SEARCH · Engineering Papers

Results for “Numerical software”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 955 records · Page 53

All sources NASA NTRS DOE OSTI

NASA NTRS1989

Stable Kalman filters for processing clock measurement data

Kalman filters have been used for some time to process clock measurement data. Due to instabilities in the standard Kalman filter algorithms, the results have been unreliable and difficult to obtain. During the past several years, stable forms of the Kalman filter have been developed, implemented, and used in many diverse applications. These algorithms, while algebraically equivalent to the standard Kalman filter, exhibit excellent numerical properties. Two of these stable algorithms, the Upper triangular-Diagonal (UD) filter and the Square Root Information Filter (SRIF), have been implemented to replace the standard Kalman filter used to process data from the Deep Space Network (DSN) hydrogen maser clocks. The data are time offsets between the clocks in the DSN, the timescale at the National Institute of Standards and Technology (NIST), and two geographically intermediate clocks. The measurements are made by using the GPS navigation satellites in mutual view between clocks. The filter programs allow the user to easily modify the clock models, the GPS satellite dependent biases, and the random noise levels in order to compare different modeling assumptions. The results of this study show the usefulness of such software for processing clock data. The UD filter is indeed a stable, efficient, and flexible method for obtaining optimal estimates of clock offsets, offset rates, and drift rates. A brief overview of the UD filter is also given.

Clements, P. A.↗

NASA NTRS1998

Expert System Architecture for Rocket Engine Numerical Simulators: A Vision

Simulation of any complex physical system like rocket engines involves modeling the behavior of their different components using mostly numerical equations. Typically a simulation package would contain a set of subroutines for these modeling purposes and some other ones for supporting jobs. A user would create an input file configuring a system (part or whole of a rocket engine to be simulated) in appropriate format understandable by the package and run it to create an executable module corresponding to the simulated system. This module would then be run on a given set of input parameters in another file. Simulation jobs are mostly done for performance measurements of a designed system, but could be utilized for failure analysis or a design job such as inverse problems. In order to use any such package the user needs to understand and learn a lot about the software architecture of the package, apart from being knowledgeable in the target domain. We are currently involved in a project in designing an intelligent executive module for the rocket engine simulation packages, which would free any user from this burden of acquiring knowledge on a particular software system. The extended abstract presented here will describe the vision, methodology and the problems encountered in the project. We are employing object-oriented technology in designing the executive module. The problem is connected to the areas like the reverse engineering of any simulation software, and the intelligent systems for simulation.

Mitra, D.↗

NASA NTRS1991

Numerical propulsion system simulation

The cost of implementing new technology in aerospace propulsion systems is becoming prohibitively expensive. One of the major contributors to the high cost is the need to perform many large scale system tests. Extensive testing is used to capture the complex interactions among the multiple disciplines and the multiple components inherent in complex systems. The objective of the Numerical Propulsion System Simulation (NPSS) is to provide insight into these complex interactions through computational simulations. This will allow for comprehensive evaluation of new concepts early in the design phase before a commitment to hardware is made. It will also allow for rapid assessment of field-related problems, particularly in cases where operational problems were encountered during conditions that would be difficult to simulate experimentally. The tremendous progress taking place in computational engineering and the rapid increase in computing power expected through parallel processing make this concept feasible within the near future. However it is critical that the framework for such simulations be put in place now to serve as a focal point for the continued developments in computational engineering and computing hardware and software. The NPSS concept which is described below will provide that framework.

R.W. Claus↗

NASA NTRS1990

Numerical propulsion system simulation

Lytle, John K.↗

NASA NTRS2007

NASA Tech Briefs, November 2007

Topics include: Wireless Measurement of Contact and Motion Between Contact Surfaces; Wireless Measurement of Rotation and Displacement Rate; Portable Microleak-Detection System; Free-to-Roll Testing of Airplane Models in Wind Tunnels; Cryogenic Shrouds for Testing Thermal-Insulation Panels; Optoelectronic System Measures Distances to Multiple Targets; Tachometers Derived From a Brushless DC Motor; Algorithm-Based Fault Tolerance for Numerical Subroutines; Computational Support for Technology- Investment Decisions; DSN Resource Scheduling; Distributed Operations Planning; Phase-Oriented Gear Systems; Freeze Tape Casting of Functionally Graded Porous Ceramics; Electrophoretic Deposition on Porous Non- Conductors; Two Devices for Removing Sludge From Bioreactor Wastewater; Portable Unit for Metabolic Analysis; Flash Diffusivity Technique Applied to Individual Fibers; System for Thermal Imaging of Hot Moving Objects; Large Solar-Rejection Filter; Improved Readout Scheme for SQUID-Based Thermometry; Error Rates and Channel Capacities in Multipulse PPM; Two Mathematical Models of Nonlinear Vibrations; Simpler Adaptive Selection of Golomb Power-of- Two Codes; VCO PLL Frequency Synthesizers for Spacecraft Transponders; Wide Tuning Capability for Spacecraft Transponders; Adaptive Deadband Synchronization for a Spacecraft Formation; Analysis of Performance of Stereoscopic-Vision Software; Estimating the Inertia Matrix of a Spacecraft; Spatial Coverage Planning for Exploration Robots; and Increasing the Life of a Xenon-Ion Spacecraft Thruster.

Source record↗

NASA NTRS2011

High-Performance Data Analysis Tools for Sun-Earth Connection Missions

The data analysis tool of choice for many Sun-Earth Connection missions is the Interactive Data Language (IDL) by ITT VIS. The increasing amount of data produced by these missions and the increasing complexity of image processing algorithms requires access to higher computing power. Parallel computing is a cost-effective way to increase the speed of computation, but algorithms oftentimes have to be modified to take advantage of parallel systems. Enhancing IDL to work on clusters gives scientists access to increased performance in a familiar programming environment. The goal of this project was to enable IDL applications to benefit from both computing clusters as well as graphics processing units (GPUs) for accelerating data analysis tasks. The tool suite developed in this project enables scientists now to solve demanding data analysis problems in IDL that previously required specialized software, and it allows them to be solved orders of magnitude faster than on conventional PCs. The tool suite consists of three components: (1) TaskDL, a software tool that simplifies the creation and management of task farms, collections of tasks that can be processed independently and require only small amounts of data communication; (2) mpiDL, a tool that allows IDL developers to use the Message Passing Interface (MPI) inside IDL for problems that require large amounts of data to be exchanged among multiple processors; and (3) GPULib, a tool that simplifies the use of GPUs as mathematical coprocessors from within IDL. mpiDL is unique in its support for the full MPI standard and its support of a broad range of MPI implementations. GPULib is unique in enabling users to take advantage of an inexpensive piece of hardware, possibly already installed in their computer, and achieve orders of magnitude faster execution time for numerically complex algorithms. TaskDL enables the simple setup and management of task farms on compute clusters. The products developed in this project have the potential to interact, so one can build a cluster of PCs, each equipped with a GPU, and use mpiDL to communicate between the nodes and GPULib to accelerate the computations on each node.

Messmer, Peter↗

NASA NTRS1987

Stochastic and hybrid-stress plate/shell finite elements for hot-section components

The research effort in the Center for the Advancement of Computational Mechanics at Georgia Tech has two main thrusts. The first of these is the development of special approaches for the numerical stress analysis of solids and structures whose material and geometric properties are uncertain. The second seeks to develop and implement high-efficiency plate and shell elements. The stochastic element method, currently being implemented, will be able to more accurately portray the probabilistic nature of stress, strain, and displacement in actual structures. Current research has provided a hybrid-stress shell element whose behavior is acceptable for aspect ratios as high as 30 to 1. Thus, substantially more complex analyses will be practicable as soon as this element is fully implemented. An additional advantage of the hybrid approach is that it permits more accurate stress-recovery at the upper and lower surfaces of the shell, an important consideration in high thickness-gradient applications. The software associated with the above research is being implemented in the form of extensions to the Nessus code. The hybrid shell element has been successfully tested in several small-deformation elastic analyses. The theoretical formulation of the stochastic elements is essentially complete; its implementation is just beginning.

Atluri, S. N.↗

NASA NTRS1992

Database activity in the Italian Astronet: DIRA 2

The development and utilization of informational archives and databases started, in the Italian Astronet Project, in the middle of 1983. In that year, a small group of astronomers and some more technical people met together in an Astronet working group, with a common, painful experience in managing astronomical catalogues and archives with computers. Nowadays, some years later, some software packages and the contents of both, a relative general database and several local databases represent the work and the effort of the group. The systems have been conceived and developed keeping in mind the original goal of the group: to allow the single atronomer to make a free use of original data. The main package (DIRA) was rewritten, after some years of use, to fully take advantage of the several suggestions of the astronomer that used it and gathered experiences in the astronomical catalog's management. A more technical goal was to install the whole system, born and developed in the vms environment, on unix and unix-like systems. This new version, DIRA2, has a new user interface, a query language with SQL style commands supporting numerical and character functions also and a set of commands to create new catalogues from existing data. The graphics commands are also more powerful with respect to the previous version. DIRA (and DIRA2 of course) philosophy and design are very simple and proved to be very appreciated by astronomers, namely, to normalize and homogenize, at minimum, astronomical catalogues, to collect satisfactory astronomical documentation on their contents and, finally, to allow an astronomical approach to the dialogue with the database. DIRA2 is currently used in most Italian astronomical institutes to retrieve data from a still growing database of about 140 well documented and controlled astronomical catalogues, for the identification of objects and the preparation of a 'medium size' survey, in astrometry and in the creation of new catalogues.

Benacchio, L.↗

NASA NTRS1998

Flight Testing and Real-Time System Identification Analysis of a UH-60A Black Hawk Helicopter with an Instrumented External Sling Load

Helicopter external air transportation plays an important role in today's world. For both military and civilian helicopters, external sling load operations offer an efficient and expedient method of handling heavy, oversized cargo. With the ability to reach areas otherwise inaccessible by ground transportation, helicopter external load operations are conducted in industries such as logging, construction, and fire fighting, as well as in support of military tactical transport missions. Historically, helicopter and load combinations have been qualified through flight testing, requiring considerable time and cost. With advancements in simulation and flight test techniques there is potential to substantially reduce costs and increase the safety of helicopter sling load certification. Validated simulation tools make possible accurate prediction of operational flight characteristics before initial flight tests. Real time analysis of test data improves the safety and efficiency of the testing programs. To advance these concepts, the U.S. Army and NASA, in cooperation with the Israeli Air Force and Technion, under a Memorandum of Agreement, seek to develop and validate a numerical model of the UH-60 with sling load and demonstrate a method of near real time flight test analysis. This thesis presents results from flight tests of a U.S. Army Black Hawk helicopter with various external loads. Tests were conducted as the U.S. first phase of this MOA task. The primary load was a container express box (CONEX) which contained a compact instrumentation package. The flights covered the airspeed range from hover to 70 knots. Primary maneuvers were pitch and roll frequency sweeps, steps, and doublets. Results of the test determined the effect of the suspended load on both the aircraft's handling qualities and its control system's stability margins. Included were calculations of the stability characteristics of the load's pendular motion. Utilizing CIFER(R) software, a method for near-real time system identification was also demonstrated during the flight test program.

McCoy, Allen H.↗

NASA NTRSDate not supplied

An Interactive MATLAB Program for Fitting Transfer Functions to Frequency Responses

A computer program called FRFit (Frequency Response Fitting) is described for fitting single-input single-output transfer function models to empirical frequency response data. The program is interactive in that the user specifies ``elementary factors'' (gain, delay, pure differentiators and integrators, and first- and second-order zeros and poles) by entering numerical values or moving sliders in a graphical user interface. A nonlinear optimization can then be performed to obtain maximum likelihood estimates of transfer function parameters and uncertainties to provide feedback on the modeling and refine estimates. Several examples are discussed, including the identification of aircraft pitch dynamics from simulation data and data reported in the literature, approximating Theodorsen's function of unsteady aerodynamics, and obtaining a reduced-order model of a computational fluid dynamics code describing the unsteady aerodynamics around an aeroelastic wing. The program has some usefulness as a teaching aid, and can be applied to model structure determination, reduced-order modeling, preliminary analysis, and simple system identification problems. The program was written in MATLAB and is planned for public release through the NASA Software Catalog.

System identification↗

NASA NTRS2004

The Office of the Materials Division

I was assigned to the Materials Division, which consists of the following branches; the Advanced Metallics Branch/5120-RMM, Ceramics Branch/5130-RMC, Polymers Branch/5150-RMP, and the Durability and Protective Coatings Branch/5160-RMD. Mrs. Pamela Spinosi is my assigned mentor. She was assisted by Ms.Raysa Rodriguez/5100-RM and Mrs.Denise Prestien/5100-RM, who are both employed by InDyne, Inc. My primary assignment this past summer was working directly with Ms. Rodriguez, assisting her with setting up the Integrated Financial Management Program (IFMP) 5130-RMC/Branch procedures and logs. These duties consisted of creating various spreadsheets for each individual branch member, which were updated daily. It was not hard to familiarize myself with these duties since this is my second summer working with Ms Rodriguez at NASA Glenn Research Center. RMC ordering laboratory, supplies and equipment for the Basic Materials Laboratory (Building 106) using the IF'MP/Purchase Card (P-card), a NASA-wide software program. I entered into the IFMP/Travel and Requisitions System, new Travel Authorizations for the 5130-RMC Civil Servant Branch Members. I also entered and completed Travel Vouchers for the 5130-RMC Ceramics Branch. I assisted in the Division Office creating new Emergency Contact list for the Materials Division. I worked with Dr. Hugh Gray, the Division Chief, and Dr. Ajay Misra, the 5130-RMC Branch Chief, on priority action items, with a close deadline, for a large NASA Proposal. Another project was working closely with Ms. Rodriguez in organizing and preparing for Dr. Ajay K. Misra's SESCDP (two year detail). This consisted of organizing files, file folders, personal information, and recording all data material onto CD's and printing all presentations for display in binders. I attended numerous Branch meetings, and observed many changes in the Branch Management organization.

Ramsey, amanda J.↗

NASA NTRS2013

Sample Analysis at Mars Instrument Simulator

The Sample Analysis at Mars Instrument Simulator (SAMSIM) is a numerical model dedicated to plan and validate operations of the Sample Analysis at Mars (SAM) instrument on the surface of Mars. The SAM instrument suite, currently operating on the Mars Science Laboratory (MSL), is an analytical laboratory designed to investigate the chemical and isotopic composition of the atmosphere and volatiles extracted from solid samples. SAMSIM was developed using Matlab and Simulink libraries of MathWorks Inc. to provide MSL mission planners with accurate predictions of the instrument electrical, thermal, mechanical, and fluid responses to scripted commands. This tool is a first example of a multi-purpose, full-scale numerical modeling of a flight instrument with the purpose of supplementing or even eliminating entirely the need for a hardware engineer model during instrument development and operation. SAMSIM simulates the complex interactions that occur between the instrument Command and Data Handling unit (C&DH) and all subsystems during the execution of experiment sequences. A typical SAM experiment takes many hours to complete and involves hundreds of components. During the simulation, the electrical, mechanical, thermal, and gas dynamics states of each hardware component are accurately modeled and propagated within the simulation environment at faster than real time. This allows the simulation, in just a few minutes, of experiment sequences that takes many hours to execute on the real instrument. The SAMSIM model is divided into five distinct but interacting modules: software, mechanical, thermal, gas flow, and electrical modules. The software module simulates the instrument C&DH by executing a customized version of the instrument flight software in a Matlab environment. The inputs and outputs to this synthetic C&DH are mapped to virtual sensors and command lines that mimic in their structure and connectivity the layout of the instrument harnesses. This module executes, and thus validates, complex command scripts prior to their up-linking to the SAM instrument. As an output, this module generates synthetic data and message logs at a rate that is similar to the actual instrument.

Benna, Mehdi↗

NASA NTRS2014

Turbulence Modeling Verification and Validation

Computational fluid dynamics (CFD) software that solves the Reynolds-averaged Navier-Stokes (RANS) equations has been in routine use for more than a quarter of a century. It is currently employed not only for basic research in fluid dynamics, but also for the analysis and design processes in many industries worldwide, including aerospace, automotive, power generation, chemical manufacturing, polymer processing, and petroleum exploration. A key feature of RANS CFD is the turbulence model. Because the RANS equations are unclosed, a model is necessary to describe the effects of the turbulence on the mean flow, through the Reynolds stress terms. The turbulence model is one of the largest sources of uncertainty in RANS CFD, and most models are known to be flawed in one way or another. Alternative methods such as direct numerical simulations (DNS) and large eddy simulations (LES) rely less on modeling and hence include more physics than RANS. In DNS all turbulent scales are resolved, and in LES the large scales are resolved and the effects of the smallest turbulence scales are modeled. However, both DNS and LES are too expensive for most routine industrial usage on today's computers. Hybrid RANS-LES, which blends RANS near walls with LES away from walls, helps to moderate the cost while still retaining some of the scale-resolving capability of LES, but for some applications it can still be too expensive. Even considering its associated uncertainties, RANS turbulence modeling has proved to be very useful for a wide variety of applications. For example, in the aerospace field, many RANS models are considered to be reliable for computing attached flows. However, existing turbulence models are known to be inaccurate for many flows involving separation. Research has been ongoing for decades in an attempt to improve turbulence models for separated and other nonequilibrium flows. When developing or improving turbulence models, both verification and validation are important steps in the process. Verification insures that the CFD code is solving the equations as intended (no errors in the implementation). This is typically done either through the method of manufactured solutions (MMS) or through careful step-by-step comparisons with other verified codes. After the verification step is concluded, validation is performed to document the ability of the turbulence model to represent different types of flow physics. Validation can involve a large number of test case comparisons with experiments, theory, or DNS. Organized workshops have proved to be valuable resources for the turbulence modeling community in its pursuit of turbulence modeling verification and validation. Workshop contributors using different CFD codes run the same cases, often according to strict guidelines, and compare results. Through these comparisons, it is often possible to (1) identify codes that have likely implementation errors, and (2) gain insight into the capabilities and shortcomings of different turbulence models to predict the flow physics associated with particular types of flows. These are valuable lessons because they help bring consistency to CFD codes by encouraging the correction of faulty programming and facilitating the adoption of better models. They also sometimes point to specific areas needed for improvement in the models. In this paper, several recent workshops are summarized primarily from the point of view of turbulence modeling verification and validation. Furthermore, the NASA Langley Turbulence Modeling Resource website is described. The purpose of this site is to provide a central location where RANS turbulence models are documented, and test cases, grids, and data are provided. The goal of this paper is to provide an abbreviated survey of turbulence modeling verification and validation efforts, summarize some of the outcomes, and give some ideas for future endeavors in this area.

Rumsey, Christopher L.↗

NASA NTRS1983

Centaur D-1A guidance/software system

The main body of this paper describes the evolution of the Centaur D-1A Guidance and Software System. Specifically, the performance of the explicit guidance equations, using a linear tangent steering law. Inherent flexibility exists in the equations in that they have multimission capability. They can accommodate both Earth-orbital and Earth-escape missions with either one or two Centaur burns. They can also guide for multi-burn orbital missions. The Centaur performance is indicated in terms of optimality (propellant usage), accuracy, flexibility and computer requirements. In the course of the Centaur Guidance development substantial changes and improvements have been made and more improvements are on the way for the Shuttle/Centaur Guidance. It is the intent of this paper to describe, provide insight into, and identify certain unique aspects of the individual Centaur flight profiles. Mission profile(s) are described narratively with some numerical data given in cases where it may be useful.

Gordan, A. L.↗

NASA NTRS1984

Centaur D-1A guidance/software system

The main body of this paper describes the evolution of the Centaur D-1A Guidance and Software System. Specifically, the performance of the explicit guidance equations, using a linear tangent steering law. Inherent flexibility exists in the equations in that they have multimission capability. They can accommodate both earth-orbital and earth-escape missions with either one or two Centaur burns. They can also guide for multi-burn orbital missions. The Centaur performance is indicated in terms of optimality (propellant usage), accuracy, flexibility and computer requirements. In the course of the Centaur Guidance development substantial changes and improvements have been made and more improvements are on the way for the Shuttle/Centaur Guidance. It is the intent of this paper to describe, provide insight into, and identify certain unique aspects of the individual Centaur flight profiles. Mission profile(s) are described narratively with some numerical data given in cases where it may be useful.

Gordan, A. L.↗

NASA NTRS1989

Application of the p-version of the finite-element method to global-local problems

A brief survey is given of some recent developments in finite-element analysis technology which bear upon the three main research areas under consideration in this workshop: (1) analysis methods; (2) software testing and quality assurance; and (3) parallel processing. The variational principle incorporated in a finite-element computer program, together with a particular set of input data, determines the exact solution corresponding to that input data. Most finite-element analysis computer programs are based on the principle of virtual work. In the following, researchers consider only programs based on the principle of virtual work and denote the exact displacement vector field corresponding to some specific set of input data by vector u(EX). The exact solution vector u(EX) is independent of the design of the mesh or the choice of elements. Except for very simple problems, or specially constructed test problems, vector u(EX) is not known. Researchers perform a finite-element analysis (or any other numerical analysis) because they wish to make conclusions concerning the response of a physical system to certain imposed conditions, as if vector u(EX) were known.

Szabo, Barna A.↗

NASA NTRS2015

LADEE Preparations for Contingency Operations for the Lunar Orbit Insertion Maneuver

The Lunar Atmosphere and Dust Environment Explorer (LADEE) spacecraft was launched on September 6, 2013, and completed its mission on April 17, 2014 with a directed impact to the Lunar Surface. Its primary goals were to examine the lunar atmosphere, measure lunar dust, and to demonstrate high rate laser communications. The LADEE mission was a resounding success, achieving all mission objectives, much of which can be attributed to careful planning and preparation. This paper discusses the specific preparations for fault conditions that could occur during a highly-critical phase of the mission. To get to the Moon, the spacecraft traversed multiple phasing loops around the Earth, and then executed a breaking maneuver to achieve lunar orbit. This Lunar Orbit Insertion (LOI) maneuver was perhaps the most time-critical phase of the entire mission. The LOI maneuver had to occur within a twenty minute window in order to achieve lunar orbit with an acceptable amount of propellant remaining. Missing this window would have likely resulted in a loss of the entire mission. An additional challenge of the maneuver was that spacecraft was out of view for approximately one hour prior to the main thruster burn, with the burn needing to occur within five minutes after coming into view. These conditions resulted in unique challenges for ground operations and the fault management system. Early in the planning stages of the mission, the criticality and challenges of this maneuver were evident to the system designers. The major concern was that any triggering of the on-board fault management system, whether it is in response to a true fault or a false positive, would result in an unacceptable delay to the burn. Therefore the flight software was designed with a flexible fault management system, such that any or all of the fault management responses could be disabled for the lead up and execution of the maneuver. Later, a triage was conducted to develop a list of fault responses, mapped to various parts of the timeline of the maneuver. Some of these contingency responses were solely ground-based if the time to detect, diagnose, and respond were adequate. Other responses were automated on-board if the response time from the ground would have been inadequate. For instance, in order to recover from a system reboot, on-board automation would have automatically reconfigured the spacecraft for the burn and reoriented the spacecraft to the burn attitude.These contingency responses were practiced, over and over, during numerous rehearsals. Although the LOI maneuver was executed without having to use any of these contingencies, the LADEE team was adequately prepared for this highly critical phase of the mission.

Cannon, Howard↗

NASA NTRS1997

Further Developments of BEM for Micro and Macromechanical Analyses of Composites: Boundary Element Software Technology-Composite User's Manual

BEST-CMS (Boundary Element Solution Technology - Composite Modeling System) is an advanced engineering system for the micro-analysis of fiber composite structures. BEST-CMS is based upon the boundary element program BEST3D which was developed for NASA by Pratt and Whitney Aircraft and the State University of New York at Buffalo under contract NAS3-23697. BEST-CMS presently has the capabilities for elastostatic analysis, steady-state and transient heat transfer analysis, steady-state and transient concurrent thermoelastic analysis and elastoplastic and creep analysis. The fibers are assumed to be perfectly bonded to the composite matrix, or in the case of static or steady-state analysis, the fibers may be assumed to have spring connections, thermal resistance, and/or frictional sliding between the fibers and the composite matrix. The primary objective of this User's Manual is to provide an overview of all BEST-CMS capabilities, along with detailed descriptions of the input data requirements. A brief review of the theoretical background is presented for each analysis category. Then, Chapter 3 discusses the key aspects of the numerical implementation, while Chapter 4 provides a tutorial for the beginning BEST-CMS user. The heart of the manual, however, is in Chapter 5, where a complete description of all data input items is provided. Within this chapter, the individual entries are grouped on a functional basis for a more coherent presentation. Chapter 6 includes sample problems and should be of considerable assistance to the novice. Chapter 7 includes capsules of a number of fiber-composite analysis problems that have been solved using BEST-CMS. This chapter is primarily descriptive in nature and is intended merely to illustrate the level of analysis that is possible within the present BEST-CMS system. Chapter 8 contains a detailed description of the BEST-CMS Neutral File which is helpful in writing an interface between BEST- CMS and any graphic post-processor program. Finally, all pertinent references are listed in Chapter 9.

Banerjee, P. K.↗