ALBERT

Description: The latest technology for structural analysis in relation to the design tasks that lie ahead for the space shuttle is reviewed. For shell-of-revolution structures, the analysis can be formulated as a one-dimensional problem which is readily solved by using finite-difference or numerical-integration techniques. For more general asymmetric shells, a two-dimensional formulation is required. However, the governing equations are readily formulated and are amenable to solution by finite-difference techniques. For a completely general structural arrangement, such as structural frameworks, recourse is usually made to discretized formulations using finite elements. Of course, the finite-element programs could be used for shell structures, but at a loss in accuracy and increase in computer time compared with the special purpose programs.

Description: The finite element method is extended to a broad class of practical nonlinear problems, treating both theory and applications from a general and unifying point of view. The thermomechanical principles of continuous media and the properties of the finite element method are outlined, and are brought together to produce discrete physical models of nonlinear continua. The mathematical properties of the models are analyzed, and the numerical solution of the equations governing the discrete models is examined. The application of the models to nonlinear problems in finite elasticity, viscoelasticity, heat conduction, and thermoviscoelasticity is discussed. Other specific topics include the topological properties of finite element models, applications to linear and nonlinear boundary value problems, convergence, continuum thermodynamics, finite elasticity, solutions to nonlinear partial differential equations, and discrete models of the nonlinear thermomechanical behavior of dissipative media.

Description: Description of an efficient digital computer method for the determination of the propagation of elastic stresses and deformations in certain geometrically nonlinear structures subjected to high impact loading. The finite-element matrix displacement approach utilizing curved quadrilateral shell elements in conjunction with a nodewise predictor-corrector method employing Runge-Kutta extrapolation techniques has been adopted for the present solution. The related computer program written in FORTRAN V for the UNIVAC 1108 computer has proved to be effective for the solution of a range of practical problems including rectangular and cylindrical panels. Numerical results are presented for a relevant structure, the cell container, and the negative electrode of an impact-resistant battery subjected to high impact, simulating its free landing on a planetary surface.

Description: The effect of slight meridional curvature on the buckling of shells subjected to an external constant directional lateral pressure is examined. A class of nearly cylindrical shells with constant meridional curvature, a central radius-to-thickness ratio of 500, and central rise-to-shell-length ratios varying from plus 5% to minus 5% is considered. A brief study is presented of the dependence of the critical lateral pressure on the meridional curvature and on the length and meridional edge restraint.

Description: The results are discussed of a study of the effect of slots on the buckling of cylinders with circular holes of systematically varied circularity. The results obtained suggest that the substantial increase in the buckling loads of cylindrical shells resulting from increases in slot length is due to a relief of the bending stress field.

Description: The paper defines the experimental phase of an objective to obtain the mechanical characteristics and coefficients required by the generalized form of Hooke's law for nylon-polyurethane-coated fabric. Test specimens were cylindrical fabric sleeves and were loaded in axial tension by an Instron, in hoop tension by pressurizing, and in shear by a torquing fixture. An extensive amount of strain data is included for a wide combination of the three membrane loads. The tests indicate highly nonlinear stress-strain characteristics of the fabric and a strong dependency on all three membrane loads.

Description: Concepts of sonic-boom pressure loading of building structures and the associated responses are reviewed, and results of pertinent theoretical and experimental research programs are summarized. The significance of sonic-boom load time histories, including waveshape effects, are illustrated with the aid of simple structural elements such as beams and plates. Also included are discussions of the significance of such other phenomena as three-dimensional loading effects, air cavity coupling, multimodal responses, and structural nonlinearities. Measured deflection, acceleration, and strain data from laboratory models and full-scale building tests are summarized, and these data are compared, where possible, with predicted values. Damage complaint and claim experience due both to controlled and uncontrolled supersonic flights over communities are summarized with particular reference to residential, commercial, and historic buildings. Sonic-boom-induced building responses are compared with those from other impulsive loadings due to natural and cultural events and from laboratory simulation tests.

Description: Study of the failure of glass windows, which is probably the most severe problem confronting the SST program outside of the psychological and sociological aspects. The structural configuration most likely to suffer a window failure due to sonic boom excitation is one representable by a single large room, a single large window, and an open door. It is suggested that if the open door were replaced with another window the resultant stresses in both windows would be substantially reduced.

Description: A constitutive theory is presented for representing the anisotropic viscoplastic behavior of high-temperature alloys that possess directional properties resulting from controlled grain growth or solidification. The theory is an extension of a viscoplastic model that has been applied in structural analyses involving isotropic metals. Anisotropy is introduced through the definition of a vector field that identifies a preferential (solidification) direction at each material point. Following the development of a full multiaxial theory, application is made to homogeneously stressed elements in pure shear and to a uniaxially stressed rectangular block in plane stress with the stress direction oriented at an arbitrary angle with the material direction. It is shown that an additional material parameter introduced to characterize the degree of anisotropy can be determined on the basis of simple creep tests.

Description: The force input mobility of an infinite elastic circular cylindrical shell filled with fluid is derived by using the spectral equations of motion. Mobilities are evaluated and their physical interpretations are discussed for a steel shell of thickness h/a = 0.05 filled with water and vibrating in the n = 0, 1 and 2 circumferential modes. The results are subsequently used to analyze the related situations of wave transmission through a radial ring constraint and the far field vibrational energy distributions between the contained fluid and the shell wall for line and point driving forces.

Description: The boundary collocation method was used to generate Mode 1 stress intensity and crack mouth opening displacement coefficients for externally radially cracked ring segments subjected to three point radial loading. Numerical results were obtained for ring segment outer-to-inner radius ratios (R sub o/R sub i) ranging from 1.10 to 2.50 and crack length to segment width ratios (a/W) ranging from 0.1 to 0.8. Stress intensity and crack mouth displacement coefficients were found to depend on the ratios R sub o/R sub i and a/W as well as the included angle between the directions of the reaction forces. Previously announced in STAR as N83-35413

Description: Solutions are given for several plane elastostatic problems of plates having a V-notch on one edge, and subjected to a variety of boundary conditions. The effect of the magnitude of the V-notch angle and specimen geometry on stress intensity factors KI and KII are obtained for unloaded notch surfaces. There is less than one per cent difference in opening model stress intensity factor in going from a zero degree notch angle to a 30 degree notch angle. Notch opening displacements at the plate edge were measured experimentally, and the results obtained were in excellent agreement with the computed results.

Description: Analysis of the panel flutter characteristics of a candidate thermal protection system (TPS) for the space shuttle, using piston theory aerodynamics and Lagrange equations. The results show the TPS candidate panel array to be deep in the 'no-flutter' region during launch and, therefore, safe from panel flutter.

Description: Consideration of Rayleigh wave effects in a homogeneous isotropic linearly elastic half-space subject to an impulsive uniform disk pressure loading. An approximate formula is obtained for the Rayleigh wave effects. It is shown that the Rayleigh waves near the center of loading arise from the portion of the dilatational and shear waves moving toward the axis, after they originate at the edge of the load disk. A study is made of the vertical displacement due to Rayleigh waves at points on the axis near the surface of the elastic half-space.

Description: Consideration of coupled stress waves generated by an impulsive load applied at one end of a semiinfinite plate. For the field equations governing the one-dimensional coupled waves a hyperbolic system of equations is obtained in which a strong coupling in the second derivatives exists. The method of characteristics described by Chou and Mortimer (1967) is extended to cover the case of strong coupling, and a study is made of the transient stress waves in a semiinfinite plate subjected to an initial step input. Coupled discontinuity fronts are found to propagate at different velocities. The normal plate stress and the bending moment at different time regimes are illustrated by graphs.

Description: The optical response to loading of a thin metallic film deposited on a low-modulus structural substrate is studied theoretically and experimentally. Two types of optical properties called total and central-image transmittance (or reflectance) are shown to be related to the mechanical state of the substrate. Empirical optical-mechanical relationships are proposed between these optical properties and the substrate strain field of a general plane-stress problem. A technique based on wrinkle and microfracture patterns is described for determining principal directions of strain. Experimental results for uniaxially loaded specimens show that it is possible to obtain a nearly linear relationship between transmittance and strain for certain materials combinations.

Description: A lumped-parameter model of a rectangular plate is developed by assuming fundamental mode solutions and using Hamilton's Principle and the Euler equations to set up the differential equation of motion for the system. The plate theory used may be described as the dynamic analogue of the von Karman large-deflection theory. Four sets of symmetrical boundary conditions are considered with the restriction of uniform pressure dynamic loads. The model takes the form of a mass on a cubic-hardening spring with each term defined by algebraic expressions of the plate parameters. The results for some specific problems are compared with two previous solutions. This method is less accurate but simpler to develop and apply.

Description: A generalized eigenvalue algorithm is presented herein along with the complete listing of the associated computer program, which may be conveniently utilized for the efficient solution of certain broad classes of eigenvalue problems. Extensive applications of the procedure are envisaged in the analysis of many important engineering problems, such as stability and natural frequency analysis of practical discrete structural systems, idealized by the finite element technique. The procedure based on the Sturm sequence method is accurate and fast, possessing several significant advantages over other known methods of such analysis. Numerical results are also presented for two representative structural engineering problems.

Description: An experimental and analytical investigation of the effect of a circular hole on the buckling of thin cylindrical shells under axial compression was carried out. The experimental results were obtained from tests performed on seamless electroformed copper shells and Mylar shells with a lap joint seam. These results indicated that the character of the shell buckling was dependent on a parameter which is proportional to the hole radius divided by the square root of the product of the shell radius and thickness. For small values of this parameter, there was no apparent effect of the hole on the buckling load. For slightly larger values of the parameter, the shells still buckled into a general collapse configuration, but the buckling loads were sharply reduced as the parameter increased. For still larger values of the parameter, the buckling loads were further reduced, and the shells buckled into a stable local buckling configuration.

Description: A boron-aluminum structural component, representative of Space Shuttle fuselage structure, has been fabricated and tested as part of a program to demonstrate boron-aluminum feasibility for Shuttle applications. The 4- by 5-foot component consists of eleven 24-ply Z section stringers and a +45 degree 8-ply skin. It was tested at room temperature and at 500 F under combined compressive and shear loadings. The components for this program were fabricated in order to encounter and solve scale-up problems, and to obtain test data representative of production hardware. The data from this program are expected to allow more accurate prediction of weights and costs of boron-aluminum structures for the Space Shuttle.

Description: An explicit formulation is developed to obtain the stored energy function, based on the Valanis-Landel separable symmetric stored energy function. This formulation is applicable to any multiaxial stress state, from simple tensile data alone, for those cases in which the stored energy function is a separable function of the stretch ratios. By direct comparison, it is also shown that styrene butadiene rubber, at least over a specific range, follows this postulated separable form.

Description: This paper gives some examples of projects underway. The projects are grouped according to the primary parameter being studied: loads, configuration, environment, or material. Significant topics include the effect of truncated loads, the effect of proof-tests, interference fasteners, accelerated and real-time tests for supersonic aircraft materials, crack-growth rates in built-up structures, and a model method by which material can be selected for a particular set of operating conditions.

Description: This paper deals with elastic stress intensity factors associated with stress fields near partially debonded interfaces in finite, bi-material plates. Bi-material stress intensity factors K1 and K2 are not associated, respectively, with symmetric and skew-symmetric loading and are functions of an arbitrary length parameter. Any fracture condition involving bi-material stress intensity factors must be independent of the arbitrary length parameter and must be consistent with experiment. We define a new parameter called the interfacial stress intensity factor which satisfies the former condition. A truncated Williams power series stress function for stresses in a cracked bi-material plate, as modified by Sih and Rice, is used with a modified boundary collocation procedure to generate interfacial stress intensity factors for finite bi-material plates.

Description: The results of an analytical study are presented on the use of boron polyimide filamentary composite material for the purpose of increasing the flutter speed of a simple titanium full depth sandwich wing structure designed for strength. The results clearly demonstrate that selective reinforcement of wing surfaces, using judiciously placed filamentary composites, promises sizable mass savings in the design of advanced aircraft structures.

Description: The problem of transient axisymmetric vibrations of thin circular elastic plates due to sonic boom excitation is investigated. The equation of motion for a solid circular plate is solved by applying the modified finite Hankel transform and the Laplace transform, and the numerical results are obtained with the help of the digital computer. From the analysis of the data, obtained for the dynamic deflections of the plates for the boom duration, it is concluded that for a normal flight the boom duration has a significant effect on the vibrations of plates as compared to the overpressure of the boom.

Description: Two methods for identifying the mass, damping and stiffness matrices of a linear vibrating system are presented. Both methods require the measurement of acceleration, velocity and displacement at various locations of the system. In the first method, the response of the system subjected to known forces is used while the second method employs the free vibration data. The unknown parameters are recovered through the standard least squares procedure. Numerical results are presented for several examples.

Description: The problem of potential instability caused by actuator dynamics is examined. Two ways of overcoming it are discussed: rate feedback with compensation and position feedback with tuning filters.

Description: (Previously announced in STAR as N82-24501)

Description: Problems encountered by aerospace designers in attempting to optimize whole aircraft are discussed, along with possible solutions. Large scale optimization, as opposed to component-by-component optimization, is hindered by computational costs, software inflexibility, concentration on a single, rather than trade-off, design methodology and the incompatibility of large-scale optimization with single program, single computer methods. The software problem can be approached by placing the full analysis outside of the optimization loop. Full analysis is then performed only periodically. Problem-dependent software can be removed from the generic code using a systems programming technique, and then embody the definitions of design variables, objective function and design constraints. Trade-off algorithms can be used at the design points to obtain quantitative answers. Finally, decomposing the large-scale problem into independent subproblems allows systematic optimization of the problems by an organization of people and machines.

Description: A simplified buckling analysis is presented for a family of periodic lattice structures such as those proposed for large space structures. A transcendental 6 x 6 matrix of eigenvalues is shown to be sufficient for modeling buckling behavior because member stiffnesses are based on an exact solution of the beam-column equation. Exact stiffnesses are derived for a curved member, thus allowing modeling of imperfect lattice structures. Comparisons of predictions of the lattice model with those available from shell and beam theory underscore the inaccuracies introduced by treating the lattice structure as a continuum. Sample calculations are provided for an isogrid cylinder and a three element double-laced truss.

Description: Truss beams with members having viscous damping are modeled with a Timoshenko beam. Procedures for deriving the equivalent bending rigidity, transverse shear rigidity, and damping are presented. Explicit expressions for these equivalent beam properties are obtained for a specific truss beam. The beam model thus established is then used to investigate the effect of damping in free vibration. Finally, the beam is employed in the estimation of structural parameters in a simply-supported truss beam using a random search algorithm.

Description: A general approach for distributed parameter modeling of complex dynamical systems is described. The method consists of dividing the system in parts which can be modeled by simple partial differential equations and coupling the equations thus obtained by applying Hamilton's variational formalism to the entire system. The modeling of a large, offset-fed, wrap-rib antenna is presented to illustrate the approach. Although such models are perhaps not as precise as finite element models, they can be useful for initial physical insight and parametric design.

Description: The hybrid experimental-numerical stress-analysis technique, which saw limited applications during the 1950's, has been resurrected with the vastly improved numerical techniques of the 1970's. By inputing the experimental results as initial and boundary conditions, modern computer codes are executed in its generation and application modes to yield results which are unobtainable when only one of the two techniques is used. The hybrid technique thus exemplifies the complementary role of the experimental and numerical techniques.

Description: Fourier transforms and the Wiener-Hopf technique are used in conjunction with plane elastostatics to examine the singular crack tip stress field in the double cantilever beam (DCB) specimen. In place of the Dirac delta function, a family of functions which duplicates the important features of the concentrated forces without introducing unmanageable mathematical complexities is used as a loading function. With terms of order h-squared/a-squared retained in the series expansion, the dimensionless stress intensity factor is found to be K (h to the 1/2)/P = 12 to the 1/2 (a/h + 0.6728 + 0.0377 h-squared/a-squared), in which P is the magnitude of the concentrated forces per unit thickness, a is the distance from the crack tip to the points of load application, and h is the height of each cantilever beam. The result is similar to that obtained by Gross and Srawley by fitting a line to discrete results from their boundary collocation analysis.

Description: A fracture mechanics approach to the well-known delamination problem in composite materials is presented. Based on the theory of anisotropic laminate elasticity and interlaminar fracture mechanics concepts, the composite delamination problem is formulated and solved. The exact order of the delamination crack-tip stress singularity is determined. Asymptotic stress and displacement fields for an interlaminar crack are obtained. Fracture mechanics parameters such as mixed-mode stress intensity factors, KI, KII, KIII, and the energy release rate, G, for composite delamination problems are defined. To illustrate the fundamental nature of the delamination crack behavior, solutions for edge-delaminated graphite-epoxy composites under uniform axial extension are presented. Effects of fiber orientation, ply thickness, and delamination length on the interlaminar fracture are examined.

Description: Previously cited in issue 13, p. 2112, Accession no. A82-30182

Description: Stress-intensity factors are obtained for point loaded equal length cracks emanating from a circular hole in an infinite plate. A series approach and the Muskhelishvili formulation in the two-dimensional theory of elasticity are used to derive the solution. The applicability of the solution is demonstrated by using it as a Green's function to obtain stress-intensity factors in the case of (1) biaxial tension and pure shear of an infinite plate and (2) tension and pin loading of a plate with cracks emanating from one hole in a row of holes.

Description: Previously cited in issue 13, p. 2111, Accession no. A82-30171

Description: Previously cited in issue 13, p. 2110, Accession no. A82-30166

Description: The objectives of the hot section technology (HOST) burner liner cyclic rig test program are basically threefold: (1) to assist in developing predictive tools needed to improve design analyses and procedures for the efficient and accurate prediction of burner liner structural response; (2) to calibrate, evaluate and validate these predictive tools by comparing the predicted results with the experimental data generated in the tests; and (3) to evaluate existing as well as advanced temperature and strain measurement instrumentation, both contact and noncontact, in a simulated engine cycle environment. The data generated will include measurements of the thermal environment (metal surface temperatures) as well as structural (strain) and life (fatigue) responses of simulated burner liners and specimens under controlled boundary and operating conditions. These data will be used to calibrate, compare and validate analytical theories, methodologies and design procedures, as well as improvements in them, for predicting liner temperatures, stress-strain responses and cycles to failure. Comparison of predicted results with experimental data will be used to show where the predictive theories, etc. need improvements. In addition, as the predictive tools, as well as the tests, test methods, and data acquisition and reduction techniques, are developed and validated, a proven, integrated analysis/experiment method will be developed to determine the cyclic life of a simulated burner liner.

Description: The HOST Liner Cyclic Program is utilizing two types of test apparatus, rectangular box rigs and a full annular rig. To date two quartz lamp cyclic box rigs have been tested and a third is to begin testing in late October 1983. The box rigs are used to evaluate 5x8 inch rectangular linear samples. A 21 inch diameter outer liner simulator is also being built up for testing beginning in April 1984. All rigs are atmospheric rigs. The first box rig, a three 6-kVA lamp installation, was operated under adverse conditions to determine feasibility of using quartz lamps for cyclic testing. This work was done in December 1981 and looked promising. The second box rig, again using three 6-kVA lamps, was operated to obtain instrumentation durability information and initial data input to a Finite Element Model. This limited test program was conducted in August 1983. Five test plates were run. Instrumentation consisted of strain gages, thermocouples and thermal paint. The strain gages were found to fail at 1200 F as expected though plates were heated to 1700 F. The third box rig, containing four 6-kVA lamps, is in build up for testing to begin in late October 1983. In addition to 33 percent greater power input, this rig has provision for 400 F backside line cooling air and a viewing port suitable for IR camera viewing. The casing is also water cooled for extended durability.

Description: The objective of this program is to produce a series of new computer codes that permit more accurate and efficient three dimensional inelastic analysis of selected hot section components - combustor liners, turbine blades and turbine vanes. The computer codes embody a progression of mathematical models and are streamlined to take advantage of geometrical features, loading conditions, and forms of material response that distinguish each group of selected components.

Description: The objective of this research is to develop an analytical tool capable of economically evaluating the cyclic time dependent plasticity which occurs in hot section engine components in areas of strain concentration resulting from the combination of both mechanical and thermal stresses. The techniques developed must be capable of accommodating large excursions in temperatures with the associated variations in material properties including plasticity and creep. The overall objective of this proposed program is to develop advanced 3-D inelastic structural/stress analysis methods and solution strategies for more accurate and yet more cost effective analysis of combustors, turbine blades, and vanes. The approach will be to develop four different theories, one linear and three higher order with increasing complexities including embedded singularities.

Description: The dynamic characteristics of the Solar Array Flight Experiment (SAFE) structure during deployment and retraction are investigated. The SAFE structure consists of a deployable mast with an attached solar blanket designed with accordion type folds to permit packaging in a small volume. The planar form of the blanket geometry during deployment is maintained by a blanket tension/guidewire system. Structurally, the mast is modeled as an Euler beam column with inplane and out of plane bending and finite torsional stiffness. For out of plane motion, the blanket is modeled as a distributed mass uniformly supported by the three guidewires. For inplane motion the blanket displacements are assumed to vary linearly from the mast base to the mast tip. The mathematical model uses a virtual work formulation, required because the axial loading on the mast is nonconservative, combined with assumed beam modes to derive the differential equations of motion. Consideration of the time dependent boundary conditions results in an infinite set of ODE with time dependent coefficients. Finally, correlation of mast tip accelerations to mast base bending moments for specified modal motions are indicated.

Description: Traditional composite lamination theory was used to predict composite graphite-epoxy laminate stiffnesses for comparison to quasi-experimental stiffnesses developed from cylindrical bottle pressure testing. Stiffness sensitivities were examined for variations in constituent materials and geometric properties. The material component interactions examined were the fiber longitudinal and transverse Young's modulus, the fiber shear modulus and primary Poisson's ratio, the resin Young's modulus, shear modulus, and Poisson's ratio. The geometric variation of the helical winding angle was also examined. Two computer programs were written to generate the data used to demonstrate the stiffness variations.

Description: An algorithm is described for synthesizing the mass and stiffness matrices from experimentally derived modal data in a way that preserves the physical significance of the individual mass and stiffness elements. The mass and stiffness matrices are derived for a rollup solar array example, and are then used to define the modal response of a modified array.

Description: An experiment to measure the elastic deflection of the DSS 14 concrete pedestal under the weight of the antenna was conducted in February 1983 and is compared to a similiar experiment made in 1968. Comparison of the results confirms the decrease in elastic modulus measured on core samples recently taken from the pedestal.

Description: An unconditionally stable implicit-explicit method is proposed for the analysis of transient coupled thermal stress waves, and the computer-implementation aspects of the method are discussed. In the method proposed here, the mechanical displacement and temperature are used as independent variables. The resulting coupled finite element matrix equations are symmetric.

Description: Previously cited in issue 13, p. 2112, Accession no. A82-30186

Description: Previously cited in issue 13, p. 2108, Accession no. A82-30124

Description: Previously cited in issue 01, p. 60, Accession no. A83-10900

Description: Previously cited in issue 13, p. 2109, Accession no. A82-30152

Description: A fracture mechanics analysis has been developed that describes the progress of delamination damage in composite plates struck by a hard spherical object. The analysis is based on large deflection plate mechanics for circular isotropic plates wherein multiple axisymmetric delaminations grow. Test data show that the analysis predicts the influence of plate thickness, support conditions, and matrix toughness on the onset and propagation of delamination.

Description: A three-dimensional element based on the total Lagrangian description of large deformations of a layered anisotropic composite medium is developed, validated, and used to analyze layered composite shells. The element contains the following features: geometric nonlinearity, dynamic (transient) behavior, and arbitrary lamination scheme and lamina properties. Numerical results of nonlinear bending, natural vibration, and transient response are presented to illustrate the capabilities of the element.

Description: The application of substructuring techniques are described for two example problems, a square plate and the static analysis of a frame-wall interaction problem in multistory structures. A DMAP routine for calculating the multipoint constraint forces is presented.

Description: A nuclear reactor vessel is supported by a Z-ring and a box ring girder. The two proposed structural configurations to transmit the loads from the Z-ring and the box ring girder to the foundation are shown. The cantilever concrete ledge transmitting the load from the Z-ring and the box girder via the cavity wall to the foundation is shown, along with the loads being transmitted through one of the six steel columns. Both of these two supporting systems were analyzed by using rigid format 9 of NASTRAN for dynamic loads, and the thermal stresses were analyzed by AXISOL. The six column configuration was modeled by a combination of plate and bar elements, and the concrete cantilever ledge configuration was modeled by plate elements. Both configurations were found structurally satisfactory; however, nonstructural considerations favored the concrete cantilever ledge.

Description: NASTRAN was chosen as the principal analytical tool for structural analysis of the Illinois Center Plaza Hotel Building in Chicago, Illinois. The building is a 40-story, reinforced concrete structure utilizing a monolithic slab-column system. The displacements, member stresses, and foundation loads due to wind load, live load, and dead load were obtained through a series of NASTRAN runs. These analyses and the input technique are described.

Description: The extent to which suitable solutions may be obtained for one physics problem and two engineering type problems is traced. NASTRAN appears to be a practical tool to solve one-group steady-state neutron diffusion equations. Transient diffusion analysis may be performed after new levels that allow time-dependent temperature calculations are developed. NASTRAN piecewise linear anlaysis may be applied to solve those plasticity problems for which a smooth stress-strain curve can be used to describe the nonlinear material behavior. The accuracy decreases when sharp transitions in the stress-strain relations are involved. Improved NASTRAN usefulness will be obtained when nonlinear material capabilities are extended to axisymmetric elements and to include provisions for time-dependent material properties and creep analysis. Rigid formats 3 and 5 proved to be very convenient for the buckling and normal-mode analysis of a nuclear fuel element.

Description: The addition of discrete elements to NASTRAN poses significant interface problems with the level 15.1 assembly modules and geometry modules. Potential problems in designing new modules for higher-order parametric discrete elements are reviewed in both areas. An assembly procedure is suggested that separates grid point degrees of freedom on the basis of admissibility. New geometric input data are described that facilitate the definition of surfaces in parametric space.

Description: The NASTRAN program output is discussed from a structural analysts point of view, and the simple modifications which were made to the program in order to improve it are also described. The convenience of the output for use in original design work is critically appraised and compared with the output from ASTRAL. It is shown that considerable hand calculation is necessary in order to extract useful load distribution data from the available NASTRAN output. For this reason, some effort was directed toward providing additional force output for the NASTRAN shear panel element.

Description: The geometric and kinematic properties of the element are described, along with development of the matrices and vectors which characterize the element. The necessity for considering small deviations from element planeness is discussed, and the approach taken to account for these deviations is described. The improved accuracy over the existing quadrilateral membrane is indicated by a sample calculation for which an analytical solution is available from beam theory. For the same finite element idealization, the errors in maximum displacement and stress were significantly reduced.

Description: Efforts to integrate NASTRAN into a complete structural analysis system for use by large airframe design projects are discussed. NASTRAN was implemented as a major finite element structural analysis program to determine the static and dynamic behavior of complete airframes, as well as structural components. This requires modifications and additions to NASTRAN, to communicate with an existing system, and to provide facilities needed to work within the integrated structural analysis. For this purpose, several special DMAP modules were developed and introduced into the CALAC version of the NASTRAN system.

Description: A static and buckling analysis of the ATS-F&G spacecraft reflector support truss (RST) and bridge truss assembly using NASTRAN was conducted. The RST is fabricated from a new material, graphite fiber reinforced plastic. A comparison is made with the NASTRAN results and the results of a similar analysis conducted using the stardyne program. The results of an actual static load test are also compared.

Description: Three finite element programs are compared to assess their capabilities as an analysis tool in a structural design process. Because of the need for repetitive analyses as an integral part of a design loop, a candidate program must be capable of handling large problems, operate efficiently, and be readily adaptable for use in computer-aided design. The three programs considered in the study, ELAS,SNAP, and NASTRAN, range from a relatively small finite element program limited to static structural analysis (ELAS) to a large complex general analysis system (NASTRAN). Results are given for comparative speeds and computer resources required for each program in the analysis of sample fuselage problems representative of practical aircraft design.

Description: A static finite element stress analysis of an inflated radial car tire was carried out. The deformed shape of the sidewall presents outward bulging. The analysis of a homogeneous isotropic toroidal shell shows that the problem is common to all solids of this type. The study suggests that the geometric stiffness due to the inflation pressure has to be taken into account. Also, the resulting large displacements make it necessary for the geometry to be updated at each load step.

Description: A composite element is presented which includes the effects of warping and offset shear centers. It is shown to be mathematically consistent with thin walled open beam theory and can be incorporated into any structural analysis program by use of NASTRAN'S standard elements. A numerical example analyzing the vibration of a channel beam is presented, and, by using the composite element, the numerical results agreed well with theoretical data.

Description: A FORTRAN subroutine to NASTRAN which constructs coriolis and centripetal acceleration matrices, and a centrifugal load vector due to spin about a selected point or about the mass center of the structure is discussed. The rigid translational degrees of freedom can be removed by using a transformation matrix T and its explicitly given inverse. These matrices are generated in the subroutine and their explicit expressions are given.

Description: The level 12 NASTRAN was used to support the NASA/LaRC advanced transport technology study, a predesign, short response time effort. Aeroelastic analyses were performed. NASTRAN calculated the vibration modes for the supported airfoil components and the entire unsupported vehicle. Other procedures were then used for the aeroelastic analysis, with procedure interfacing accomplished through use of the NASTRAN-produced restart tape. Stiffness matrices were used in static aeroelastic analyses; natural vibration modes were used for flutter and flight control system definition. Various level 12 NASTRAN characteristics were discovered and are discussed; e.g., the ability to solve singular matrices in rigid format 1, run times using multipoint constraints, restart tape problems, and the inaccurate stresses from the quad membrane when used with anisotropic materials.

Description: A lumped mass model was used to represent the impact condition between a fuel duct and an IVHM in-vessel fuel handling machine. The nonlinear effects of a Bellville spring and the free fall impact of the fuel duct on the IVHM were included. The purpose of the tests was to determine the loads on the fuel duct due to the impact. A comparison between experimental and theoretical results is presented.

Description: To evaluate the effectiveness of NASTRAN for predicting the vibration modes of panels with bending-membrane coupling, a cross-stiffened ship deck was analyzed. In correlation with experimental data, one NASTRAN finite element representation gave results slightly more accurate than a previous analytical solution. Computational time was excessively long, due to the Guyan method of reducing the eigenvalue problem. It is recommended that a more efficient method of matrix reduction be implemented for the lumped mass formulation.

Description: Structural analysis applications of NASTRAN to the isogrid structure of the Delta launch vehicle are discussed. Isogrid is a method employed to stiffen the booster cylindrical shell surface by integrally machining ribs and skin from one piece of metal. The ribs are arranged in a repetitive equilateral triangular pattern; this results in a structural surface whose stiffness is orthogonally isotopic. For that structure, both static and general instability buckling analyses are described and the theoretical results are compared to test data. One of the parameters included in the analysis is the effect of pressure loadings on the buckling allowable load. In addition, a description of a supplementary computer program is presented.

Description: The coupling of NASTRAN to another finite element program developed for the static analysis of automotive structures is discussed. The two programs were coupled together to use the substructuring capability of the in-house program and the normal mode analysis capability of NASTRAN. Modifications were made to the NASTRAN program in order to make the coupling feasible.

Description: For the improvement of rail service, the Department of Transportation, Federal Rail Administration, is sponsoring a test track on the Atchison, Topeka, and Santa Fe Railway. The test track will contain nine separate rail support structures, including one conventional section for control and three reinforced concrete structures on grade, one slab and two beam sections. The analysis and design of these latter structures was accomplished by means of the finite element method, NASTRAN, and is presented.

Description: An analytical study of a two-lobed circular arc pressure vessel (double-bubble tank) with a local perturbation from the cylindrical shape was made. It can be concluded that NASTRAN provides a good linear buckling analysis capability for structures that cannot be handled by other analysis techniques. However, solutions are relatively expensive from a computational standpoint. Two worthwhile additions to the NASTRAN program would be the inclusion of a new beam element that adequately represents the shear transfer when modeling stiffeners on a shell and the capability, in a rigid format, to keep certain prescribed loads constant during the eigenvalue extraction process.

Description: The computer run time required for a buckling analysis using NASTRAN is considerably greater than for a linear static analysis of the same structure. It is very important to obtain an optimal model size for the structure being analyzed, such that the model is neither so large as to increase running time unnecessarily, nor so small as to hinder accuracy. The problem of critical load accuracy versus model complexity is considered for a thin walled cylinder, using both Level 12 and Level 15 NASTRAN releases.

Description: The NASTRAN program was used to find the buckling location and the degradation factor due to a specified temperature field for an interstage of a typical three stage missile. The model was made up of 6332 independent degrees of freedom. This large size required the use of an IBM 370/195 for evaluation of the eigenvalues. The effect of elevated temperature was to lower the critical buckling load by 3%.

Description: The buckling of isotropic and waffle-stiffened circular cylinders with and without cutouts was studied using NASTRAN's Rigid Format 5 for the case of axial compressive loading. The results obtained for the cylinders without cutouts are compared with available reference solutions. The results for the isotropic cylinders containing a single circular cutout with selected radii are compared with available experimental data. For the waffle-stiffened cyclinder, the effect of two diametrically opposed rectangular cutouts was studied. A DMAP alter sequence was used to permit the necessary application of different prebuckling and buckling boundary conditions. Advantage was taken of available symmetry planes to formulate equivalent NASTRAN model segments which reduced the associated computational cost of performing the analyses. Limitations of the applicability of NASTRAN for the solution of problems with nonlinear characteristics are discussed.

Description: Significant NASTRAN-related events since September, 1971 are reviewed. The present operation of the NASTRAN systems management office is described, as well as new capabilities and improvements incorporated in Level 15 of NASTRAN, and priorities for future levels of NASTRAN.

Description: A summary of tests conducted on the Concorde aircraft nacelle structure is presented. The tests were conducted as a part of the structural development and certification program. The nacelle structural specimens are described. The problems associated with the intake testing and engine-bay and nozzle testing are discussed.

Description: Fatigue tests on structural assemblies of the Concorde supersonic transport aircraft are reported. Two main sections of the aircraft were subjected to pressure, mechanical load, and thermal static tests. The types of fatigue tests conducted and the results obtained are discussed. It was concluded that on a supersonic aircraft whose structural weight is a significant part of the weight analysis, many fatigue and static strength development tests should be made and fatigue and thermal tests of the structures are absolutely necessary.

Description: Airline operations involving the detection of structural deterioration and associated maintenance problems are discussed. The standard approach to the maintenance and inspection of aircraft components and systems is described. The frequency of inspections and the application of preventive maintenance practices are examined. The types of failure which airline transport aircraft encounter and the steps taken to prevent catastrophic failure are reported.

Description: A recorder system has been installed on two operational fighter aircrafts. Signal values from a c.g.-acceleration transducer and a strain-gage installation at the wing root were sampled and recorded in digital format on the recorder system. To analyse such load-time histories for fatigue evaluation purposes, a number of counting methods are available in which level crossings, peaks, or ranges are counted. Ten different existing counting principles are defined. The load-time histories are analysed to evaluate these counting methods. For some of the described counting methods, the counting results might be affected by arbitrarily chosen parameters such as the magnitude of load ranges that will be neglected and other secondary counting restrictions. Such influences might invalidate the final counting results entirely. The evaluation shows that for the type of load-time histories associated with most counting methods, a sensible value of the parameters involved can be found.

Description: Rectangular specimens of 7075 and 2014 aluminum alloys with two holes (stress concentration factor of 3.24) have been tested under axial fatigue loading on a six-rod test bed with modifications of the loading program, the surface particulars, and the frequency. The length of the precrack stage was investigated by use of a new crack detector. In most cases the two alloys behaved similarly, with similar life to crack start under the same loading. Some overloads lengthened the life. Truncation by omission of the lowest peak loads should be limited to about 20 percent of the ultimate load. Simplifying counting methods gave misleading results. Very thin surface layers of anodizing, protection by vinyl, dry nitrogen atmosphere, as well as stepwise reaming or grinding the surface of the holes, lengthened the life; thick anodized layers shortened the life. Compressing the hole surface by rolling had no influence. Frequencies at about 210 to 240 cpm produced shorter lives than those at 40 cpm. At 5.4 cpm the life was considerably longer. A model to better understand the precrack-stage fatigue mechanism is discussed.

Description: The application of applied fracture mechanics in the design, analysis, and qualification of aircraft structural systems are reviewed. Recent service experiences are cited. Current trends in high-strength materials application are reviewed with particular emphasis on the manner in which fracture toughness and structural efficiency may affect the material selection process. General fracture control procedures are reviewed in depth with specific reference to the impact of inspectability, structural arrangement, and material on proposed analysis requirements for safe crack growth. The relative impact on allowable design stress is indicated by example. Design criteria, material, and analysis requirements for implementation of fracture control procedures are reviewed together with limitations in current available data techniques. A summary of items which require further study and attention is presented.

Description: A parametric approach to irregular fatigue protection is presented. The method proposed consists of two parts: empirical determination of certain characteristics of a material by means of a relatively small number of well-defined standard tests, and arithmetical application of the results obtained to arbitrary loading histories. The following groups of parameters are thus taken into account: (1) the variations of the mean stress, (2) the interaction of these variations and the superposed oscillating stresses, (3) the spectrum of the oscillating-stress amplitudes, and (4) the sequence of the oscillating-stress amplitudes. It is pointed out that only experimental verification can throw sufficient light upon possibilities and limitations of this (or any other) prediction method.

Description: The application of procedures for designing and evaluating structural integrity of various construction techniques is discussed. The fatigue performance improvement of the following conditions is described: (1) conical fasteners, (2) hole preparation, (3) interference fit, and (4) interference protection. The application of fatigue tests to determine fail-safe conditions is analyzed.

Description: The elastic-plastic deformation behavior under cyclic stress of a number of different engineering materials was experimentally investigated with the aid of high-precision methods of measuring, some of which had been newly developed. Experiments made with a variety of steels, the titanium alloy Ti-A16-V4, a cobalt (tungsten) alloy, the high-temperature material Nimonic 90 and Dural (A1-Cu) are reported. The theory given in an attempt to explain these experiments is aimed at finding general formulas for the cyclic stress-strain behavior materials.

Description: The failure mechanisms in the fatigue of composite materials are analyzed in terms of the requirements for designing fatigue-critical composite structures. Fiber reinforced polymers, fiber reinforced metals, fatigue of composite structures, and composite design considerations are discussed. It is concluded that composite materials offer the engineer the opportunity for tailoring stiffness in different directions for designing dynamic components.

Description: For supersonic airline operations, significantly higher environmental temperature is the primary new factor affecting structural service life. Methods for incorporating the influence of temperature in detailed fatigue analyses are shown along with current test indications. Thermal effects investigated include real-time compared with short-time testing, long-time temperature exposure, and stress-temperature cycle phasing. A method is presented which allows designers and stress analyzers to check fatigue resistance of structural design details. A communicative rating system is presented which defines the relative fatigue quality of the detail so that the analyst can define cyclic-load capability of the design detail by entering constant-life charts for varying detail quality. If necessary then, this system allows the designer to determine ways to improve the fatigue quality for better life or to determine the operating stresses which will provide the required service life.

Description: The application of reliability theory to predict, from structural fatigue test data, the risk of failure of a structure under service conditions because its load-carrying capability is progressively reduced by the extension of a fatigue crack, is considered. The procedure is applicable to both safe-life and fail-safe structures and, for a prescribed safety level, it will enable an inspection procedure to be planned or, if inspection is not feasible, it will evaluate the life to replacement. The theory has been further developed to cope with the case of structures with initial cracks, such as can occur in modern high-strength materials which are susceptible to the formation of small flaws during the production process. The method has been applied to a structure of high-strength steel and the results are compared with those obtained by the current life estimation procedures. This has shown that the conventional methods can be unconservative in certain cases, depending on the characteristics of the structure and the design operating conditions. The suitability of the probabilistic approach to the interpretation of the results from full-scale fatigue testing of aircraft structures is discussed and the assumptions involved are examined.

Description: Crack propagation was studied in a full-scale wing structure under different simulated flight conditions. Omission of low-amplitude gust cycles had a small effect on the crack rate. Truncation of the infrequently occurring high-amplitude gust cycles to a lower level had a noticeably accelerating effect on crack growth. The application of fail-safe load (100 percent limit load) effectively stopped subsequent crack growth under resumed flight-simulation loading. In another flight-simulation test series on sheet specimens, the variables studied are the design stress level and the cyclic frequency of the random gust loading. Inflight mean stresses vary from 5.5 to 10.0 kg/sq mm. The effect of the stress level is larger for the 2024 alloy than for the 7075 alloy. Three frequencies were employed: namely, 10 cps, 1 cps, and 0.1 cps. The frequency effect was small. The advantages and limitations of flight-simulation tests are compared with those of alternative test procedures such as constant-amplitude tests, program tests, and random-load tests. Various testing purposes are considered. The variables of flight-simulation tests are listed and their effects are discussed. A proposal is made for performing systematic flight-simulation tests in such a way that the compiled data may be used as a source of reference.

Description: The United States Air Force has published a document entitled Aircraft Structural Integrity Program. One phase of the program is concerned with the fatigue life certification of all types of military aircraft. The document describes the criteria, analyses, and tests that are necessary in order to satisfy the USAF fatigue life requirement. Some recent and valid criticism has been directed toward the document, particularly the fatigue-life requirements contained in it. Some changes are proposed based on surveys conducted in the United States and abroad as well as some recent systems' experience. The surveys covered both military and civilian organizations. The fatigue certification case histories of selected military and commercial aircraft are presented. The design development element tests, preproduction design verification tests, and full-scale fatigue tests of each are described. A brief status report on the revisions to the MIL-A-008860 series specifications is included.

Description: The methods adopted in the United Kingdom to ensure the structural integrity of military aeroplanes and helicopters from the fatigue point of view are described. The procedure adopted from the writing of the specification to the monitoring of fatigue life in service are presented along with the requirements to be met and the way in which they are satisfied. Some of the outstanding problems that remain to be solved are indicated.

Description: The philosophy and methods used in the design of the DC-10 aircraft to assure structural reliability against cracks under repeated service loads are described in detail. The approach consists of three complementary parts: (1) the structure is designed to be fatigue resistant for a crack-free life of 60,000 flight hours; (2) inasmuch as small undetected cracks could develop from other sources, such as material flaws and manufacturing preloads, the structure also is designed to arrest and control cracks within a reasonable service-inspection interval; and (3) a meaningful service-inspection program has been defined on the basis of analysis and test experience from the design development program. This service-inspection program closes the loop to assure the structural integrity of the DC-10 airframe. Selected materials, fasteners, and structural arrangements are used to achieve these design features with minimum structural weight and with economy in manufacturing and maintenance. Extensive analyses and testing were performed to develop and verify the design. The basic design considerations for fatigue-resistant structure are illustrated in terms of material selection, design loads spectra, methods for accurate stress and fatigue damage analysis, and proven concepts for efficient detail design.

Description: The fatigue integrity program which was established to insure economic operations and to provide foundation data for inspection and maintenance is discussed. Significant features of the 747 fatigue integrity program are: (1) fatigue analyses which are continually updated to reflect design changes, fatigue test results, and static and flight load survey measurements; (2) material selection and detail design by using initial fatigue analyses, service experience, and testing; and (3) fatigue testing to check detail design quality and to verify the analyses, culminated by the test of a structurally complete airframe. Fatigue stress analyses were performed with the aid of experimental as well as analytical procedures. Extensive application was made of the stress severity factor, developed at Boeing, for evaluating peak stresses in complex joints. A frame of reference was established by families of structural fatigue performance curves (S-N curves) encompassing the range of materials and fatigue qualities anticipated for the 747 airplane design.

Description: A part of the lower side of the main wing at the joint of the main spar with the fuselage frame was investigated. This wing beam area was simulated by a test specimen consisting of a spar boom of AZ 74 forging (7075 aluminum alloy modified with 0.3 percent Ag) and a portion of a honeycomb sandwich panel attached to the boom flange with steel bolts. The cross section was reduced to half scale. However, the flange thickness, the panel height, and the bolt size were full scale. Further, left and right portions of the fuselage frame intended to carry over the bending moment of the main wing were tested. Each of these frame halves consisted of a forward and a rear forging (7079 aluminum alloy, overaged) connected by an outer and inner skin (Alclad 7075) creating a box beam. These test specimens were full scale and were constructed principally of ordinary aircraft components. The test load spectrum was common to both types of specimens with regard to percentage levels. It consisted of maneuver and gust loads, touchdown loads, and loads due to ground roughness. A load history of 200 hours of flight with 15,000 load cycles was punched on a tape. The loads were randomized in groups according to the flight-by-flight principle. The highest positive load level was 90 percent of limit load and the largest negative load was -27 percent. A total of 20 load levels were used. Both types of specimens were provided with strain gages and had a nominal stress of about 300 MN/sq m in some local areas. As a result of the tests, steps were taken to reduce the risk of fatigue damage in aircraft. Thus stress levels were lowered, radii were increased, and demands on surface finish were sharpened.

Description: The information presented is based on data obtained from the Concorde. Much of this data also applies to other supersonic transport aircraft. The design and development of the Concorde is a joint effort of the British and French, and the structural test program is shared, as are all the other activities. Vast numbers of small specimens have been tested to determine the behavior of the materials used in the aircraft. Major components of the aircraft structure, totalling almost a complete aircraft, have been made and are being tested to help the constructors in each country in the design and development of the structure. Tests on two complete airframes will give information for the certification of the aircraft. A static test was conducted in France and a fatigue test in the United Kingdom. Fail-safe tests are being made to demonstrate the crack-propagation characteristics of the structure and its residual strength. Aspects of the structural test program are described in some detail, dealing particularly with the problems associated with the thermal cycle. The biggest of these problems is the setting up of the fatigue test on the complete airframe; therefore, this is covered more extensively with a discussion about how the test time can be shortened and with a description of the practical aspects of the test.

Description: A structural thermal optical computer program is developed which uses a finite element approach and applies the Ritz method for solving heat transfer problems. Temperatures are represented at the vertices of each element and the displacements which yield deformations at any point of the heated surface are interpolated through grid points.