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  • Analytical Chemistry and Spectroscopy  (5,640)
  • STRUCTURAL MECHANICS  (1,910)
  • 1985-1989  (7,550)
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Year
  • 101
    Publication Date: 2013-08-31
    Description: Delamination characterization of a plate with a hole/inclusion is presented. A closed form solution is developed to obtain stresses on the boundary of hole/inclusion in the plate. Once the location with the highest tangential stress is identified, a Finite Element Method analysis of a laminate under tensile loading is considered. The models are presented for the closed form and Finite Element Method. The examples are for (+ or - 35/0/90)s laminate of AS4/3501-6. Tensile, biaxial, and shear loads are considered.
    Keywords: STRUCTURAL MECHANICS
    Type: NASA, Langley Research Center, Research in Structures, Structural Dynamics and Materials, 1989; p 3-12
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  • 102
    Publication Date: 2013-08-31
    Description: An important consideration in the global local finite-element method (GLFEM) is the availability of global functions for the given problem. The role and mathematical requirements of these global functions in a GLFEM analysis of localized stress states in prismatic structures are discussed. A method is described for determining these global functions. Underlying this method are theorems due to Toupin and Knowles on strain energy decay rates, which are related to a quantitative expression of Saint-Venant's principle. It is mentioned that a mathematically complete set of global functions can be generated, so that any arbitrary interface condition between the finite element and global subregions can be represented. Convergence to the true behavior can be achieved with increasing global functions and finite-element degrees of freedom. Specific attention is devoted to mathematically two-dimensional and three-dimensional prismatic structures. Comments are offered on the GLFEM analysis of NASA flat panel with a discontinuous stiffener. Methods for determining global functions for other effects are also indicated, such as steady-state dynamics and bodies under initial stress.
    Keywords: STRUCTURAL MECHANICS
    Type: NASA, Langley Research Center, Computational Methods for Structural Mechanics and Dynamics, Part 1; p 135-149
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  • 103
    Publication Date: 2013-08-31
    Description: The various types of local-global finite-element problems point out the need to develop a new generation of software. First, this new software needs to have a complete analysis capability, encompassing linear and nonlinear analysis of 1-, 2-, and 3-dimensional finite-element models, as well as mixed dimensional models. The software must be capable of treating static and dynamic (vibration and transient response) problems, including the stability effects of initial stress, and the software should be able to treat both elastic and elasto-plastic materials. The software should carry a set of optional diagnostics to assist the program user during model generation in order to help avoid obvious structural modeling errors. In addition, the program software should be well documented so the user has a complete technical reference for each type of element contained in the program library, including information on such topics as the type of numerical integration, use of underintegration, and inclusion of incompatible modes, etc. Some packaged information should also be available to assist the user in building mixed-dimensional models. An important advancement in finite-element software should be in the development of program modularity, so that the user can select from a menu various basic operations in matrix structural analysis.
    Keywords: STRUCTURAL MECHANICS
    Type: NASA, Langley Research Center, Computational Methods for Structural Mechanics and Dynamics, Part 1; p 89-101
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  • 104
    Publication Date: 2013-08-31
    Description: The needs for computerized structural mechanics (CSM) as seen from the standpoint of the aircraft industry are discussed. These needs are projected into the 1990's with special focus on the new advanced materials. Preliminary design/analysis, research, and detail design/analysis are identified as major areas. The role of local/global analyses in these different areas is discussed. The lessons learned in the past are used as a basis for the design of a CSM framework that could modify and consolidate existing technology and include future developments in a rational and useful way. A philosophy is stated, and a set of analyses needs driven by the emerging advanced composites is enumerated. The roles of NASA, the universities, and the industry are identified. Finally, a set of rational research targets is recommended based on both the new types of computers and the increased complexity the industry faces. Computerized structural mechanics should be more than new methods in structural mechanics and numerical analyses. It should be a set of engineering applications software products that combines innovations in structural mechanics, numerical analysis, data processing, search and display features, and recent hardware advances and is organized in a framework that directly supports the design process.
    Keywords: STRUCTURAL MECHANICS
    Type: NASA, Langley Research Center, Computational Methods for Structural Mechanics and Dynamics, Part 1; p 25-49
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  • 105
    Publication Date: 2013-08-31
    Description: A structural optimization algorithm was researched including global displacements as decision variables. The algorithm was applied to planar reinforced concrete frames with nonlinear material behavior submitted to static loading. The flexural performance of the elements was evaluated as a function of the actual stress-strain diagrams of the materials. Formation of rotational hinges with strain hardening were allowed and the equilibrium constraints were updated accordingly. The adequacy of the frames was guaranteed by imposing as constraints required reliability indices for the members, maximum global displacements for the structure and a maximum system probability of failure.
    Keywords: STRUCTURAL MECHANICS
    Type: NASA, Langley Research Center, Research in Structures, Structural Dynamics and Materials, 1989; p 47-54
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  • 106
    Publication Date: 2013-08-31
    Description: DYSCO is a versatile, general purpose dynamic analysis program which assembles equations and solves dynamics problems. The executive manages a library of technology modules which contain routines that compute the matrix coefficients of the second order ordinary differential equations of the components. The executive performs the coupling of the equations of the components and manages the solution of the coupled equations. Any new component representation may be added to the library if, given the state vector, a FORTRAN program can be written to compute M, C, K, and F. The problem described demonstrates the generality of this statement.
    Keywords: STRUCTURAL MECHANICS
    Type: NASA, Langley Research Center, Research in Structures, Structural Dynamics and Materials, 1989; p 23-33
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  • 107
    Publication Date: 2013-08-31
    Description: Due to increasing need to account for the uncertainties in material properties, loading conditions, or geometries, a methodology was developed to determine structural reliability and the assess the risk associated with it. The methodology consists of a probabilistic structural analysis by a probabilistic finite element computer code Nonlinear Evaluation of Stochastic Structures Under Stress (NESSUS) and a generic probabilistic material properties model. The methodology is versatile and is equally applicable to high and cryogenic temperature structures. Results obtained demonstrate that the whole issue of structural reliability and risk can be formally evaluated using the methodology developed which is inclusive of uncertainties in material properties, structural parameters and loading conditions. The methodology is described in some detail with illustrative examples.
    Keywords: STRUCTURAL MECHANICS
    Type: Johns Hopkins Univ., The 1989 JANNAF Propulsion Meeting, Volume 1; p 135-162
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  • 108
    Publication Date: 2013-08-31
    Description: The focus here is on one aspect of the Computational Structural Mechanics (CSM) Testbed: finite element technology. The approach involves a Generic Element Processor: a command-driven, database-oriented software shell that facilitates introduction of new elements into the testbed. This shell features an element-independent corotational capability that upgrades linear elements to geometrically nonlinear analysis, and corrects the rigid-body errors that plague many contemporary plate and shell elements. Specific elements that have been implemented in the Testbed via this mechanism include the Assumed Natural-Coordinate Strain (ANS) shell elements, developed with Professor K. C. Park (University of Colorado, Boulder), a new class of curved hybrid shell elements, developed by Dr. David Kang of LPARL (formerly a student of Professor T. Pian), other shell and solid hybrid elements developed by NASA personnel, and recently a repackaged version of the workhorse shell element used in the traditional STAGS nonlinear shell analysis code. The presentation covers: (1) user and developer interfaces to the generic element processor, (2) an explanation of the built-in corotational option, (3) a description of some of the shell-elements currently implemented, and (4) application to sample nonlinear shell postbuckling problems.
    Keywords: STRUCTURAL MECHANICS
    Type: NASA, Langley Research Center, NASA Workshop on Computational Structural Mechanics 1987, Part 2; p 571-651
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  • 109
    Publication Date: 2013-08-31
    Description: An outline of the organization and capabilities of the Engine Structures Computational Simulator (Simulator) at NASA Lewis Research Center is given. One of the goals of the research at Lewis is to integrate various discipline specific structural mechanics codes into a software system which can be brought to bear effectively on a wide range of engineering problems. This system must possess the qualities of being effective and efficient while still remaining user friendly. The simulator was initially designed for the finite element simulation of gas jet engine components. Currently, the simulator has been restricted to only the analysis of high pressure turbine blades and the accompanying rotor assembly, although the current installation can be expanded for other applications. The simulator presently assists the user throughout its procedures by performing information management tasks, executing external support tasks, organizing analysis modules and executing these modules in the user defined order while maintaining processing continuity.
    Keywords: STRUCTURAL MECHANICS
    Type: NASA, Langley Research Center, NASA Workshop on Computational Structural Mechanics 1987, Part 2; p 487-519
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  • 110
    facet.materialart.
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    In:  CASI
    Publication Date: 2013-08-31
    Description: The Computational Structural Mechanics (CSM) Activity at Langley Research Center is developing methods for structural analysis on modern computers. To facilitate that research effort, a Testbed Development environment is being constructed. It is the purpose of the Testbed to insulate researchers from differences in the computer operating systems of modern computer systems and permit concentrated effort on the analytical problem rather than the analytical tools required to solve that problem. While modern computers enable the solution of larger problems of increasing complexity, they do so at a cost. Distributed computer environments, vector processing hardware and multiple processors dominate the current computer environment and threaten to overwhelm future analysis software. The systems software for current computers becomes more complex in order to manage the increasing complexity. The applications developer is caught between conflicting goals. They must take advantage of the computing power of new computer systems while maintaining a stable software development system. The CSM Testbed is being developed to address this problem for the computational structural analysis research community. The Langley CSM activity was initiated in October 1984. The current directions for the Testbed Development Team of the Langley CSM activity are discussed.
    Keywords: STRUCTURAL MECHANICS
    Type: NASA Workshop on Computational Structural Mechanics 1987, Part 2; p 387-417
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  • 111
    Publication Date: 2013-08-31
    Description: Information on concurrent algorithms for transient finite element analysis is given in viewgraph form. Information is given on concurrent dynamic algorithms, interprocessor communication, the performance of the BAR problem on the 32 Processor Hypercube, computational efficiency and accuracy analysis.
    Keywords: STRUCTURAL MECHANICS
    Type: NASA. Langley Research Center, NASA Workshop on Computational Structural Mechanics 1987, Part 3; p 1067-1103
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  • 112
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    In:  CASI
    Publication Date: 2013-08-31
    Description: The intent here is to discuss the status of the boundary element method (BEM) for structural analysis, both in terms of the present and anticipated capabilities of the method and in terms of the incorporation of the method in the design/analysis process, particularly for gas turbine engine components.
    Keywords: STRUCTURAL MECHANICS
    Type: NASA. Langley Research Center, NASA Workshop on Computational Structural Mechanics 1987, Part 3; p 763-829
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  • 113
    Publication Date: 2013-08-31
    Description: The Boundary Element Method (BEM) is chosen as a basic analysis tool principally because the definition of quantities like fluxes, temperature, displacements, and velocities is very precise on a boundary base discretization scheme. One fundamental difficulty is, of course, that the entire analysis requires a very considerable amount of analytical work which is not present in other numerical methods. During the last 18 months all of this analytical work was completed and a two-dimensional, general purpose code was written. Some of the early results are described. It is anticipated that within the next two to three months almost all two-dimensional idealizations will be examined. It should be noted that the analytical work for the three-dimensional case has also been done and numerical implementation will begin next year.
    Keywords: STRUCTURAL MECHANICS
    Type: NASA. Langley Research Center, NASA Workshop on Computational Structural Mechanics 1987, Part 3; p 831-863
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  • 114
    Publication Date: 2013-08-31
    Description: Analysis and design methods for laminated composite materials have been the subject of considerable research over the past 20 years, and are currently well developed. In performing the detailed three-dimensional analyses which are often required in proximity to discontinuities, however, analysts often encounter difficulties due to large models. Even with the current availability of powerful computers, models which are too large to run, either from a resource or time standpoint, are often required. There are several approaches which can permit such analyses, including substructuring, use of superelements or transition elements, and the global/local approach. This effort is based on the so-called zoom technique to global/local analysis, where a global analysis is run, with the results of that analysis applied to a smaller region as boundary conditions, in as many iterations as is required to attain an analysis of the desired region. Before beginning the global/local analyses, it was necessary to evaluate the accuracy of the three-dimensional elements currently implemented in the Computational Structural Mechanics (CSM) Testbed. It was also desired to install, using the Experimental Element Capability, a number of displacement formulation elements which have well known behavior when used for analysis of laminated composites.
    Keywords: STRUCTURAL MECHANICS
    Type: NASA, Langley Research Center, NASA Workshop on Computational Structural Mechanics 1987, Part 2; p 683-732
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  • 115
    Publication Date: 2013-08-31
    Description: The goal is to remove the influence of the choice of algorithm used for a particular application and to remove the effects of the high-level language and the efficiency of the program. The study concentrates on only those characteristics of the structure of the architecture. The structure of the architecture is defined to include those parameters that distinguish an architectural design at the diagram level. For example, the interconnection network plays an integral part in such a description while the capabilities of the individual processing elements, while crucial to the execution of the program, are not represented in the diagram.
    Keywords: STRUCTURAL MECHANICS
    Type: NASA. Langley Research Center, NASA Workshop on Computational Structural Mechanics 1987, Part 1; p 299-321
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  • 116
    Publication Date: 2013-08-31
    Description: Over the past 15 years numerous new techniques have been developed for solving systems of equations and eigenvalue problems arising in finite element computations. A package called SPARSPAK has been developed by the author and his co-workers which exploits these new methods. The broad objective of this research project is to incorporate some of this software in the Computational Structural Mechanics (CSM) testbed, and to extend the techniques for use on multiprocessor architectures.
    Keywords: STRUCTURAL MECHANICS
    Type: NASA. Langley Research Center, NASA Workshop on Computational Structural Mechanics 1987, Part 1; p 202-238
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  • 117
    Publication Date: 2013-08-31
    Description: The purpose is to summarize a Phase 1 SBIR project performed for the NASA/Langley Computational Structural Mechanics Group. The project was performed from February to August 1987. The main objectives of the project were to: (1) expand upon previous research into the application of chordal ring architectures to the general problem of designing multi-microcomputer architectures, (2) attempt to identify a family of chordal rings such that each chordal ring can be simply expanded to produce the next member of the family, (3) perform a preliminary, high-level design of an expandable multi-microprocessor computer based upon chordal rings, (4) analyze the potential use of chordal ring based multi-microprocessors for sparse matrix problems and other applications arising in computational structural mechanics.
    Keywords: STRUCTURAL MECHANICS
    Type: NASA. Langley Research Center, NASA Workshop on Computational Structural Mechanics 1987, Part 1; p 137-170
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  • 118
    Publication Date: 2013-08-31
    Description: The transputer parallel processing lab at NASA Lewis Research Center (LeRC) consists of 69 processors (transputers) that can be connected into various networks for use in general purpose concurrent processing applications. The main goal of the lab is to develop concurrent scientific and engineering application programs that will take advantage of the computational speed increases available on a parallel processor over the traditional sequential processor. Current research involves the development of basic programming tools. These tools will help standardize program interfaces to specific hardware by providing a set of common libraries for applications programmers. The thrust of the current effort is in developing a set of tools for graphics rendering/animation. The applications programmer currently has two options for on-screen plotting. One option can be used for static graphics displays and the other can be used for animated motion. The option for static display involves the use of 2-D graphics primitives that can be called from within an application program. These routines perform the standard 2-D geometric graphics operations in real-coordinate space as well as allowing multiple windows on a single screen.
    Keywords: STRUCTURAL MECHANICS
    Type: NASA. Langley Research Center, NASA Workshop on Computational Structural Mechanics 1987, Part 1; p 107-136
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  • 119
    Publication Date: 2013-08-31
    Description: Only recently have engineers begun making use of Artificial Intelligence (AI) tools in the area of conceptual design. To continue filling this void in the design process, a prototype knowledge-based system, called STRUTEX has been developed to initially configure a structure to support point loads in two dimensions. This prototype was developed for testing the application of AI tools to conceptual design as opposed to being a testbed for new methods for improving structural analysis and optimization. This system combines numerical and symbolic processing by the computer with interactive problem solving aided by the vision of the user. How the system is constructed to interact with the user is described. Of special interest is the information flow between the knowledge base and the data base under control of the algorithmic main program. Examples of computed and refined structures are presented during the explanation of the system.
    Keywords: STRUCTURAL MECHANICS
    Type: Recent Advances in Multidisciplinary Analysis and Optimization, Part 1; p 317-331
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  • 120
    Publication Date: 2013-08-31
    Description: A NASTRAN bulk dataset preprocessor was developed to facilitate the integration of filamentary composite laminate properties into composite structural resizing for stiffness requirements. The NASCOMP system generates delta stiffness and delta mass matrices for input to the flutter derivative program. The flutter baseline analysis, derivative calculations, and stiffness and mass matrix updates are controlled by engineer defined processes under an operating system called CBUS. A multi-layered design variable grid system permits high fidelity resizing without excessive computer cost. The NASCOMP system uses ply layup drawings for basic input. The aeroelastic resizing for stiffness capability was used during an actual design exercise.
    Keywords: STRUCTURAL MECHANICS
    Type: NASA. Langley Research Center, Recent Advances in Multidisciplinary Analysis and Optimization, Part 1; p 403-429
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  • 121
    Publication Date: 2013-08-31
    Description: Because of the emphasis being placed on crashworthiness as a design requirement, increasing demands are being made by various organizations to analyze a wide range of complex structures that must perform safely when subjected to severe impact loads, such as those generated in a crash event. The ultimate goal of crashworthiness design and analysis is to produce vehicles with the ability to reduce the dynamic forces experienced by the occupants to specified levels, while maintaining a survivable envelope around them during a specified crash event. DYCAST is a nonlinear structural dynamic finite element computer code that started from the plans systems of a finite element program for static nonlinear structural analysis. The essential features of DYCAST are outlined.
    Keywords: STRUCTURAL MECHANICS
    Type: NASA, Langley Research Center, Computational Methods for Structural Mechanics and Dynamics; p 383-406
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  • 122
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    In:  CASI
    Publication Date: 2013-08-31
    Description: Time integration methods can be separated into two groups: explicit and implicit. Methods which do not involve the solution of any algebraic equations are called explicit, while those that require the solution of equations are called implicit. The relative advantages and disadvantages of explicit and implicit methods are summarized. The major trend in the past decade of research was to use hybrization methods to take advantage of the complementary nature of the positive attributes of explicit and implicit integration. These trends are briefly discussed.
    Keywords: STRUCTURAL MECHANICS
    Type: NASA, Langley Research Center, Computational Methods for Structural Mechanics and Dynamics; p 355-368
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  • 123
    Publication Date: 2013-08-31
    Description: 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.
    Keywords: STRUCTURAL MECHANICS
    Type: NASA, Langley Research Center, Computational Methods for Structural Mechanics and Dynamics, Part 1; p 169-178
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  • 124
    Publication Date: 2013-08-31
    Description: An overview is given of global-local stress analysis methods and associated difficulties and recommendations for future research. The phrase global-local analysis is understood to be an analysis in which some parts of the domain or structure are identified, for reasons of accurate determination of stresses and displacements or for more refined analysis than in the remaining parts. The parts of refined analysis are termed local and the remaining parts are called global. Typically local regions are small in size compared to global regions, while the computational effort can be larger in local regions than in global regions.
    Keywords: STRUCTURAL MECHANICS
    Type: NASA, Langley Research Center, Computational Methods for Structural Mechanics and Dynamics, Part 1; p 123-134
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  • 125
    Publication Date: 2013-08-31
    Description: The problem of calculating detailed stress distributions around discontinuities in buckled, composite structural components for use with the various analytical failure prediction techniques has not been thoroughly explored. The purpose here is the application of computational methods to the detailed stress analysis problem which is the focus of this session of the workshop. One approach to uncovering the difficulties of this type of analysis and to providing specific directions for future research in this area is a direct attack on the problem using currently available analysis tools. A candidate problem has been selected and experiences from calculating its structural response are described.
    Keywords: STRUCTURAL MECHANICS
    Type: Computational Methods for Structural Mechanics and Dynamics, Part 1; p 51-65
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  • 126
    Publication Date: 2013-08-31
    Description: Multi-body dynamics programs require characterization of each body. The Galileo spacecraft system modes to be retained were determined using available criteria, modal influence coefficients, and bode. The descent to component level was achieved via a two-phase diagonalization process starting with submatrices of truncated augmented system modal matrix.
    Keywords: STRUCTURAL MECHANICS
    Type: NASA, Langley Research Center, Computational Methods for Structural Mechanics and Dynamics; p 517-526
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  • 127
    Publication Date: 2013-08-31
    Description: A family of algorithms was outlined which would appear to be particularly well-suited for implementation in a parallel environment. This is due to the fact that for any partition of the mesh each subdomain in the partition can be processed over a time step simultaneously and independently of the rest. The method eliminates the need for assembling and factorizing large global arrays while retaining the unconditional stability properties of the algorithms used at the local level. To critically appraise the proposed methodology, two limiting cases were considered: element-by-element mesh partitions, and coarse mesh partitions. It was concluded that while the proposed methodology can be useful in sequential machines, it would appear to be promising as it bears on computation. It should also be emphasized that extensions of the method to nonlinear problems are possible.
    Keywords: STRUCTURAL MECHANICS
    Type: NASA, Langley Research Center, Computational Methods for Structural Mechanics and Dynamics; p 369-381
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  • 128
    Publication Date: 2013-08-31
    Description: An assessment is made of the potential of different global-local analysis strategies for predicting the nonlinear and postbuckling responses of structures. Two postbuckling problems of composite panels are used as benchmarks and the application of different global-local methodologies to these benchmarks is outlined. The key elements of each of the global-local strategies are discussed and future research areas needed to realize the full potential of global-local methodologies are identified.
    Keywords: STRUCTURAL MECHANICS
    Type: NASA, Langley Research Center, Computational Methods for Structural Mechanics and Dynamics, Part 1; p 151-167
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  • 129
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    In:  CASI
    Publication Date: 2013-08-31
    Description: The main theme concerns methods that may be classified as global (approximate) and local (exact). Some specific applications of these methods are found in: fracture and fatigue analysis of structures with 3-D surface flaws; large-deformation, post-buckling analysis of large space trusses and space frames, and their control; and stresses around holes in composite laminates.
    Keywords: STRUCTURAL MECHANICS
    Type: NASA, Langley Research Center, Computational Methods for Structural Mechanics and Dynamics, Part 1; p 103-121
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  • 130
    Publication Date: 2011-08-19
    Description: Closed-form analytical solutions, which govern the displacements and stresses in an adhesive shear beam, are discussed. The remarkable precision with which the shear stresses in the adhesive can be predicted forms the basis of the proposed characterization procedure. The shear modulus of the adhesive is obtained by means of a parameter estimation procedure which requires a symbiosis of theoretical and experimental stress analysis.
    Keywords: STRUCTURAL MECHANICS
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  • 131
    Publication Date: 2011-08-19
    Description: The fatigue behavior of composite laminates under tension-compression loading is analyzed and compared with behavior under tension-tension and compression-compression loading. It is shown that for meaningful fatigue conditions, the tension-compression case is the dominant one. Both tension and compression failure modes can occur under the reversed loading, and failure is dependent on the specific lay-up of the laminate and the difference between the tensile static strength and the absolute value of the compressive static strength. The use of a fatigue failure envelope for determining the fatigue life and mode of failure is proposed and demonstrated.
    Keywords: STRUCTURAL MECHANICS
    Type: Composites Science and Technology (ISSN 0266-3538); 36; 1, 19
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  • 132
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    In:  Other Sources
    Publication Date: 2011-08-19
    Description: The fundamental mechanics of free-edge effects in laminated fiber-reinforced composites is examined, reviewing the results of recent experimental and analytical investigations. The derivation of the governing equations for the basic problem is outlined, including the equilibrium and mismatch conditions and the elasticity formulation, and experimental data on axial displacement and shear strain in angle-ply laminates are summarized. Numerical predictions of free-edge deformation and interlaminar and through-thickness stress distributions are presented for cross-ply, angle-ply, and quasi-isotropic laminates, and the mechanisms of edge damage and failure in angle-ply laminates are briefly characterized. Extensive diagrams, drawings, graphs, and photographs are provided.
    Keywords: STRUCTURAL MECHANICS
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  • 133
    Publication Date: 2011-08-19
    Description: The service life of aircraft structural components undergoing random stress cycling was analyzed by the application of fracture mechanics. The initial crack sizes at the critical stress points for the fatigue crack growth analysis were established through proof load tests. The fatigue crack growth rates for random stress cycles were calculated using the half-cycle method. A new equation was developed for calculating the number of remaining flights for the structural components. The number of remaining flights predicted by the new equation is much lower than that predicted by the conventional equation. This report describes the application of fracture mechanics and the half-cycle method to calculate the number of remaining flights for aircraft structural components.
    Keywords: STRUCTURAL MECHANICS
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  • 134
    Publication Date: 2011-08-19
    Keywords: STRUCTURAL MECHANICS
    Type: Journal of Spacecraft and Rockets (ISSN 0022-4650); 26; 201-209
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  • 135
    Publication Date: 2011-08-19
    Description: Strong coupling of structure and fluids is common in many engineering environments, particularly when the flow is nonlinear and very sensitive to structural motions. Such coupling can give rise to physically important phenomena, such as a dip in the transonic flutter boundary of a wing. The coupled phenomenon can be analyzed in closed form for simple cases that are defined by linear structural and fluid equations of motion. However, complex cases defined by nonlinear equations pose a more difficult task for solution. It is important to understand these nonlinear coupled problems, since they may lead to physically important new phenomena. Flow discontinuities, such as a shock wave, and structural discontinuities, such as a hinge line of a control surface of a wing, can magnify the coupled effects and give rise to new phenomena. To study such a strongly coupled phenomenon, an integrated approach is presented in this paper. The aerodynamic and structural equations of motion are simultaneously integrated by a time-accurate numerical scheme. The theoretical simulation is done using the time-accurate unsteady transonic aerodynamic equations coupled with modal structural equations of motion. As an example, the coupled effect of shock waves and hinge-line discontinuities are studied for aeroelastically flexible wings with active control surfaces. The simulation in this study is modeled in the time domain and can be extended to simulate accurately other systems where fluids and structures are strongly coupled.
    Keywords: STRUCTURAL MECHANICS
    Type: AIAA Journal (ISSN 0001-1452); 27; 788-793
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  • 136
    Publication Date: 2011-08-19
    Description: The inability to adequately model connections has limited the ability to predict overall system dynamic response. Connections between structural components are often mechanically complex and difficult to accurately model analytically. Improved analytical models for connections are needed to improve system dynamic predictions. This study explores combining Component Mode synthesis methods for coupling structural components with Parameter Identification procedures for improving the analytical modeling of the connections. Improvements in the connection properties are computed in terms of physical parameters so the physical characteristics of the connections can be better understood, in addition to providing improved input for the system model. Two sample problems, one utilizing simulated data, the other using experimental data from a rotor dynamic test rig, are presented.
    Keywords: STRUCTURAL MECHANICS
    Type: ASME, Transactions, Journal of Vibration, Acoustics, Stress, and Reliability in Design (ISSN 0739-3717); 111; 140-147
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  • 137
    Publication Date: 2011-08-19
    Keywords: STRUCTURAL MECHANICS
    Type: AIAA Journal (ISSN 0001-1452); 27; 652-655
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  • 138
    Publication Date: 2011-08-19
    Description: Step-by-step procedures are described which can be used for the preliminary design of fiber composite box beams subjected to combined loadings. These procedures include a collection of approximate closed-form equations so that all the required calculations can be performed using pocket calculators. Included is an illustrative example of a tapered cantilever box beam subjected to combined loads. The box beam is designed to satisfy strength, displacement, buckling, and frequency requirements.
    Keywords: STRUCTURAL MECHANICS
    Type: Journal of Reinforced Plastics and Composites (ISSN 0731-6844); 8; 370-397
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  • 139
    Publication Date: 2011-08-19
    Keywords: STRUCTURAL MECHANICS
    Type: Journal of Aircraft (ISSN 0021-8669); 26; 772-780
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  • 140
    Publication Date: 2011-08-19
    Description: The effects of fatigue, moisture conditioning, and heating on the residual tension strengths of center-cracked graphite/epoxy buffer strip panels were evaluated using specimens made with T300/5208 graphite epoxy in a 16-ply quasi-isotropic layup, with two different buffer strip materials, Kevlar-49 or S-glass. It was found that, for panels subjected to fatigue loading, the residual strengths were not significantly affected by the fatigue loading, the number of repetitions of the loading spectrum, or the maximum strain level. The moisture conditioning reduced the residual strengths of the S-glass buffer strip panels by 10 to 15 percent below the ambient results, but increased the residual strengths of the Kevlar-49 buffer strip panels slightly. For both buffer strip materials, the heat increased the residual strengths of the buffer strip panels slightly over the ambient results.
    Keywords: STRUCTURAL MECHANICS
    Type: Experimental Mechanics (ISSN 0014-4851); 29; 90-94
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  • 141
    Publication Date: 2011-08-19
    Description: This paper presents a numerical model for the thermo-elasto-plastic behavior of an isotropic material. The model is based on the assumption that the yielding of the material obeys von Mises distortion energy theory and the material exhibits isotropic strain hardening. This unique model can be used both for isothermal and non-isothermal cases. The original formulation for the non-isothermal three-dimensional case has been specialized for plane stress conditions and the equations for the computation of warping and thickness change are provided. The finite element implementation of this model is also outlined.
    Keywords: STRUCTURAL MECHANICS
    Type: International Journal for Numerical Methods in Engineering (ISSN 0029-5981); 28; 1103-111
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  • 142
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    Publication Date: 2011-08-19
    Description: Microsandwich honeycombs are honeycombs in which the cell walls are themselves sandwich structures. This article develops the idea of microsandwich honeycombs, outlining their design principles, fabrication techniques and properties.
    Keywords: STRUCTURAL MECHANICS
    Type: SAMPE Journal (ISSN 0091-1062); 25; 43-46
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  • 143
    Publication Date: 2011-08-19
    Description: Static crushing tests were conducted on graphite/epoxy and Kevlar/epoxy square cross section tubes to study the influence of specimen geometry on the energy-absorption capability and scalability of composite materials. The tube inside width-to-wall thickness (W/t) ratio was determined to significantly affect the energy-absorption capability of composite materials. As W/t ratio decreases, the energy-absorption capability increases nonlinearly. The energy-absorption capability of Kevlar epoxy tubes was found to be geometrically scalable, but the energy-absorption capability of graphite/epoxy tubes was not geometrically scalable.
    Keywords: STRUCTURAL MECHANICS
    Type: American Helicopter Society, Journal (ISSN 0002-8711); 34; 59-62
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  • 144
    Publication Date: 2011-08-19
    Description: A structural ceramic analysis and reliability evaluation code has recently been developed encompassing volume and surface flaw induced fracture, modeled by the two-parameter Weibull probability density function. A segment of the software involves computing the Weibull polydimensional stress state crack density coefficient from uniaxial stress experimental fracture data. The relationship of the polydimensional stress coefficient to the uniaxial stress coefficient is derived for a shear-insensitive material with a random surface flaw population.
    Keywords: STRUCTURAL MECHANICS
    Type: American Ceramic Society, Communications (ISSN 0002-7820); 72; 506
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  • 145
    Publication Date: 2011-08-19
    Description: A direct solution procedure for computing the flutter Mach number and the flutter frequency is applied to the aeroelastic analysis of propfans using a finite element structural model and an unsteady aerodynamic model based on a three-dimensional subsonic compressible lifting surface theory. An approximation to the Jacobian matrix that improves the efficiency of the iterative process is presented. The Jacobian matrix is indirectly approximated from approximate derivatives of the flutter matrix, which are updated only in the direction of the last move. Examples are used to illustrate the convergence properties. The direct solution procedure facilitates the automated flutter analysis in addition to contributing to the efficient use of computer time as well as the analyst's time.
    Keywords: STRUCTURAL MECHANICS
    Type: Communications in Applied Numerical Methods (ISSN 0748-8025); 5; 29-37
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  • 146
    Publication Date: 2011-08-19
    Keywords: STRUCTURAL MECHANICS
    Type: Journal of Aircraft (ISSN 0021-8669); 26; 07-74
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  • 147
    Publication Date: 2011-08-19
    Keywords: STRUCTURAL MECHANICS
    Type: AIAA Journal (ISSN 0001-1452); 27; 1274-127
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  • 148
    Publication Date: 2011-08-19
    Description: The width and loading conditions effects on free-edge stress fields in composite laminates are investigated using a three-dimensional finite element analysis. This analysis includes a special free-edge region refinement or superelement with progressive substructuring (mesh refinement) and finite thickness interply layers. The different loading conditions include in-plane and out-of-plane bending, combined axial tension and in-plane shear, twisting, uniform temperature and uniform moisture. Results obtained indicate that: axial tension causes the smallest magnitude of interlaminar free edge stress compared to other loading conditions; free-edge delamination data obtained from laboratory specimens cannot be scaled to structural components; and composite structural components are not likely to delaminate.
    Keywords: STRUCTURAL MECHANICS
    Type: Journal of Composites Technology and Research (ISSN 0885-6804); 11; 15-22
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  • 149
    Publication Date: 2011-08-19
    Description: A nondimensional model of microstructurally short crack growth in creep is developed based on a detailed observation of the creep fracture process of 304 stainless steel. In order to deal with the scatter of small crack growth rate data caused by microstructural inhomogeneity, a random variable technique is used in the model. A cumulative probability of the crack length at an arbitrary time, G(bar a, bar t), and that of the time when a crack reaches an arbitrary length, F(bar t, bar a), are obtained numerically by means of a Monte Carlo method. G(bar a, bar t), and F(bar t, bar a) are the probabilities for a single crack. However, multiple cracks generally initiate on the surface of a smooth specimen from the early stage of creep life to the final stage. Taking into account the multiple crack initiations, the actual crack length distribution observed on the surface of a specimen is predicted by the combination of probabilities for a single crack. The prediction shows a fairly good agreement with the experimental result for creep of 304 stainless steel at 923 K. The probability of creep life is obtained from an assumption that creep fracture takes place when the longest crack reaches a critical length. The observed and predicted scatter of the life is fairly small for the specimens tested.
    Keywords: STRUCTURAL MECHANICS
    Type: ASME, Transactions, Journal of Engineering Materials and Technology (ISSN 0094-4289); 111; 169-175
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  • 150
    Publication Date: 2011-08-19
    Description: Studies making use of higher vibration modes and frequencies have indicated a need for a more accurate beam theory. Equations of motion are developed here that give a more accurate representation of the dynamic behavior of a beam than conventional beam theory. Results are obtained using these equations for the natural vibrations of simply-supported aluminum beams of rectangular cross-sections. These results are compared to results from conventional beam theory, and they are examined to identify where various effects are important.
    Keywords: STRUCTURAL MECHANICS
    Type: ASME, Transactions, Journal of Applied Mechanics (ISSN 0021-8936); 56; 228-231
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  • 151
    Publication Date: 2011-08-19
    Description: The dynamic response of a composite laminate plate to transverse impact loading is simulated numerically. An FEM scheme based on an eight-point brick element and three-dimensional linear elasticity theory is employed, assuming that the laminate layers are homogeneous and orthotropic. The derivation of the model is given in detail; the numerical implementation is briefly outlined; and results for the impact of 0.5-inch-diameter Al spheres at 500, 1000, and 1500 inch/sec on clamped or simply supported 3 x 3-inch plates made of T300/934 graphite/epoxy prepreg with ply orientation (0/-45/45/90)2S are presented in extensive graphs. The model is shown to provide accurate information on the histories of impactor-plate contact force; impactor displacement and velocity; and displacement, velocity, strain, and stress throughout the plate.
    Keywords: STRUCTURAL MECHANICS
    Type: Computers and Structures (ISSN 0045-7949); 31; 3, 19; 453-466
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  • 152
    Publication Date: 2011-08-19
    Keywords: STRUCTURAL MECHANICS
    Type: AIAA Journal (ISSN 0001-1452); 27; 472-478
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  • 153
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    Publication Date: 2011-08-19
    Keywords: STRUCTURAL MECHANICS
    Type: Finite Elements in Analysis and Design (ISSN 0168-874X); 5; 269-279
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  • 154
    Publication Date: 2011-08-19
    Description: A linear finite strip plate element based on Mindlin-Reissner plate theory is developed. The analysis is suitable for both thin and thick plates. In the formulation, new transverse shear strains are introduced and assumed constant in each two-node linear strip. The element stiffness matrix is explicitly formulated for efficient computation and computer implementation. Numerical results showing the efficiency and predictive capability of the element for the analysis of plates are presented for different support and loading conditions and a wide range of thicknesses. No sign of shear locking is observed with the newly developed element.
    Keywords: STRUCTURAL MECHANICS
    Type: Computers and Structures (ISSN 0045-7949); 33; 2, 19
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  • 155
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    Publication Date: 2019-01-25
    Description: The development of probabilistic structural analysis methodology consists of the following program elements: (1) composite load spectra models, (2) computational probabilistic structural analysis methods, and (3) probabilistic constitutive relationships. The development of the probabilistic structural analysis methodology is a joint program of NASA Lewis in-house and sponsored research. The objective of this session is to illustrate recent progress on the application of this methodology to determine the reliability of structural components for rocket propulsion systems. The session contains descriptions of and progress reports on the following specific activities: (1) The NESSUS computer code, (2) approximate methods, (3) advanced methods, (4) composite load spectra applications, (5) probabilistic fracture mechanisms, and (6) probability of failure and risk analysis. Collectively, the progress to date demonstrates that the structural durability of hot engine structural components can be effectively evaluated in a formal probabilistic/reliability framework.
    Keywords: STRUCTURAL MECHANICS
    Type: Structural Integrity and Durability of Reusable Space Propulsion Systems; p 137-138
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  • 156
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    Publication Date: 2019-06-28
    Description: The story of research and technology at NASA Lewis Research Center's Structures Division is presented. The job and designs of the Structures Division needed for flight propulsion is described including structural mechanics, structural dynamics, fatigue, and fracture. The video briefly explains why properties of metals used in structural mechanics need to be tested. Examples of tests and simulations used in structural dynamics (bodies in motion) are briefly described. Destructive and non-destructive fatigue/fracture analysis is also described. The arc sprayed monotape (a composite material) is explained, as are the programs in which monotape plays a roll. Finally, the National Aero-Space Plane (NASP or x-30) is introduced, including the material development and metal matrix as well as how NASP will reduce costs for NASA.
    Keywords: STRUCTURAL MECHANICS
    Type: NASA-TM-109762 , NONP-NASA-VT-94-9962
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  • 157
    Publication Date: 2019-06-28
    Description: A finite-element analysis was conducted to evaluate the stress distributions within mode I and mode II failure specimens, assuming both isotropic and orthotropic elastic material properties. The effects of anisotropy on both the magnitude and the location of the highest stress concentration at the vicinity of the crack tip are significant. The results from modeling realistic blunt crack tip geometry and resin-rich zones imply that local variations in the microstructure strongly influence the stress state near the crack tip and therefore the measured fracture properties. In addition, the features of a viscoelastic model for thermoplastic matrices are described. This model will be used in future investigations of matrix-dominated failure phenomena.
    Keywords: STRUCTURAL MECHANICS
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  • 158
    Publication Date: 2019-06-28
    Description: The development of turbine blade analysis tools as they moved from research contracts under the NASA HOST (Hot Section Technology) program to a PC-based system for preliminary design and to use in evaluating the SSME HPFTP (Space Shuttle Main Engine High Pressure Fuel Turbo Pump) blade is discussed. The heat transfer and structural analysis of the blade, the development of a data base for constitutive modeling of the blade materials, including coatings, and the use of advanced nonlinear finite element methods are addressed.
    Keywords: STRUCTURAL MECHANICS
    Type: ASME PAPER 89-GT-130
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  • 159
    Publication Date: 2019-06-28
    Description: A macroscopic noninteractive reliability model for ceramic matrix composites is presented. The model is multiaxial and applicable to composites that can be characterized as orthotropic. Tensorial invariant theory is used to create an integrity basis with invariants that correspond to physical mechanisms related to fracture. This integrity basis is then used to construct a failure function per unit volume (or area) of material. It is assumed that the overall strength of the composite is governed by weakest link theory. This leads to a Weibull type model similar in nature to the principle of independent action (PIA) model for isotropic monolithic ceramics. An experimental program to obtain model parameters is briefly discussed. In addition, qualitative features of the model are illustrated by presenting reliability surfaces for various model parameters.
    Keywords: STRUCTURAL MECHANICS
    Type: ASME PAPER 89-GT-129
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  • 160
    Publication Date: 2019-06-28
    Description: The various methods that have been studied in the past to allow probabilistic analysis of dynamic response for systems with random parameters are reviewed. Dynamic response may have been obtained deterministically if the variations about the nominal values were small; however, for space structures which require precise pointing, the variations about the nominal values of the structural details and of the environmental conditions are too large to be considered as negligible. These uncertainties are accounted for in terms of probability distributions about their nominal values. The quantities of concern for describing the response of the structure includes displacements, velocities, and the distributions of natural frequencies. The exact statistical characterization of the response would yield joint probability distributions for the response variables. Since the random quantities will appear as coefficients, determining the exact distributions will be difficult at best. Thus, certain approximations will have to be made. A number of techniques that are available are discussed, even in the nonlinear case. The methods that are described were: (1) Liouville's equation; (2) perturbation methods; (3) mean square approximate systems; and (4) nonlinear systems with approximation by linear systems.
    Keywords: STRUCTURAL MECHANICS
    Type: NASA-CR-186171 , NAS 1.26:186171 , POLY-WRI-1569-89
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  • 161
    Publication Date: 2019-06-28
    Description: Under the NASA-sponsored DAMVIBS (Design Analysis Methods for VIBrationS) program, a series of ground vibration tests and NASTRAN finite element model (FEM) correlations were conducted on the Bell AH-1G helicopter gunship to investigate the effects of difficult components on the vibration response of the airframe. Previous correlations of the AG-1G showed good agreement between NASTRAN and tests through 15 to 20 Hz, but poor agreement in the higher frequency range of 20 to 30 Hz. Thus, this effort emphasized the higher frequency airframe vibration response correlations and identified areas that need further R and T work. To conduct the investigations, selected difficult components (main rotor pylon, secondary structure, nonstructural doors/panels, landing gear, engine, furl, etc.) were systematically removed to quantify their effects on overall vibratory response of the airframe. The entire effort was planned and documented, and the results reviewed by NASA and industry experts in order to ensure scientific control of the testing, analysis, and correlation exercise. In particular, secondary structure and damping had significant effects on the frequency response of the airframe above 15 Hz. Also, the nonlinear effects of thrust stiffening and elastomer mounts were significant on the low frequency pylon modes below main rotor 1p (5.4 Hz). The results of the NASTRAN FEM correlations are given.
    Keywords: STRUCTURAL MECHANICS
    Type: NASA-CR-181916-VOL-2 , NAS 1.26:181916-VOL-2 , BHT-699-099-251-VOL-2
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  • 162
    Publication Date: 2019-06-28
    Description: The following analysis is a comparison of analytical methods for calculation of wind load pressures. The analytical methods specified in ASCE Paper No. 3269, ANSI A58.1-1982, the Standard Building Code, and the Uniform Building Code were analyzed using various hurricane speeds to determine the differences in the calculated results. The winds used for the analysis ranged from 100 mph to 125 mph and applied inland from the shoreline of a large open body of water (i.e., an enormous lake or the ocean) a distance of 1500 feet or ten times the height of the building or structure considered. For a building or structure less than or equal to 250 feet in height acted upon by a wind greater than or equal to 115 mph, it was determined that the method specified in ANSI A58.1-1982 calculates a larger wind load pressure than the other methods. For a building or structure between 250 feet and 500 feet tall acted upon by a wind rangind from 100 mph to 110 mph, there is no clear choice of which method to use; for these cases, factors that must be considered are the steady-state or peak wind velocity, the geographic location, the distance from a large open body of water, and the expected design life and its risk factor.
    Keywords: STRUCTURAL MECHANICS
    Type: NASA-TM-102782 , KSC-DM-3282 , NAS 1.15:102782
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  • 163
    Publication Date: 2019-06-28
    Description: The results of a recent surface adjustment of the 15-meter diameter hoop-column antenna are presented. A least-squares differential algorithm is used to adjust the surface shape as close as possible to a perfect parabola. Since the desired perfect parabola is not uniquely known a priori, parameters of the perfect parabola are included in the design vector along with the cable length changes. As an extension to an earlier study, lateral sensitivity is included in the least-squares adjustment procedure. In addition, the effect of cable length uncertainties on the surface RMS error is considered and an error bound is derived. The results in this study indicate an improvement over earlier studies. The sensitivity analysis provided a quantitative measure of the needed accuracy of the cable adjustments in the laboratory. Recommendations are included to further enhance shape adjustment.
    Keywords: STRUCTURAL MECHANICS
    Type: NASA-TM-101538 , NAS 1.15:101538
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  • 164
    Publication Date: 2019-06-28
    Description: The stability of a frequency response curve under mild perturbations of the system's matrix is investigated. Using recent developments in the theory of singularities of differentiable maps, it is shown that the stability of a response curve depends on the structure of the system's matrix. In particular, the frequency response curves of a cylic system are shown to be unstable. Consequently, slight parameter variations engendered by mistuning will induce a significant difference in the topology of the forced response curves, if the mistuning transformation crosses the bifurcation set.
    Keywords: STRUCTURAL MECHANICS
    Type: NASA-TM-102290 , ICOMP-89-17 , E-4960 , NAS 1.15:102290
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  • 165
    Publication Date: 2019-06-28
    Description: The role of adaptive structures in meeting the structural requirements for future NASA missions is described. Many of NASA's future missions require large precision truss type structures where prespecified locations on the structure must maintain micron level accuracies with respect to each other when subjected to manufacturing errors and static, thermal, and dynamic inputs. In many cases the incorporation of the adaptive structures concepts into the structural design to adjust the on-orbit structure will be the only feasible means to attain the desired accuracies. In order for the structures to be able to change structural characteristics on orbit they must be uncoupled and independent of the control system used to impart the required rigid body motion to the spacecraft.
    Keywords: STRUCTURAL MECHANICS
    Type: ESA, Spacecraft Structures and Mechanical Testing; p 121-126
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  • 166
    Publication Date: 2019-06-28
    Description: A method for performing a global/local stress analysis is described and its capabilities are demonstrated. The method employs spline interpolation functions which satisfy the linear plate bending equation to determine displacements and rotations from a global model which are used as boundary conditions for the local model. Then, the local model is analyzed independent of the global model of the structure. This approach can be used to determine local, detailed stress states for specific structural regions using independent, refined local models which exploit information from less-refined global models. The method presented is not restricted to having a priori knowledge of the location of the regions requiring local detailed stress analysis. This approach also reduces the computational effort necessary to obtain the detailed stress state. Criteria for applying the method are developed. The effectiveness of the method is demonstrated using a classical stress concentration problem and a graphite-epoxy blade-stiffened panel with a discontinuous stiffener.
    Keywords: STRUCTURAL MECHANICS
    Type: NASA-TM-101640 , NAS 1.15:101640
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  • 167
    Publication Date: 2019-06-28
    Description: The user options available for running the MHOST finite element analysis package is described. MHOST is a solid and structural analysis program based on the mixed finite element technology, and is specifically designed for 3-D inelastic analysis. A family of 2- and 3-D continuum elements along with beam and shell structural elements can be utilized, many options are available in the constitutive equation library, the solution algorithms and the analysis capabilities. The outline of solution algorithms is discussed along with the data input and output, analysis options including the user subroutines and the definition of the finite elements implemented in the program package.
    Keywords: STRUCTURAL MECHANICS
    Type: NASA-CR-182235-VOL-2 , NAS 1.26:182235-VOL-2 , FEF/PD/1101/89-VOL-2
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  • 168
    Publication Date: 2019-01-25
    Description: Panel flutter is the self excited oscillations of a plate in supersonic flow. Linear theory gives no information about the panel's deflections and stresses. Hence, the service life of the panel cannot be predicted by linear methods. Nonlinear structural theory determines the limit cycle oscillating frequency, and also panel deflections and stresses. Panel fatigue life, therefore, can be predicted. For a more thorough understanding of panel flutter behavior, the geometric nonlinearity effects due to large deflections must be considered in the formulation. The Galerkin's method was used in the investigation of limit cycle oscillations of panels in supersonic flow in the spatial domain, and the panel deflections. All nonlinear flutter methods and results presently available were limited to a linear or linearized aerodynamic theory. Extension of the finite element flutter formulation to include nonlinear hypersonic aerodynamic loading and finite element nonlinear panel flutter results are presented.
    Keywords: STRUCTURAL MECHANICS
    Type: Carleton Univ., Proceedings of the Twelfth Canadian Congress of Applied Mechanics, Volumes 1 and 2; p 118-119
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  • 169
    Publication Date: 2018-12-01
    Description: The prediction of the ultimate load carrying capability for compressively loaded shell structures is a challenging nonlinear analysis problem. Selected areas of finite element technology research and nonlinear solution technology are assessed. Herein, a finite element analysis procedure is applied to four shell collapse problems which have been used by computational structural mechanics researchers in the past. This assessment will focus on a number of different shell element formulations and on different approaches used to account for geometric nonlinearities. The results presented confirm that these aspects of nonlinear shell analysis can have a significant effect on the predicted nonlinear structural response. All analyses were performed using the CSM Testbed software system which allowed a convenient assessment of different element formulations with a consistent approach to solving the discretized nonlinear equations.
    Keywords: STRUCTURAL MECHANICS
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  • 170
    Publication Date: 2018-12-01
    Description: The postbuckling behavior of square compression-loaded graphite-epoxy plates and isotropic plates with a central circular cutout is studied. The results suggest that the change in the plate's axial stiffness is strongly dependent on cutout size and plate orthotropy. It is found that the cutout size and stacking sequence of a composite plate may be tailored to optimize postbuckling stiffness. Also, it is suggested that a cutout may influence model interaction in a plate. The effects of load-path eccentricity on buckling behavior are examined.
    Keywords: STRUCTURAL MECHANICS
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  • 171
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    Publication Date: 2019-06-28
    Description: A hypothesis proposed by Nefske and Sung (1987) that the mechanical energy flow in acoustic/structural systems can be modeled using a thermal energy flow analogy was tested for both longitudinal vibration in rods and transverse flexural vibrations in beams. It was found that the rod behaves according to the energy flow analogy. However, the beam solutions behaved significantly differently than predicted by the thermal analogy, unless spatially averaged energy and power flow were considered. Otherwise, the beam analysis is restricted to frequencies where the near-field terms in the displacement solution are negligible over most of the beam.
    Keywords: STRUCTURAL MECHANICS
    Type: AIAA PAPER 89-1122
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  • 172
    Publication Date: 2019-06-28
    Description: The effects of nonlinear damping on the large-deflection response of symmetrically laminated composite panels is studied by time-domain simulation in an attempt to quantify experimentally observed phenomena. A single-mode deflection approach is used in the equations of motion and in the linear and nonlinear damping models. The probability, peak-probability, and spectral-density data are compiled for both strains and deflection. The rms responses as a function of input excitation level are also obtained and compared to linear, equivalent-linearization, and Fokker-Planck equation solutions.
    Keywords: STRUCTURAL MECHANICS
    Type: AIAA PAPER 89-1104
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  • 173
    Publication Date: 2019-06-28
    Description: By using the linear mode shapes of a thermally buckled structure, a governing system of finite element equations for large-deflection random vibrations is reduced to a system of nonlinear modal equations. This system is then solved using the method of equivalent linearization. The methodology developed in this study is applicable to the design of aerospace vehicles subjected to combined thermal/acoustic loads.
    Keywords: STRUCTURAL MECHANICS
    Type: AIAA PAPER 89-1100
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  • 174
    Publication Date: 2019-06-28
    Description: The motion of an elastically supported cylinder forced by a nonlinear, quasi-static, aerodynamic model with the unusual feature of a motion-dependent forcing frequency was studied. Numerical solutions for the motion and the Lyapunov exponents are presented for three forcing amplitudes and two frequencies (1.0 and 1.1 times the Strouhal frequency). Initially, positive Lyapunov exponents occur and the motion can appear chaotic. After thousands of characteristic times, the motion changes to a motion (verified analytically) that is periodic and damped. This periodic, damped motion was not observed experimentally, thus raising questions concerning the modeling.
    Keywords: STRUCTURAL MECHANICS
    Type: NASA-TM-101038 , A-88302 , NAS 1.15:101038
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  • 175
    Publication Date: 2019-06-28
    Description: The environmental aspect of elevated temperature and its relationship to the science of strain gage calibrations of aircraft structures are addressed. A section of a wing designed for a high-speed aircraft structure was used to study this problem. This structure was instrumented with strain gages calibrated at both elevated and room temperatures. Load equations derived from a high-temperature load calibration were compared with equations derived from an identical load calibration at room temperature. The implications of the high temperature load calibration were studied from the viewpoint of applicability and necessity. Load equations derived from the room temperature load calibration resulted in generally lower equation standard errors than equations derived from the elevated temperature load calibration. A distributed load was applied to the structure at elevated temperature and strain gage outputs were measured. This applied load was then calculated using equations derived from both the room temperature and elevated temperature calibration data. It was found that no significant differences between the two equation systems existed in terms of computing this applied distributed load, as long as the thermal shifts resulting from thermal stresses could be identified. This identification requires a heating of the structure. Therefore, it is concluded that for this structure, a high temperature load calibration is not required. However, a heating of the structure is required to determine thermal shifts.
    Keywords: STRUCTURAL MECHANICS
    Type: NASA-TP-2921 , H-1331 , NAS 1.60:2921
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  • 176
    Publication Date: 2019-06-28
    Description: When welded structures depend on properties beyond the elastic limit to qualify their ultimate safety factor, and weld-parent materials abruptly change at the interface, then stress discontinuity is inevitable. The stress concentration is mildly sensitive to material relative strain hardening and acutely sensitive to applied stress fields. Peak stresses occur on the weld surface, at the interface, and dissipate within a 0.01-inch band. When the stress is intense, the weld will always fracture at the interface. The analysis incorporates a classical mechanics model to more sharply define stress spikes within the bandwidth, and suggests a relative material index and Poisson's ratio related to strain hardening. Implications are discussed which are applicable to industries of high performance structures.
    Keywords: STRUCTURAL MECHANICS
    Type: NASA-TP-2935 , NAS 1.60:2935
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  • 177
    Publication Date: 2019-06-28
    Description: The research work performed during the past year on finite element implementation and computational techniques pertaining to high temperature composites is outlined. In the present research, two main issues are addressed: efficient geometric modeling of composite structures and expedient numerical integration techniques dealing with constitutive rate equations. In the first issue, mixed finite elements for modeling laminated plates and shells were examined in terms of numerical accuracy, locking property and computational efficiency. Element applications include (currently available) linearly elastic analysis and future extension to material nonlinearity for damage predictions and large deformations. On the material level, various integration methods to integrate nonlinear constitutive rate equations for finite element implementation were studied. These include explicit, implicit and automatic subincrementing schemes. In all cases, examples are included to illustrate the numerical characteristics of various methods that were considered.
    Keywords: STRUCTURAL MECHANICS
    Type: NASA-CR-185120 , NAS 1.26:185120
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  • 178
    Publication Date: 2019-06-28
    Description: Three-dimensional finite-element analyses of middle-crack tension (M-T) and bend specimens subjected to mode I loadings were performed to study the stress singularity along the crack front. The specimen was modeled using 20-node isoparametric elements. The displacements and stresses from the analysis were used to estimate the power of singularities using a log-log regression analysis along the crack front. The analyses showed that finite-sized cracked bodies have two singular stress fields of the form rho = C sub o (theta, z) r to the -1/2 power + D sub o (theta, phi) R to the lambda rho power. The first term is the cylindrical singularity with the power -1/2 and is dominant over the middle 96 pct (for Poisson's ratio = 0.3) of the crack front and becomes nearly zero at the free surface. The second singularity is a vertex singularity with the vertex point located at the intersection of the crack front and the free surface. The second term is dominant at the free surface and becomes nearly zero away from the the boundary layer. The thickness of the boundary layer depends on Poisson's ratio of the material and is independent of the specimen type. The thickness of the boundary layer varied from 0 pct to about 5 pct of the total specimen thickness as Poisson's ratio varied from 0.0 to 0.45. Because there are two singular stress fields near the free surface, the strain energy release rate (G) is an appropriate parameter to measure the severity of the crack.
    Keywords: STRUCTURAL MECHANICS
    Type: NASA-CR-181840 , NAS 1.26:181840
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  • 179
    Publication Date: 2019-06-28
    Description: Boeing Helicopters, together with other U.S. Helicopter manufacturers, is engaged in a finite element applications program designed to emplace in the U.S. a superior capability to utilize finite element analysis models in support of helicopter airframe structurel design. This program was given the acronym DAMVIBS (Design Analysis Methods for VIBrationS). The test plan is reviewed and results are presented for a shake test of the Boeing Model 360 helicopter. Results of the test will serve as the basis for validation of a finite element vibration model of the helicopter.
    Keywords: STRUCTURAL MECHANICS
    Type: NASA-CR-181766 , NAS 1.26:181766 , D210-12328-3
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  • 180
    Publication Date: 2019-06-28
    Description: Analytical expressions for the crack-face displacements of an embedded elliptic crack in infinite solid subjected to arbitrary tractions are obtained. The tractions on the crack faces are assumed to be expressed in a polynomial form. These displacements expressions complete the exact solution of Vijayakumar and Atluri, and Nishioki and Atluri. For the special case of an embedded crack in an infinite solid subjected to uniform pressure loading, the present displacements agree with those by Green and Sneddon. The displacement equations derived were used with the finite-element alternating method (FEAM) for the analysis of a semi-elliptic surface crack in a finite solid subjected to remote tensile loading. The maximum opening displacements obtained with FEAM are compared to those with the finite-element method with singularity elements. The maximum crack opening displacements by the two methods showed good agreement.
    Keywords: STRUCTURAL MECHANICS
    Type: NASA-CR-181822 , NAS 1.26:181822
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  • 181
    Publication Date: 2019-06-28
    Description: The use of special interface finite elements to model frictional restraint in composite interfaces is described. These elements simulate Coulomb friction at the interface, and are incorporated into a standard finite element analysis of a two-dimensional isolated fiber pullout test. Various interfacial characteristics, such as the distribution of stresses at the interface, the extent of slip and delamination, load diffusion from fiber to matrix, and the amount of fiber extraction or depression are studied for different friction coefficients. The results are compared to those obtained analytically using a singular integral equation approach, and those obtained by assuming a constant interface shear strength. The usefulness of these elements in micromechanical modeling of fiber-reinforced composite materials is highlighted.
    Keywords: STRUCTURAL MECHANICS
    Type: NASA-CR-182281 , NAS 1.26:182281
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  • 182
    Publication Date: 2019-06-28
    Description: A simplified stochastic model is proposed for crack initiation and short-crack growth under creep and creep-fatigue conditions. Material inhomogeneity provides the random nature of crack initiation and early growth. In the model, the influence of microstructure is introduced by the variability of: (1) damage accumulation along grain boundaries, (2) critical damage required for crack initiation or growth, and (3) the grain-boundary length. The probabilities of crack initiation and growth are derived by using convolution integrals. The model is calibrated and used to predict the crack density and crack-growth rate of short cracks of 304 stainless steel under creep and creep-fatigue conditions. The mean-crack initiation lives are predicted to be within an average deviation of about 10 percent from the experimental results. The predicted cumulative distributions of crack-growth rate follow the experimental data closely. The applicability of the simplified stochastic model is discussed and the future research direction is outlined.
    Keywords: STRUCTURAL MECHANICS
    Type: NASA-TM-101358 , E-4386 , NAS 1.15:101358
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  • 183
    Publication Date: 2019-06-28
    Description: This is the fourth of a set of five volumes which describe the software architecture for the Computational Structural Mechanics Testbed. Derived from NICE, an integrated software system developed at Lockheed Palo Alto Research Laboratory, the architecture is composed of the command language CLAMP, the command language interpreter CLIP, and the data manager GAL. Volumes 1, 2, and 3 (NASA CR's 178384, 178385, and 178386, respectively) describe CLAMP and CLIP and the CLIP-processor interface. Volumes 4 and 5 (NASA CR's 178387 and 178388, respectively) describe GAL and its low-level I/O. CLAMP, an acronym for Command Language for Applied Mechanics Processors, is designed to control the flow of execution of processors written for NICE. Volume 4 describes the nominal-record data management component of the NICE software. It is intended for all users.
    Keywords: STRUCTURAL MECHANICS
    Type: NASA-CR-178387 , NAS 1.26:178387 , LMSC/D878511-VOL-4
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  • 184
    Publication Date: 2019-06-28
    Description: The objectives of the project were to investigate numerical methodology for the determination of narrowband response in the geometrically nonlinear regime, to determine response characteristics for geometrically nonlinear plates subjected to random loading and to compare the predictions with experiments to be performed at NASA-Langley. The first two objectives were met. The response of composite plates subjected to both narrowband and broadband excitation were studied and the results are presented and discussed.
    Keywords: STRUCTURAL MECHANICS
    Type: NASA-CR-184618 , NAS 1.26:184618
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  • 185
    Publication Date: 2019-06-28
    Description: This paper considers complex transcendental eigenvalue problems where one is interested in pairs of eigenvalues that are restricted to take real values only. Such eigenvalue problems arise in dynamic stability analysis of nonconservative physical systems, i.e., flutter analysis of aeroelastic systems. Some available solution methods are discussed and a new method is presented. Two computational approaches are described for analytical evaluation of the sensitivities of these eigenvalues when they are dependent on other parameters. The algorithms presented are illustrated through examples.
    Keywords: STRUCTURAL MECHANICS
    Type: NASA-CR-182241 , E-4560 , NAS 1.26:182241
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  • 186
    Publication Date: 2019-06-28
    Description: Asymptotic modal analysis (AMA) is used to study a rectangular cavity with a flexible vibrating portion on one wall and five rigid walls. The agreement between mean square pressure levels of the cavity interior calculated from classical modal analysis and from the AMA method improved as the number of responding modes increased. It is shown that intensification effects were due to both the excitation location and the response location.
    Keywords: STRUCTURAL MECHANICS
    Type: AIAA PAPER 89-1073
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  • 187
    Publication Date: 2019-06-28
    Description: An experiment is designed to demonstrate and verify the performance of the on-orbit assessment approach for large flexible space truss structures. The on-orbit assessment approach can be accomplished, in principle, with dynamic response information, structural identification methods, and model correlation techniques which produce an adjusted mathematical model. An optimal update of the structure model is formed using the response data, then examined to locate damaged members. The experiment uses a laboratory scale model truss structure which exhibits characteristics expected for large space truss structures. Vibration experiments are performed to generate response data for the damaged truss. The damage location approach is described, as well as analytical work performed in support of the vibration tests, the measured response of the test article, and some preliminary results.
    Keywords: STRUCTURAL MECHANICS
    Type: AIAA PAPER 89-1291
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  • 188
    Publication Date: 2019-06-28
    Description: The effects of manufacture flaws and repairs in high altitude scientific balloons was examined. A right circular cylinder was used to induce a biaxial tension-tension stress field in the polyethlene film used to manufacture these balloons. A preliminary investigation of the effect that cylinder geometry has on stress rate as a function of inflation rate was conducted. The ultimate goal was to rank, by order of degrading effects, the flaws and repairs commonly found in current high altitude balloons.
    Keywords: STRUCTURAL MECHANICS
    Type: NASA-CR-181872 , NAS 1.26:181872
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  • 189
    Publication Date: 2019-06-28
    Description: The postbuckling response of circular rings (or long cylinders) is examined. The rings are subjected to four types of external pressure loadings; each type of pressure is defined by its magnitude and direction at points on the buckled ring. Newton's method is applied to the nonlinear differential equations of the exact inextensional theory for the ring problem. A zeroth approximation for the solution of the nonlinear equations, based on the mode shape corresponding to the first buckling pressure, is derived in closed form for each of the four types of pressure. The zeroth approximation is used to start the iteration cycle in Newton's method to compute numerical solutions of the nonlinear equations. The zeroth approximations for the postbuckling pressure-deflection curves are compared with the converged solutions from Newton's method and with similar results reported in the literature.
    Keywords: STRUCTURAL MECHANICS
    Type: NASA-TP-2941 , L-16578 , NAS 1.60:2941
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  • 190
    Publication Date: 2019-06-28
    Description: The determination of the fundamental (lowest) natural vibration frequencies and associated mode shapes is a key step used to uncover and correct potential failures or problem areas in most complex structures. However, the computation time taken by finite element codes to evaluate these natural frequencies is significant, often the most computationally intensive part of structural analysis calculations. There is continuing need to reduce this computation time. This study addresses this need by developing methods for parallel computation.
    Keywords: STRUCTURAL MECHANICS
    Type: NASA. Langley Research Center, NASA Workshop on Computational Structural Mechanics 1987, Part 1; p 261-272
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  • 191
    Publication Date: 2019-06-28
    Description: The responses of an unsymmetrically laminated fiber-reinforced composite cylinder to an axial compressive load, a torsional load, and the temperature change associated with cooling from the processing temperature to the service temperature are investigated. These problems are considered axisymmetric and the response is studied in the context of linear elastic material behavior and geometrically linear kinematics. Four different laminates are studied: a general unsymmetric laminate; two unsymmetric but more conventional laminates; and a conventional quasi-isotropic symmetric laminate. The responses based on closed-form solutions for different boundary conditions are computed and studied in detail. Particular emphasis is directed at understanding the influence of elastic couplings in the laminates. The influence of coupling decreased from a large effect in the general unsymmetric laminate, to practically no effect in the quasi-isotropic laminate. For example, the torsional loading of the general unsymmetric laminate resulted in a radial displacement. The temperature change also caused a significant radial displacement to occur near the ends of the cylinder. On the other hand, the more conventional unsymmetric laminate and the quasi-isotropic cylinder did not deform radially when subjected to a torsional load. From the results obtained, it is clear the degree of elastic coupling can be controlled and indeed designed into a cylinder, the degree and character of the coupling being dictated by the application.
    Keywords: STRUCTURAL MECHANICS
    Type: NASA-CR-185834 , NAS 1.26:185834 , UM-TR-89-2
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  • 192
    Publication Date: 2019-06-28
    Description: The Objectives, FY 1989 Plans, Approach, and FY 1989 Milestones for the Structural Mechanics Division's research programs are presented. Fiscal year 1988 Accomplishments are presented where applicable. This information is useful in program coordination with other governmental organizations in areas of mutual interest.
    Keywords: STRUCTURAL MECHANICS
    Type: NASA-TM-101592 , NAS 1.15:101592
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  • 193
    Publication Date: 2019-06-28
    Description: The results of a stability design study are presented for a slender column with curved longitudinal stiffeners for large space structure applications. Linear stability analyses are performed using a link-plate representation of the stiffeners to determine stiffener local buckling stresses. Results from a set of parametric analyses are used to determine an approximate explicit expression for stiffener local buckling in terms of its geometric parameters. This expression along with other equations governing column stability and mass are assembled into a determinate system describing minimum mass stiffened column design. An iterative solution is determined to solve this system and a computer program incorporating this routine is presented. Example design problems are presented which verify the solution accuracy and illustrate the implementation of the solution routine. Also, observations are made which lead to a greatly simplified first iteration design equation relating the percent increase in column mass to the percent increase in column buckling load. From this, generalizations are drawn as to the mass savings offered by the stiffened column concept. Finally, the percent increase in fundamental column vibration frequency due to the addition of deployable stiffeners is studied.
    Keywords: STRUCTURAL MECHANICS
    Type: NASA-TM-101636 , NAS 1.15:101636
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  • 194
    Publication Date: 2019-06-28
    Description: In January 1989 an accident occurred in the National Transonic Facility wind tunnel at NASA Langley Research Center that was believed to be caused by the failure of a thermal insulation retainer. A structural analysis of this retainer assembly was performed in order to understand the possible failure mechanisms. Two loading conditions are important and were considered in the analysis. The first is the centrifugal force due to the fact that this retainer is located on the fan drive shaft. The second loading is a differential temperature between the retainer assembly and the underlying shaft. Geometrically nonlinear analysis is required to predict the stiffness of this component and to account for varying contact regions between various components in the assembly. High, local stresses develop in the band part of the assembly near discontinuities under both the centrifugal and thermal loadings. The presence of an aluminum ring during a portion of the part's operating life was found to increase the stresses in other regions of the band. Under the centrifugal load, high bending stresses develop near the intersection of the band with joints in the assembly. These high bending stresses are believed to be the most likely cause for failure of the assembly.
    Keywords: STRUCTURAL MECHANICS
    Type: NASA-TM-101580 , NAS 1.15:101580
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  • 195
    Publication Date: 2019-06-28
    Description: As a part of the redesign of the Space Shuttle Solid Rocket Motor, the field and nozzle-to-case joints were redesigned to minimize the dynamic flexure caused by internal motor pressurization during ignition. The O-ring seals and glands for the joints were designed to accommodate both structural deflections and to promote pressure assistance. A test program was conducted to determine if a fluorocarbon elastomeric O-ring could meet this criteria in the redesigned gland. Resiliency tests were used to investigate the O-ring response to gap motion while static seal tests were used to verify design criteria of pressure assistance for sealing. All tests were conducted in face seal fixtures mounted in servo-hydraulic test machines. The resiliency of the O-ring was found to be extremely sensitive to the effects of temperature. The External Tank/Solid Rocket Booster attach strut loads had a negligible affect on the ability of the O-ring to track the simulated SRB field joint deflection. In the static pressure-assisted seal tests, as long as physical contact was maintained between the O-ring and the gland sealing surface, pressure assistance induced instantaneous sealing.
    Keywords: STRUCTURAL MECHANICS
    Type: NASA-TM-101591 , NAS 1.15:101591
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  • 196
    Publication Date: 2019-06-28
    Description: The use of simplified elasticity solutions to determine the mechanical response of thick laminated beams and plates subject to out-of-plane loading is demonstrated. Excellent results were obtained which compare favorably with theoretical, numerical and experimental analyses from other sources. The most important characteristic of the solution methodology presented is that it combines great mathematical precision with simplicity. This symbiosis has been needed for design with advanced composite materials.
    Keywords: STRUCTURAL MECHANICS
    Type: NASA-CR-185391 , NAS 1.26:185391
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  • 197
    Publication Date: 2019-06-28
    Description: This work is concerned with modeling the mechanical deformation or constitutive behavior of composites comprised of a periodic microstructure under small displacement conditions at elevated temperature. A mesomechanics approach is adopted which relates the microimechanical behavior of the heterogeneous composite with its in-service macroscopic behavior. Two different methods, one based on a Fourier series approach and the other on a Green's function approach, are used in modeling the micromechanical behavior of the composite material. Although the constitutive formulations are based on a micromechanical approach, it should be stressed that the resulting equations are volume averaged to produce overall effective constitutive relations which relate the bulk, volume averaged, stress increment to the bulk, volume averaged, strain increment. As such, they are macromodels which can be used directly in nonlinear finite element programs such as MARC, ANSYS and ABAQUS or in boundary element programs such as BEST3D. In developing the volume averaged or efective macromodels from the micromechanical models, both approaches will require the evaluation of volume integrals containing the spatially varying strain distributions throughout the composite material. By assuming that the strain distributions are spatially constant within each constituent phase-or within a given subvolume within each constituent phase-of the composite material, the volume integrals can be obtained in closed form. This simplified micromodel can then be volume averaged to obtain an effective macromodel suitable for use in the MARC, ANSYS and ABAQUS nonlinear finite element programs via user constitutive subroutines such as HYPELA and CMUSER. This effective macromodel can be used in a nonlinear finite element structural analysis to obtain the strain-temperature history at those points in the structure where thermomechanical cracking and damage are expected to occur, the so called damage critical points of the structure.
    Keywords: STRUCTURAL MECHANICS
    Type: NASA-TM-102051 , E-4670 , NAS 1.15:102051
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  • 198
    Publication Date: 2019-06-28
    Description: The shear loading of a composite rectangular plate with a centrally located circular cutout was analyzed in order to predict the buckling load of the plate. The first step in this analysis is to calculare the in-plane stress distribution of the plate prior to buckling. This problem can be solved using finite element methods, but a quicker and more cost efficient method is desired. The method chosen to determine the pre-buckling stresses is that of boundary collocation using complex variables. The real valued force functions are written in terms of two complex valued functions, each of which is a function of a different complex variable. The solution of the generalized biharmonic function is a superposition of functions of these two complex variables. For this analysis, the force functions are represented with a Laurent series. The constants in these series are found using boundary collocation. Two force equations for complex variables are satisfied over the plate boundaries to obtain these constants. The stresses in the plate are then known for any particular locations on the plate given the applied shear on the edges of the plate.
    Keywords: STRUCTURAL MECHANICS
    Type: NASA-CR-185346 , NAS 1.26:185346
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  • 199
    Publication Date: 2019-06-28
    Description: Excessive vibration is the most common technical problem to arise as a show stopper in the development of a new rotorcraft. Vibration predictions have not been relied on by the industry during design because of deficiencies in finite element dynamic analyses. A rotorcraft structural dynamics program aimed at meeting the industry's long-term needs in this key technical area was implemented at Langley in 1984. The subject program is a cooperative effort involving NASA, the Army, academia, and the helicopter industry in a series of generic research activities directed at establishing the critical elements of the technology base needed for development of a superior finite element dynamics design analysis capability in the U.S. helicopter industry. An executive overview of the background, status, accomplishments, and future direction of this program is presented.
    Keywords: STRUCTURAL MECHANICS
    Type: NASA-TM-101618 , NAS 1.15:101618
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  • 200
    Publication Date: 2019-06-28
    Description: A tapered p-version beam finite element suitable for dynamic applications is derived. The taper in the element is represented by allowing the area moments of inertia to vary as quartic polynomials along the length of the beam, and the cross-sectional area to vary as a quadratic polynomial. The p-version finite-element characteristics are implemented through a set of polynomial shape functions. The lower-order shape functions are identical to the classical cubic and linear shape functions normally associated with a beam element. The higher-order shape functions are a hierarchical set of polynomials that are integrals of orthogonal polynomials. Explicit expressions for the mass and stiffness matrices are presented for an arbitrary value of p. The element has been verified to be numerically stable using shape functions through 22nd order.
    Keywords: STRUCTURAL MECHANICS
    Type: NASA-TP-2931 , L-16577 , NAS 1.60:2931 , AVSCOM-TR-B-002 , AD-A213443
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