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MATHPAC image-analysis library is collection of general-purpose mathematical and statistical routines and special-purpose data-analysis and pattern-recognition routines for image analysis. MATHPAC library consists of Linear Algebra, Optimization, Statistical-Summary, Densities and Distribution, Regression, and Statistical-Test packages.
A stress analysis of a pressurized shallow cylindrical shell containing two collinear axial cracks of equal length was conducted. The mathematical relationships for conducting the stress analysis are developed. Graphs are presented to show the stress intensity factor ratio in the cylindrical shell and the bending components of the stress intensity factor ratio.
Analytical techniques for the analysis of stall/spin flight test data are reviewed by discussing (1) certain special flight instrumentation issues, (2) the mathematical modeling techniques, and (3) the analysis of post stall and spinning flight of general aviation airplanes. The angles of attack, sideslip, roll, pitch, and yaw are derived from measurements of angular velocity and linear acceleration. The key to the success of this approach is to simultaneously estimate both the biases in the instrumentation and the initial conditions. Techniques for determining stability derivatives from flight data are applied to angles of attack too high for stabilized flight. This practice greatly expands the range over which aerodynamic characteristics can be determined from flight test. Nonlinear terms in certain aerodynamic functions are shown to be valid by comparing them with the trends of results at different angles of attack. A very old technique of studying spins is extended and applied to some modern light airplanes. Airplanes for which the wing provides the dominant moments during spins, offer the possibility of linking spin characteristics to longitudinal data.
Concepts regarding approximate mathematical models treated rigorously. Paper presents new results in analysis of structural identifiability, equivalence, and near equivalence between mathematical models and physical processes they represent. Helps establish rigorous mathematical basis for concepts related to structural identifiability and equivalence revealing fundamental requirements, tacit assumptions, and sources of error. "Structural identifiability," as used by workers in this field, loosely translates as meaning ability to specify unique mathematical model and set of model parameters that accurately predict behavior of corresponding physical system.
Because launch cost of a space structural system is often proportional to the launch volume and mass and there is no significant gravity in space, NASA's space exploration programs and various science missions have stimulated extensive use of ultra-lightweight deployable/inflatable structures. These structures are named here as Highly Flexible Structures (HFSs) because they are designed to undergo large displacements, rotations, and/or buckling without plastic deformation under normal operation conditions. Except recent applications to space structural systems, HFSs have been used in many mechanical systems, civil structures, aerospace vehicles, home appliances, and medical devices to satisfy space limitations, provide special mechanisms, and/or reduce structural weight. The extensive use of HFSs in today's structural engineering reveals the need of a design and analysis software and a database system with design guidelines for practicing engineers to perform computer-aided design and rapid prototyping of HFSs. Also to prepare engineering students for future structural engineering requires a new and easy-to- understand method of presenting the complex mathematics of the modeling and analysis of HFSs. However, because of the high flexibility of HFSs, many unique challenging problems in the modeling, design and analysis of HFSs need to be studied. The current state of research on HFSs needs advances in the following areas: (1) modeling of large rotations using appropriate strain measures, (2) modeling of cross-section warpings of structures, (3) how to account for both large rotations and cross- section warpings in 2D (two-dimensional) and 1D structural theories, (4) modeling of thickness thinning of membranes due to inflation pressure, pretension, and temperature change, (5) prediction of inflated shapes and wrinkles of inflatable structures, (6) development of efficient numerical methods for nonlinear static and dynamic analyses, and (7) filling the gap between geometrically exact elastic analysis and elastoplastic analysis. The objectives of this research project were: (1) to study the modeling, design, and analysis of deployable/inflatable ultra-lightweight structures, (2) to perform numerical and experimental studies on the static and dynamic characteristics and deployability of HFSs, (3) to derive guidelines for designing HFSs, (4) to develop a MATLAB toolbox for the design, analysis, and dynamic animation of HFSs, and (5) to perform experiments and establish an adequate database of post-buckling characteristics of HFSs.
Mathematical models based on the finite element method of structural analysis, as embodied in the NASTRAN computer code, are routinely used by the helicopter industry to calculate airframe static internal loads used for sizing structural members. Historically, less reliance has been placed on the vibration predictions based on these models. Beginning in the early 1980's NASA's Langley Research Center initiated an industry wide program with the objective of engendering the needed trust in vibration predictions using these models and establishing a body of modeling guides which would enable confident future prediction of airframe vibration as part of the regular design process. Emphasis in this paper is placed on the successful modeling of the Army/Boeing CH-47D which showed reasonable correlation with test data. A principal finding indicates that improved dynamic analysis requires greater attention to detail and perhaps a finer mesh, especially the mass distribution, than the usual stress model. Post program modeling efforts show improved correlation placing key modal frequencies in the b/rev range with 4 percent of the test frequencies.
Mathematical models describing vehicle dynamics as well as human behavior may be useful in evaluating driver performance and in establishing design criteria for vehicles more compatible with man. In 1977, a two level model of driver steering behavior was developed, but its parameters were identified for clear visibility conditions only. Since driver performance degrades under conditions of reduced visibility, e.g., fog, the two level model should be investigated to determine its applicability to such conditions. The data analysis of a recently performed driving simulation experiment showed that the model still performed reasonably well under fog conditions, although there was a degradation in its predictive capacity during fog. Some additional parameters affecting anticipation and lag time may improve the model's performance for reduced visibility conditions.
Flight control system design and analysis for aircraft rely on mathematical models of the vehicle dynamics. In addition to a six degree of freedom nonlinear simulation, the X-29A flight controls group developed a set of programs that calculate linear perturbation models throughout the X-29A flight envelope. The models include the aerodynamics as well as flight control system dynamics and were used for stability, controllability, and handling qualities analysis. These linear models were compared to flight test results to help provide a safe flight envelope expansion. A description is given of the linear models at three flight conditions and two flight control system modes. The models are presented with a level of detail that would allow the reader to reproduce the linear results if desired. Comparison between the response of the linear model and flight measured responses are presented to demonstrate the strengths and weaknesses of the linear models' ability to predict flight dynamics.
A program to develop analytical tools for evaluating the dynamic performance of Air Cushion Landing Systems (ACLS) is described. The heave (vertical) motion of the ACLS was analyzed, and the analysis was extended to cover coupled heave-pitch motions. The mathematical models developed are based on a fundamental analysis of the body dynamics and fluid mechanics of the aircraft-cushion-runway interaction. The air source characteristics, flow losses in the feeding ducts, trunk and cushion, the effects of fluid compressibility, and dynamic trunk deflections, including ground contact are considered. A computer program, based on the heave-pitch analysis, was developed to simulate the dynamic behavior of an ACLS during landing impact and taxi over an irregular runway. The program outputs include ACLS motions, loadings, pressures, and flows as a function of time. To illustrate program use, three basic types of simulations were carried out. The results provide an initial indication of ACLS performance during (1) a static drop, (2) landing impact, and (3) taxi over a runway irregularity.
This document contains papers presented at the Dual-Use Space Technology Transfer Conference and Exhibition held at the Johnson Space Center February 1-3, 1994. Possible technology transfers covered during the conference were in the areas of information access; innovative microwave and optical applications; materials and structures; marketing and barriers; intelligent systems; human factors and habitation; communications and data systems; business process and technology transfer; software engineering; biotechnology and advanced bioinstrumentation; communications signal processing and analysis; new ways of doing business; medical care; applications derived from control center data systems; human performance evaluation; technology transfer methods; mathematics, modeling, and simulation; propulsion; software analysis and decision tools systems/processes in human support technology; networks, control centers, and distributed systems; power; rapid development perception and vision technologies; integrated vehicle health management; automation technologies; advanced avionics; ans robotics technologies. More than 77 papers, 20 presentations, and 20 exhibits covering various disciplines were presented b experts from NASA, universities, and industry.
Selection of the best shape of a fillet in a tension bar such that no yielding occurs has long attracted the attention of engineers. Dimensions and notations for the bar and fillet are shown. With symmetry, only the upper half of the bar is considered. The optimal design problem is to find a boundary shape to minimize the total area of the fillet such that no yielding occurs. The classical boundary value problem is reduced to a variational or energy related problem which not only has excellent properties of existence and uniqueness but also provides the mathematical foundation for finite element analysis. The variational formulation may be viewed as the principle of virtual work and the finite element method as a application of the Galerkin method to the variational equation for approximate solution of the boundary value problem.
The overall objective of the gas chromatograph system studies is to generate fundamental design criteria and techniques to be used in the optimum design of the system. The particular tasks currently being undertaken are the comparison of two mathematical models of the chromatograph and the analysis of binary system data. The predictions of two mathematical models, an equilibrium absorption model and a non-equilibrium absorption model exhibit the same weaknesses in their inability to predict chromatogram spreading for certain systems. The analysis of binary data using the equilibrium absorption model confirms that, for the systems considered, superposition of predicted single component behaviors is a first order representation of actual binary data. Composition effects produce non-idealities which limit the rigorous validity of superposition.
The methodology for the establishment of spacecraft loads is strongly influenced by project constraints which include the cost, schedule and allowable weight. The most rigorous approach is the transient loads analysis which requires a composite mathematical model of the spacecraft and launch vehicle. The structural member loads for the entire composite structure are computed by applying the forcing functions, which represent various dynamic environments during the mission, to the composite model. Although this method ideally leads to a lightweight design, it is costly and time consuming due to complex interfaces involving many organizations. To reduce complexity and cost a shock spectra method has been used to design spacecraft structures. This method utilizes envelopes of shock spectra of launch vehicle accelerations obtained from analysis and/or flight measurements. Since only limited information on the launch vehicle model is involved in this process the design loads iteration cycle can be rapidly performed within the payload organization. In the present paper, these two methods will be evaluated by comparing the loads for several spacecraft. Flight measured loads will also be used in the evaluation.
The feasibility of a control system analysis approach to provide a design base for respiratory protective devices is considered. A system design approach requires that all functions and components of the system be mathematically identified in a model of the RPD. The mathematical notations describe the operation of the components as closely as possible. The individual component mathematical descriptions are then combined to describe the complete RPD. Finally, analysis of the mathematical notation by control system theory is used to derive compensating component values that force the system to operate in a stable and predictable manner.
Analytical model for generation of earth-moon trajectory analysis data
Numerical methods, programs, and mathematical models for use in digital computer-aided circuit analysis and design
Test facility to verify design concepts and mathematical models of chromatograph for atmospheric composition analysis of Mars
Mathematical model for predicting droplet radius, charge-to-mass, and velocity of electrostatic dispersion in liquid