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This project aims to demonstrate the feasibility of run-time mission-oriented assessment of assurance and tradeoff in a distributed system. Distributed mission support systems today incorporate various QoS and security mechanisms, but there is no clear way to judge whether the system is delivering QoS and security assurance at the level needed for mission success. Security is treated as an all or nothing quality--which leads to missed opportunities as well as undue risk taking. Measuring security is difficult. QIAAMU took an approach similar to QoS management where assurance is measured against requirements specified by mission stakeholders. This approach enables us to treat QoS and security in a uniform way as well as consider QoS-Security tradeoffs when the system fails to deliver QoS and Security at the required level. Starting with the metrics to observe and measure, this project developed a foundation for run time assessment and tradeoff including an assessment scheme, an innovative distributed tradeoff algorithm and usability support, and instantiated the assessment and tradeoff framework within a security architecture, which underwent a final demonstration and evaluation phase in December 2012. This report is the final technical report for the QIAAMU project and describes the research, development, and evaluation results from the project., Prepared in cooperation with the University of Illinois, Champaign, IL. The original document contains color images.

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2007., Includes bibliographical references (p. 101-103)., Modularity is a promising design concept for space systems. In a modular satellite, the individual subsystems would be broken down into physically distinct modules, which would then dynamically recombine into an aggregate vehicle. This could improve the flexibility and reusability of satellites, and could even enable some mission objectives which are not possible at all with monolithic vehicles. However, modularity requires that some additional new elements be included in the design that are not needed with a monolithic satellite. Two of these are a docking interface to allow modules to attach, and a position measurement system to allow modules to fly accurately in formation and dock with each other. These two additional elements are explored in this thesis. The central focus is on a relative state estimator based on an extended Kalman filter. The estimator is first presented theoretically, then the results of implementation and hardware testing are discussed. This thesis presents two main hardware applications for the estimator, both of which mirror prime space-based applications of modularity itself: docking and formation maintenance/reconfiguration., by Nicholas R. Hoff, III., S.M.

Formulas and methods are presented in a self-contained manner to aid when dealing with problems that arise when elements of metal structures and machinery creep at high temperatures.

A correction is given to the small-displacement theory of the axisymmetric creep buckling of axially compressed circular cylindrical shells. The correction takes into account the possibility of a non-axisymmetric elastic snap through in agreement with Koiter's theory after a sufficient amount of axisymmetric permanent deformation has developed in consequence of creep. (Author)

The development of our knowledge of the buckling of thin-walled circular cylindrical shells subjected to axial compression is outlined from the beginning of the century until the present, with particular emphasis on advances made in the last twenty-five years. It is shown that practical shells generally buckle under stresses much smaller than the classical critical value derived by Lorenz, Timoshenko, Southwell and Flugge. A first explanation of the reasons for the discrepancy was given by Donnell and the problem was explored in detail by von Karman, Tsien and their collaborators. More recently, Yoshimura discovered the existence of an inextensional displacement pattern which the wall of the shell can suddenly assume, and Koiter found an explanation of the sensitivity of the buckling stress to small initial deviations from the exact circular cylindrical shape. In the last few years further interesting discoveries were made in Japan and in California regarding the effects of details of the boundary conditions, and many additional numerical results were obtained with the aid of high-speed electronic digital computers. Improvements in experimental techniques have also contributed significantly to a clarification of the problem and to an establishment of the unavoidable deviations from the exact shape as the major causes of the large differences between theory and experiment.

It is shown that the creep buckling of slender or thin-walled structures whose material deforms elastically as well as in consequence of time- hardening creep can be analyzed first as if the deformations were due entirely to steady creep. The results of this analysis can be easily modified to account for time-hardening creep, and this modification does not involve any approximation when the time-hardening creep strain rate is expressed as the product of a function of stress by a function of time.

Initial axisymmetric deviations from the exact circular cylindrical shape increase with time in consequence of creep when a uniformly distributed axial compressive load is acting on a thin-walled cylindrical shell. The increasing deformations are accompanied by the development of hoop stresses. When the hoop compression reaches a sufficiently high value, the shell can buckle elastically in agreement with Koiter's special theory.

Experimental results obtained with 31 nickel circular cylindrical shell specimens are evaluated in the light of the theory. The test results have already been reported in SUDAAR No. 415. The experimental creep buckling times obtained in axial compression at a temperature of 650F were found to be in reasonable agreement with the theoretical formulas. (Author)

The actually observed buckle pattern of a thin-walled circular cylindrical shell is idealized to an inextensional pattern with sharp creases. This pattern is represented by an infinite double series containing trigonometric functions in the circumferential direction. For the axial direction more suitable sets of functions are found with the aid of Gegenbauer polynomials. (Author)

Test equipment suitable for the study of the creep buckling of axially compressed circular cylindrical shells was developed and built. With the aid of this equipment, thirty-one electroformed nickel cylinders of radius-to-thickness ratios ranging from 30.6 to 96.4 were tested at a temperature of 650F. The loading of each specimen was interrupted usually once, and in some cases twice, to permit an exact measurement of the creep deformations produced by the axial compression. Diagrams showing the deformed shapes of eight generators of each specimen are presented at two or three stages of the creep buckling process. Inspection of the figures reveals that specimens of this kind either buckle axisymmetrically, or begin the creep buckling process in a axisymmetric manner but change over to a multilobed pattern in later stages of the deformations. (Author)

The two simultaneous nonlinear first-order differential equations characterizing the problems that were derived by the senior author in a paper in 1956 and were at that time solved for a few cases by numerical integration are solved here analytically with the aid of a few simplifying assumptions. The very simple formula derived in this manner is used to compute the critical times of a series of shells tested in the laboratory. It is found that the formula predicts somewhat larger values for the critical time than the experimental results. (Author)

The purpose of the investigation described in this paper is the study of the effect of very small nonaxisymmetric initial deviations from the exact shape upon the deformations and the critical time of a thin-walled circular cylindrical shell which was manufactured with larger initial deviations of an axisymmetric type. The calculations are carried out in a manner similar to that of a recent paper by the senior author. It is assumed that all the deformations are due to nonlinear steady creep governed by Odqvist's law. In consequence of the nonlinearity of the constitutive equation and the use of three terms in the expressions for the deformations and the stresses the trigonometric calculations become so complicated that they must be carried out by means of the high-speed digital computer. For this purpose use is made of the 'REDUCE' program. It is found that in a particular case the critical time of the shell is reduced to about one-half the original value when one adds to the small axially symmetric component of the initial deviations a nonaxisymmetric component which is ten orders of magnitude smaller. The reduction in critical time is represented by a factor of about 1/15 when the amplitudes of the axisymmetric and nonaxisymmetric initial deviations are equal. (Author)

After a brief summary of the development of present knowledge of the buckling process of thin shells, the results of recent investigations are discussed in some detail. In particular, information is given on analyses of the maximum stress a circular cylindrical shell of infinite or finite length can carry in axial compression in the presence of an initial deviation of the shell wall from the perfect cylindrical shape, and on the number of circumferential waves into which finite cylindrical shells buckle. The maximum external pressure is calculated that can be supported by a complete spherical shell in the presence of known deviations of its wall from the perfect spherical shape. The results of recent experiments on cylindrical and complete spherical shells are also presented. Recommendations are made for the practical calculation of the buckling stresses of circular cylindrical shells and spherical shells. (Author), Revision of report dated Dec 67.

The report describes contributions made to the clarification of the buckling process of thin shells. One of the results was the discovery that a very slight modification of the classical boundary conditions results in a reduction in the value of the critical stress of the linear theory by a factor of about one-half. Another result of importance was that the procedure of Karman and Tsien in finding a minimal value of the post-buckling stress loads to a perfectly correct but trival result. The maximal value of the equilibrium stress of the imperfect shell reached in testing machine loading has been calculated by Prof. Hoff by two methods. The number of buckles around the circumference were shown experimentally and theoretically to decrease as the length-to-radius ratio of the shell is increased. A tie-in between buckling in testing machine loading and buckling under thermal stresses was obtained theoretically and experimentally. (Author)

A theoretical investigation of the axisymmetric buckling of complete thin-walled spherical shells under uniform external pressure is undertaken to determine the effect of axisymmetric initial imperfections. In the analysis, the complete spherical shell is divided into two parts; the shallow cap in which the initial imperfection exists, and the remaining portion of the shell most of which deforms in simple contraction. The rotation of the meridian of the cap is assumed in the form of a polynomial function. Four matching conditions are enforced at the juncture of the cap and remainder. The total potential energy of the complete spherical shell is minimized in accordance with the Rayleigh-Ritz approximation method. Two types of initial imperfections are studied; one is an axisymmetric dimple, and the other is a spherical region whose radius of curvature is greater than that of the perfect spherical shell. The maximal values of the pressure parameter rho in the equilibrium state before snap-through were calculated for various values of the geometric parameter lambda, which is proportional to the angular extent of the imperfection for a given radius-to-thickness ratio, and the imperfection amplitude parameter delta, which is the ratio of the initial deviation of the shell mid-surface at the axis of rotation to the wall-thickness. The results of numerical computations show that for all values of delta the lowest buckling pressure is reached when lambda is about 4. (Author)

The nonlinear partial differential equations of von Karman and Donnell governing the deformations of initially imperfect cylindrical shells are reduced to a consistent set of ordinary differential equations. A numerical procedure is then developed for the solution of these equations together with the associated boundary conditions. This method is used to determine the number of waves at buckling as well as the load carrying capacity of imperfect cylindrical shells of finite length subjected to uniform axial compression in the presence of the least amount of restraint along the simply supported boundaries. It is found that details of the boundary conditions have little effect on the number of waves into which the shell buckles around the circumference. This number is determined essentially by the length-to-radius and radius-to-thickness ratios. The absence of an edge restraint to circumferential displacements reduces the classical value of the buckling load by a factor of about two as compared to the classical value. On the other hand, shells with these boundary conditions are less sensitive to initial imperfections in the shape, and thus the maximal load supported in the presence of unavoidable initial deviations can be the same for shells with and without a restraint to circumferential displacements along the edges. (Author)

The general problem considered was the finite deflection analysis of the effects of concentrated loads - line loads and point loads in particular - upon very thin walled shells. During the course of the research, the orginal statement was modifed in view of the results obtained in the following two respects. First, the idea of a point load, which is represented in linear, small deflection theory by a singular solution to the governing differential equations, must be defined for finite deflection theory as the limit of a localized load, applied over a finite area, as the area shrinks to zero. Second, a restriction to infinitesimal elastic strain under localized loads is valid for real materials only for extremely small values of load, and this makes it very difficult to check by experiment the results of theory developed under such restriction. Results were obtained for two classes of problems: (a) line loads on rotationally symmetric, inflated membranes in a state of finite strain; (b) localized loads on stretched, elastic-perfectly plastic membranes. (Author)

A study is made of the effect of initial deviations on the load carrying capacity of thin circular cylindrical shells under uniform axial compression. A perturbation expansion is used to reduce the nonlinear equations of von Karman-Donnell to an infinite set of linear equations, of which only the first few need be solved to obtain a reasonable accurate solution. The results for both infinite shells and shells of finite length indicate that a small imperfection can sharply reduce the maximum load that a thin-walled cylinder will sustain. In addition, for a particular set of boundary conditions, it is shown that the effect of the length for a finite shell, is small.

The analysis was begun with an investigation of the effect that a more accurate displacement assumption, in conjunction with the exact strain-displacement relations, has on the postbuckling equilibrium behavior. It was hoped that the limiting behavior of wall thickness and wave number parameter would be altered, and that the stress coefficient would not tend to zero. Particular attention was given to an exact representation of membrane strains because it was known that in the limit as the radius-to-thickness ratio of the shell approaches infinity, the displacements approach the inextensional polyhedral surface. While all the strains in the middle surface of this limiting polyhedral shell are zero, the Donnell strain-displacement relations yield strains amounting to 0.1% if the number of waves around the circumference is 10. The results obtained did not differ significantly from the Donnell strain-displacement relations. (Author)

Earlier numerical solutions of the von Karman-Donnell large-displacement equations for thin circular cylindrical shells have been extended by considering larger numbers of terms in the double Fourier series representing the radial displacements after buckling. In the most comprehensive one of the calculations whose results are presented here a total potential energy expression consisting of about 1100 terms was minimized with respect to 16 unknowns. The results of the computations as well as theoretical considerations indicate that the solution for long shells of the von Karman-Donnell equations with the aid of the von Karman-Tsien Leggett procedure leads in the limit to the trivial solution in which the amplitude of the displacements tends to zero, the number of waves around the circumference tends to infinity and the average axial compressive stress capable of maintaining equilibrium in the post-buckling state tends to zero. (Author)

The behavior of imperfect columns in conventional testing machine loading is investigated in the case when the buckling stress exceeds the elastic limit of the material. The behavior of the perfect column is then obtained through a limiting process in which the amplitude of the initial deviations from straightness is made to approach zero. It is found that a perfect column cannot bend at or above the tangent modulus load without stress reversal. The maximum load supported by the column is smaller than the reduced modulus load, and it can be smaller than, equal to, or greater than the tangent modulus load. (Author), Presented at the Symposium on the Theory of Shells (70th Anniversary) 5 Apr 66, at Houston Univ., Tex.