Monograph records
https://feeds.library.caltech.edu/people/Schapery-R-A/monograph.rss
A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenTue, 16 Apr 2024 14:14:11 +0000Two Simple Approximate Methods of Laplace Transform Inversion for Viscoelastic Stress Analysis
https://resolver.caltech.edu/CaltechAUTHORS:20141114-114344034
Authors: {'items': [{'id': 'Schapery-R-A', 'name': {'family': 'Schapery', 'given': 'R. A.'}}]}
Year: 2014
DOI: 10.7907/y7eq-dk48
Two approximate methods of Laplace transform inversion are given which are simple to use and are particularly applicable to stress analysis problems in quasi-static linear viscoelasticity. Once an associated elastic
solution is known numerically or analytically, the time-dependent viscoelastic response can be easily calculated using realistic material properties,
regardless of how complex the property dependence of the elastic solution may be. The new feature of these methods is that it is necessary to know only 1) an elastic solution numerically for certain ranges of elastic constants and 2) numerical values of the operational moduli or compliances
for real, positive values of the transform parameter. One method utilizes a mathematical property of the Laplace transform, while the other is based on some results obtained from Irreversible Thermodynamics and variational
principles. Because of this, they are quite general and can be used with anisotropic and inhomogeneous materials. Two numerical examples are given: As the first one, we calculate the time-dependent strain in a long,
internally. pressurized cylinder with an elastic case. The second example consists of inverting a transform which was derived by Muki and Sternberg in the thermo-viscoelastic analysis of a slab and a sphere(1). Both methods
were found to provide results which are within the usual engineering requirements of accuracy. Application of the approximate methods to problems in dynamic viscoelasticity is discussed briefly.
Supplementing the stress analysis, two techniques for calculating operational moduli and compliances from experimental stress-strain data are discussed and applied. Both can be used with creep, relaxation, and
steady-state oscillation data. The most direct one consists of numerically integrating experimental data, while the other is a model-fitting scheme. With this latter method finite-element spring and dashpot models are readily
found which fit the entire response.curves. In using these methods to calculate the operational functions employed in the stress analysis examples, we found that model-fitting was the fastest of the two, yet was very accurate.https://authors.library.caltech.edu/records/b636n-43f27A Simple Collocation Method for Fitting Viscoelastic Models to Experimental Data
https://resolver.caltech.edu/CaltechAUTHORS:20141114-115330896
Authors: {'items': [{'id': 'Schapery-R-A', 'name': {'family': 'Schapery', 'given': 'R. A.'}}]}
Year: 2014
DOI: 10.7907/92j7-g843
An easily applied collocation method is discussed for fitting the response of finite-element viscoelastic models to experimental stress-strain curves. It can be used with creep, relaxation, and steady-state oscillation data. The method is illustrated by means of two examples. As the first one, a model is obtained utilizing the dynamic shear compliance of polyisobutylene. In the second example we calculate a model from the tensile relaxation modulus of polymethyl methacrylate. With each case the model's response agreed with the experimental data within graphical accuracy over the entire frequency (or time) scale.https://authors.library.caltech.edu/records/zn3mx-jvd54Fundamental Studies Relating to Systems Analysis of Solid Propellants, January 1, 1960-May 31, 1960
https://resolver.caltech.edu/CaltechAUTHORS:20150604-135847602
Authors: {'items': [{'id': 'Blatz-P-J', 'name': {'family': 'Blatz', 'given': 'P. J.'}}, {'id': 'Knauss-W-G', 'name': {'family': 'Knauss', 'given': 'W. G.'}}, {'id': 'Schapery-R-A', 'name': {'family': 'Schapery', 'given': 'R. A.'}}, {'id': 'Williams-M-L', 'name': {'family': 'Williams', 'given': 'M. L.'}}]}
Year: 2015
DOI: 10.7907/6wsw-zw77
Previous reports of this series have attempted to
define some of the important parameters affecting structural
integrity of solid propellant rocket grains. Three general
areas have been discussed, namely material properties,
analytical procedures, and criteria for mechanical failure.
This particular report is devoted to failure criteria,
including both limiting deformation and fracture. First of all, the characteristic material properties of filled and unfilled elastomers are described, followed by a brief description of current and proposed tests which can be conducted to obtain experimental information relating to these characteristics in such a form that they can be incorporated in structural integrity analyses. In particular, the necessity for multi-axial
tests is stressed in conjunction with minor requirements
for new experimental equipment.
The selection of appropriate fracture criteria is discussed.
Most progress, however, can be reported only in criteria for
unfilled elastomers for small and large strains where it appears a distortion strain energy density may be used. It is necessary to delay any really definitive remarks upon filled elastomers or actual grain composites, and subsequent use with cumulative
damage analyses, until additional experimental data for propellants is forthcoming.https://authors.library.caltech.edu/records/5dasw-zyj96Fundamental Studies Relating to Systems Analysis of Solid Propellants
https://resolver.caltech.edu/CaltechAUTHORS:20151201-154118684
Authors: {'items': [{'id': 'Schapery-R-A', 'name': {'family': 'Schapery', 'given': 'R. A.'}}, {'id': 'Stimpson-L-D', 'name': {'family': 'Stimpson', 'given': 'L. D.'}}, {'id': 'Williams-M-L', 'name': {'family': 'Williams', 'given': 'M. L.'}}]}
Year: 2015
The earlier progress reports presented some essentials
of model representation and a summary of some elastic solutions as preliminary material for viscoelastic analyses of solid propellants under various loading conditions. The present report is a continuation of the above with a brief section on Thermal Distributions, a section
called Engineering Analysis, and one on Failure Criteria. The thermal distributions, obtained from heat transfer theory, are required for the thermoelastic formulations of section II. The Engineering Analysis section includes several varied examples to assist in understanding the
analysis techniques presented in the other sections. The final section relates to mechanical failure of propellants and presents some preliminary thoughts as to how the study of this important problem area will be conducted.https://authors.library.caltech.edu/records/tawqe-7zq80Fundamental Studies Relating to Systems Analysis of Solid Propellants
https://resolver.caltech.edu/CaltechAUTHORS:20151202-160659665
Authors: {'items': [{'id': 'Blatz-P-J', 'name': {'family': 'Blatz', 'given': 'P. J.'}}, {'id': 'Schapery-R-A', 'name': {'family': 'Schapery', 'given': 'R. A.'}}, {'id': 'Stimpson-L-D', 'name': {'family': 'Stimpson', 'given': 'L. D.'}}, {'id': 'Williams-M-L', 'name': {'family': 'Williams', 'given': 'M. L.'}}]}
Year: 2015
As in the previous progress reports, the contents in this report have been categorized so as to present a clear picture of their role in contributing to the problem of mechanical failure analysis. The subject of material representation by mechanical failure analysis. The subject of material representation by mechanical models is discussed in Section I, while Section II contains additions to the subject of Elastic Solutions for cylinders. The Engineering Analysis section includes an example of the strain response of an internal star grain to pressure. A damped sinusoid has been assumed for the pressure rise, and the use of stress concentration factors for a star grain is demonstrated. Section V on failure includes some preliminary test results which indicate the feasibility of the cumulative damage concept for composite (polyurethane) propellants, at least in the limited range tested. Recommendations are given which would expand this testing to show how damage accumulates under other conditions such as low temperatures, high strain-rates and with other types of propellant.https://authors.library.caltech.edu/records/qav8g-b8e97Fundamental Studies Relating to Systems Analysis of Solid Propellants, October l, 1959-December 31, 1959
https://resolver.caltech.edu/CaltechAUTHORS:20151203-165233805
Authors: {'items': [{'id': 'Blatz-P-J', 'name': {'family': 'Blatz', 'given': 'P. J.'}}, {'id': 'Knauss-W-G', 'name': {'family': 'Knauss', 'given': 'W. G.'}}, {'id': 'Schapery-R-A', 'name': {'family': 'Schapery', 'given': 'R. A.'}}, {'id': 'Stimpson-L-D', 'name': {'family': 'Stimpson', 'given': 'L. D.'}}, {'id': 'Williams-M-L', 'name': {'family': 'Williams', 'given': 'M. L.'}}]}
Year: 2015
DOI: 10.7907/0sxn-1k84
Previous reports of this series have attempted to define some of the important parameters affecting the structural integrity of solid propellant rocket grains. Three general areas have been discussed, namely material properties, analytical procedures, and criteria for mechanical
failure.
This particular report is devoted to a more detailed examination of the properties of a filled viscoelastic resin, and their representation by appropriate mechanical models. In addition, a comparison of two methods of computing viscoelastic strains in a pressurized cylinder is
presented.
In the category of material properties, linear viscoelastic model theory is reviewed, and certain important relations among sets of experimental data are deduced. A justification for the application of this theory is provided by the analytic representation of available dynamic
data in terms of a well-known distribution function. Since the inception of this work additional experimental data on propellants has become available.
In the category of analytical procedures, the usual approach of representing material properties by a four-element model, as determined from the dynamic data in a limited frequency range, is compared with the
more sophisticated Fourier transform method in which the entire frequency range is utilized. The two approaches are applied to calculate the viscoelastic hoop strain at the inner boundary of an internally pressurized infinitely
long hollow cylinder subjected to a ramp-type pressure pulse. In this example, the dilatation is assumed elastic or frequency independent and the distortion viscoelastic.
In the following quarter, primary effort will be devoted to the determination of a criterion for mechanical failure of propellants. Two steps are involved. One is the analytical representation of ultimate strain as a function of temperature on strain rate by means of a mechanical model. In addition to the usual distribution of relaxation (or retardation) times, this model will be supplied with a distribution of ultimate strain. Step two involves
the choice of a suitable criterion for compounding ultimate strain or ultimate stress components into a single parameter, which, when exceeded at a given
rate and temperature, denotes the onset of fracture or mechanical failure.https://authors.library.caltech.edu/records/ge1wj-66q37Fundamental Studies Relating to Systems Analysis of Solid Propellants, October 1, 1958- December 31, 1958
https://resolver.caltech.edu/CaltechAUTHORS:20151203-155555299
Authors: {'items': [{'id': 'Schapery-R-A', 'name': {'family': 'Schapery', 'given': 'R. A.'}}, {'id': 'Stimpson-L-D', 'name': {'family': 'Stimpson', 'given': 'L. D.'}}]}
Year: 2015
DOI: 10.7907/rnjk-nb74
In this report the groundwork is laid for the proposed work scope which stressed the need for a greater understanding of the solid mechanics of grains. Particular emphasis will be directed toward the multi-axial behavior of thick walled configurations. The work falls naturally into
three areas; (1) analysis procedures, (2) material properties, and (3) failure criteria.
As a necessary preliminary to treating specific designs, certain material of general applicability must be developed, collected, and summarized. The following sections therefore deal with a general
description of viscoelastic analysis and material representation, discussed by contrast with more conventional engineering analysis. By this means
a background is established for the collection of elastic design formulas which are included in the second section of the report.https://authors.library.caltech.edu/records/r0xbp-gn259Fundamental Studies Relating to Systems Analysis of Solid Propellants, January 1, 1959-March 31, 1959
https://resolver.caltech.edu/CaltechAUTHORS:20151203-164854569
Authors: {'items': [{'id': 'Schapery-R-A', 'name': {'family': 'Schapery', 'given': 'R. A.'}}, {'id': 'Stimpson-L-D', 'name': {'family': 'Stimpson', 'given': 'L. D.'}}, {'id': 'Williams-M-L', 'name': {'family': 'Williams', 'given': 'M. L.'}}]}
Year: 2015
DOI: 10.7907/822k-jv84
In continuing the investigation of analysis procedures to be used in studying the structural integrity of solid propellant grains, we amplify the content of the first progress report without at this time opening up any new areas. However it is perhaps appropriate to enumerate some of the specific subjects to be presented later. Following
the earlier pattern of (1) model representation and (2) tabulated elastic solutions, both of which are supplemented in this report, it is expected to include (3) heat transfer and temperature distributions, (4) engineering analysis, i.e. the practical combination of items (1), (2),
and possibly (3) above, (5) failure criteria and strength analysis.https://authors.library.caltech.edu/records/mwjhp-6ft75