, the ends of the crack can open. The resulting stresses at the crack-tips are singular, implying that crack growth is possible. The extent of the opening and the crack-top stress intensity factors depend on the width of the pressure distribution zone, the layer thickness, and the relative material properties of the layer and half-plane.
Presented is structural dynamics modeling of two multibody space structural configurations. The first configuration is a generic space station model of a cylindrical habitation module, two solar array panels, radiator panel, and central connecting tube. The second is a 15-m hoop-column antenna. Discussed is the special joint elimination sequence used for these large finite element models, so that eigenvalues could be extracted. The generic space station model aided test configuration design and analysis/test data correlation. The model consisted of six finite element models, one of each substructure and one of all substructures as a system. Static analysis and tests at the substructure level fine-tuned the finite element models. The 15-m hoop-column antenna is a truss column and structural ring interconnected with tension stabilizing cables. To the cables, pretensioned mesh membrane elements were attached to form four parabolic shaped antennae, one per quadrant. Imposing thermal preloads in the cables and mesh elements produced pretension in the finite element model. Thermal preload variation in the 96 control cables was adjusted to maintain antenna shape within the required tolerance and to give pointing accuracy.
Practical and reliable estimators of the discretization errors in engineering problems are developed. Error indicators for identifying the regions or elements of the solution domain which are likely to have the largest discretization errors are presented, and a simple computational procedure for improving the accuracy of the finite element solutions for shell problems is given. The similarities between the proposed procedure and a preconditioned conjugate gradient (PCG) technique are identified and exploited to generate pointwise error indicators from the PCG technique. Numerical examples in the linear static analysis of shells are presented.
General mixing formulas are derived for discrete scatterers immersed in a host medium. The inclusion particles are assumed to be ellipsoidal. The electric field inside the scatterers is determined by quasi-static analysis, assuming the diameter of the inclusion particles to be much smaller than one wavelength. The results are applicable to general multiphase mixtures, and the scattering ellipsoids of the different phases can have different sizes and arbitrary ellipticity distribution and axis orientation, i.e., the mixture may be isotropic or anisotropic. The resulting mixing formula is nonlinear and is suitable for iterative solutions. The formula contains a quantity called the apparent permittivity, and with different choices of this quantity, the result leads to the generalized Lorentz-Lorenz formula, the generalized Polder-van Santen formula, and the generalized coherent potential-quasicrystalline approximation formula. The results are applied to calculating the complex effective permittivity of dry and wet snow, and sea ice.
Report describes theoretical and experimental studies of perception of depth by human operators through stereoscopic video systems. Purpose of such studies to optimize dual-camera configurations used to view workspaces of remote manipulators at distances of 1 to 3 m from cameras. According to analysis, static stereoscopic depth distortion decreased, without decreasing stereoscopitc depth resolution, by increasing camera-to-object and intercamera distances and camera focal length. Further predicts dynamic stereoscopic depth distortion reduced by rotating cameras around center of circle passing through point of convergence of viewing axes and first nodal points of two camera lenses.
Knowledge-based systems have the potential to greatly increase the capabilities of future aircraft and spacecraft and to significantly reduce support manpower needed for the space station and other space missions. However, a credible validation methodology must be developed before knowledge-based systems can be used for life- or mission-critical applications. Experience with conventional software has shown that the use of good software engineering techniques and static analysis tools can greatly reduce the time needed for testing and simulation of a system. Since exhaustive testing is infeasible, reliability must be built into the software during the design and implementation phases. Unfortunately, many of the software engineering techniques and tools used for conventional software are of little use in the development of knowledge-based systems. Therefore, research at Langley is focused on developing a set of guidelines, methods, and prototype validation tools for building highly reliable, knowledge-based systems. The use of a comprehensive methodology for building highly reliable, knowledge-based systems should significantly decrease the time needed for testing and simulation. A proven record of delivering reliable systems at the beginning of the highly visible testing and simulation phases is crucial to the acceptance of knowledge-based systems in critical applications.
Despite its powerful analytical capabilities, COSMIC/NASTRAN lacks adequate post-processing adroitness. PATRAN, on the other hand is widely accepted for its graphical capabilities. A nonproprietary, public domain code mnemonically titled CPI (for COSMIC/NASTRAN-PATRAN Interface) is designed to manipulate a large number of files rapidly and efficiently between the two parent codes. In addition to PATRAN's results file preparation, CPI also prepares PATRAN's P/PLOT data files for xy plotting. The user is prompted for necessary information during an interactive session. Current implementation supports NASTRAN's displacement approach including the following rigid formats: (1) static analysis, (2) normal modal analysis, (3) direct transient response, and (4) modal transient response. A wide variety of data blocks are also supported. Error trapping is given special consideration. A sample session with CPI illustrates its simplicity and ease of use.