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NASA NTRS1993

Preconditioning for the Navier-Stokes equations with finite-rate chemistry

The preconditioning procedure for generalized finite-rate chemistry and the proper preconditioning for the one-dimensional Navier-Stokes equations are presented. Eigenvalue stiffness is resolved and convergence-rate acceleration is demonstrated over the entire Mach-number range from the incompressible to the hypersonic. Specific benefits are realized at low and transonic flow speeds. The extended preconditioning matrix accounts for thermal and chemical non-equilibrium and its implementation is explained for both explicit and implicit time marching. The effect of higher-order spatial accuracy and various flux splittings is investigated. Numerical analysis reveals the possible theoretical improvements from using proconditioning at all Mach numbers. Numerical results confirm the expectations from the numerical analysis. Representative test cases include flows with previously troublesome embedded high-condition-number regions.

Godfrey, Andrew G.↗

NASA NTRS2007

Convergence Acceleration of Runge-Kutta Schemes for Solving the Navier-Stokes Equations

The convergence of a Runge-Kutta (RK) scheme with multigrid is accelerated by preconditioning with a fully implicit operator. With the extended stability of the Runge-Kutta scheme, CFL numbers as high as 1000 can be used. The implicit preconditioner addresses the stiffness in the discrete equations associated with stretched meshes. This RK/implicit scheme is used as a smoother for multigrid. Fourier analysis is applied to determine damping properties. Numerical dissipation operators based on the Roe scheme, a matrix dissipation, and the CUSP scheme are considered in evaluating the RK/implicit scheme. In addition, the effect of the number of RK stages is examined. Both the numerical and computational efficiency of the scheme with the different dissipation operators are discussed. The RK/implicit scheme is used to solve the two-dimensional (2-D) and three-dimensional (3-D) compressible, Reynolds-averaged Navier-Stokes equations. Turbulent flows over an airfoil and wing at subsonic and transonic conditions are computed. The effects of the cell aspect ratio on convergence are investigated for Reynolds numbers between 5:7 x 10(exp 6) and 100 x 10(exp 6). It is demonstrated that the implicit preconditioner can reduce the computational time of a well-tuned standard RK scheme by a factor between four and ten.

Swanson, Roy C., Jr.↗

NASA NTRS2006

Graphite Composite Booms with Integral Hinges

A document discusses lightweight instrument booms under development for use aboard spacecraft. A boom of this type comprises a thin-walled graphite fiber/ matrix composite tube with an integral hinge that can be bent for stowage and later allowed to spring back to straighten the boom for deployment in outer space. The boom design takes advantage of both the stiffness of the composite in tubular geometry and the flexibility of thin sections of the composite. The hinge is formed by machining windows in the tube at diametrically opposite locations so that there remain two opposing cylindrical strips resembling measuring tapes. Essential to the design is a proprietary composite layup that renders the hinge tough yet flexible enough to be bendable as much as 90 in either of two opposite directions. When the boom is released for deployment, the torque exerted by the bent hinge suffices to overcome parasitic resistance from harnesses and other equipment, so that the two sections of the hinge snap to a straight, rigid condition in the same manner as that of measuring tapes. Issues addressed in development thus far include selection of materials, out-of-plane bending, edge cracking, and separation of plies.

Alexander, Wes↗

NASA NTRS1977

NASTRAN hydroelastic modal studies. Volume 3: NASTRAN 3-D hydroelastic analysis and MESHGEN user's manuals

The method used to formulate the fluid/structure equations is described in the updates to the NASTRAN Theoretical Manual. The basis for defining the fluid are three dimensional finite elements connected to fluid grid points defining the Eulerian pressure at a point fixed in space. The use of a pressure single degree of freedom at each point rather than three displacements allows a finer mesh of elements with a reasonable matrix order. In the formulation of the fluid/structure system the interior fluid degrees of freedom are transformed and removed from the solution matrices. The eigenvalues of the combination are extracted from small, fully dense, symmetric mass and stiffness matrices, efficiently processed with the Givens method. The solution matrices are defined by the free surface displacements and the reduced structure coordinates.

Source record↗

NASA NTRS2004

Metal Foam Analysis: Improving Sandwich Structure Technology for Engine Fan and Propeller Blades

The Life Prediction Branch of the NASA Glenn Research Center is searching for ways to construct aircraft and rotorcraft engine fan and propeller blades that are lighter and less costly. One possible design is to create a sandwich structure composed of two metal faces sheets and a metal foam core. The face sheets would carry the bending loads and the foam core would have to resist the transverse shear loads. Metal foam is ideal because of its low density and energy absorption capabilities, making the structure lighter, yet still stiff. The material chosen for the face sheets and core was 17-4PH stainless steel, which is easy to make and has appealing mechanical properties. This material can be made inexpensively compared to titanium and polymer matrix composites, the two current fan blade alternatives. Initial tests were performed on design models, including vibration and stress analysis. These tests revealed that the design is competitive with existing designs; however, some problems were apparent that must be addressed before it can be implemented in new technology. The foam did not hold up as well as expected under stress. This could be due to a number of issues, but was most likely a result of a large number of pores within the steel that weakened the structure. The brazing between the face sheets and the foam was also identified as a concern. The braze did not hold up well under shear stress causing the foam to break away from the face sheets. My role in this project was to analyze different options for improving the design. I primarily spent my time examining various foam samples, created with different sintering conditions, to see which exhibited the most favorable characteristics for our purpose. Methods of analysis that I employed included examining strut integrity under a microscope, counting the number of cells per inch, measuring the density, testing the microhardness, and testing the strength under compression. Shear testing will also be done to examine the strengths of different types of brazes.

Fedor, Jessica L.↗

NASA NTRS1978

Quiet Clean Short-haul Experimental Engine (QCSEE) composite fan frame design report

An advanced composite frame which is flight-weight and integrates the functions of several structures was developed for the over the wing (OTW) engine and for the under the wing (UTW) engine. The composite material system selected as the basic material for the frame is Type AS graphite fiber in a Hercules 3501 epoxy resin matrix. The frame was analyzed using a finite element digital computer program. This program was used in an iterative fashion to arrive at practical thicknesses and ply orientations to achieve a final design that met all strength and stiffness requirements for critical conditions. Using this information, the detail design of each of the individual parts of the frame was completed and released. On the basis of these designs, the required tooling was designed to fabricate the various component parts of the frame. To verify the structural integrity of the critical joint areas, a full-scale test was conducted on the frame before engine testing. The testing of the frame established critical spring constants and subjected the frame to three critical load cases. The successful static load test was followed by 153 and 58 hours respectively of successful running on the UTW and OTW engines.

Mitchell, S. C.↗

NASA NTRS1999

Design Tool Developed for Probabilistic Modeling of Ceramic Matrix Composite Strength

Ceramic matrix composites are being evaluated as candidate materials for many high temperature applications such as engine combustor liners for the High-Speed Civil Transport (HSCT). They are required to have an assured life of several thousand hours. Estimating the reliability of these components is quite a complex process and requires knowledge of the uncertainties that occur at various scales. The properties of ceramic matrix composites (CMC) are known to display a considerable amount of scatter due to variations in fiber/matrix properties, interphase/coating properties, bonding, amount of matrix voids, and many geometry- and fabrication-related parameters such as ply thickness and ply orientations. The objective of this research effort is to account for these uncertainties in a formal way by probabilistically analyzing both the stiffness- and strength related properties of CMC's. In current deterministic approaches, uncertainties are usually accounted for by safety factors. This approach often yields overly conservative designs, thereby reducing the potential of many advanced composite materials.

Murthy, Pappu L. N.↗

NASA NTRSDate not supplied

Variational Coupled Loads Analysis using the Hybrid Parametric Variation Method

Time-domain coupled loads analysis (CLA)is used to determine the response of a launch vehicle and payload system to transient forces, such as liftoff, engine ignitions and shutdowns, jettison events, and atmospheric flight loads, such as buffet. CLA, using Hurty/Craig-Bampton (HCB)component models, is the accepted method for the establishment of design-level loads for launch systems. However, uncertainty in the component models flows into uncertainty in predicted system results. Uncertainty in the structural responses during launch is a significant concern because small variations in launch vehicle and payload mode shapes and their interactions can result in significant variations in system loads. Uncertainty quantification (UQ)is used to determine statistical bounds on prediction accuracy based on model uncertainty. In this paper uncertainty is treated at the HCB component-model level. In an effort to account for model uncertainties and statistically bound their effect on CLA predictions, this work combines CLA with UQ in a process termed variational coupled loads analysis (VCLA). The modeling of uncertainty using a parametric approach, in which input parameters are represented by random variables, is common, but its major drawback is the resulting uncertainty is limited to the form of the nominal model. Uncertainty in model form is one of the biggest contributors to uncertainty in complex built-up structures. Model-form uncertainty can be represented using a nonparametric approach based on random matrix theory (RMT). In this work, UQ is performed using the hybrid parametric variation (HPV)method, which combines parametric with nonparametric uncertainty at the HCB component model level. The HPV method requires the selection of dispersion values for the HCB fixed-interface (FI)eigenvalues, and the HCB mass and stiffness matrices. The dispersions are based upon component test-analysis modal correlation results. During VCLA, random component models are assembled into an ensemble of random systems using a Monte Carlo (MC)approach. CLA is applied to each of the ensemble members to produce an ensemble of system-level responses for statistical analysis. The proposed methodology is demonstrated through its application to a buffet loads analysis of NASA’s Space Launch System (SLS)during the transonic regime fifty seconds after liftoff. Core stage (CS)section shears and moments are recovered, and statistics are computed.

Uncertainty Quantification↗

NASA NTRS1986

Analysis of Delamination Growth from Matrix Cracks in Laminates Subjected to Bending Loads

A major source of delamination damage in laminated composite materials is from low-velocity impact. In thin composite laminates under point loads, matrix cracks develop first in the plies, and delaminations then grow from these cracks at the ply interfaces. The purpose of this study was to quantify the combined effects of bending and transverse shear loads on delamination initiation from matrix cracks. Graphite-epoxy laminates with 90 deg. plies on the outside were used to provide a two-dimensional simulation of the damage due to low-velocity impact. Three plate bending problems were considered: a 4-point bending, 3-point bending, and an end-clamped center-loaded plate. Under bending, a matrix crack will form on the tension side of the laminate, through the outer 90 deg. plies and parallel to the fibers. Delaminations will then grow in the interface between the cracked 90 deg. ply and the next adjacent ply. Laminate plate theory was used to derive simple equations relating the total strain energy release rate, G, associated with the delamination growth from a 90 deg. ply crack to the applied bending load and laminate stiffness properties. Three different lay-ups were tested and results compared. Test results verified that the delamination always formed at the interface between the cracked 90 deg. ply and the next adjacent ply. Calculated values for total G sub c from the analysis showed good agreement for all configurations. The analysis was able to predict the delamination onset load for the cases considered. The result indicated that the opening mode component (Mode I) for delamination growth from a matrix crack may be much larger than the component due to interlaminar shear (Mode II).

Murri, G. B.↗

NASA NTRS1988

Analysis of delamination growth from matrix cracks in laminates subjected to bending loads

A major source of delamination damage in laminated composite materials is from low-velocity impact. In thin composite laminates under point loads, matrix cracks develop first in the plies, and delaminations then grow from these cracks at the ply interfaces. The purpose of this study was to quantify the combined effects of bending and transverse shear loads on delamination initiation from matrix cracks. Graphite-epoxy laminates with 90 deg plies on the outside were used to provide a two-dimensional simulation of the damage due to low-velocity impact. Three plate bending problems were considered: a 4-point bending, 3-point bending, and an end-clamped center-loaded plate. Under bending, a matrix crack will form on the tension side of the laminate, through the outer 90 deg plies and parallel to the fibers. Delaminations will then grow in the interface between the cracked 90 deg ply and the next adjacent ply. Laminate plate theory was used to derive simple equations relating the total strain energy release rate, G, associated with the delamination growth from a 90 deg ply crack to the applied bending load and laminate stiffness properties. Three different lay-ups were tested and results compared. Test results verified that the delamination always formed at the interface between the cracked 90 deg ply and the next adjacent ply. Calculated values for total G sub c from the analysis showed good agreement for all configurations. The analysis was able to predict the delamination onset load for the cases considered. The result indicated that the opening mode component (Mode I) for delamination growth from a matrix crack may be much larger than the component due to interlaminar shear (Mode II).

Murri, Gretchen Bostaph↗

NASA NTRS2000

Ordering Unstructured Meshes for Sparse Matrix Computations on Leading Parallel Systems

The ability of computers to solve hitherto intractable problems and simulate complex processes using mathematical models makes them an indispensable part of modern science and engineering. Computer simulations of large-scale realistic applications usually require solving a set of non-linear partial differential equations (PDES) over a finite region. For example, one thrust area in the DOE Grand Challenge projects is to design future accelerators such as the SpaHation Neutron Source (SNS). Our colleagues at SLAC need to model complex RFQ cavities with large aspect ratios. Unstructured grids are currently used to resolve the small features in a large computational domain; dynamic mesh adaptation will be added in the future for additional efficiency. The PDEs for electromagnetics are discretized by the FEM method, which leads to a generalized eigenvalue problem Kx = AMx, where K and M are the stiffness and mass matrices, and are very sparse. In a typical cavity model, the number of degrees of freedom is about one million. For such large eigenproblems, direct solution techniques quickly reach the memory limits. Instead, the most widely-used methods are Krylov subspace methods, such as Lanczos or Jacobi-Davidson. In all the Krylov-based algorithms, sparse matrix-vector multiplication (SPMV) must be performed repeatedly. Therefore, the efficiency of SPMV usually determines the eigensolver speed. SPMV is also one of the most heavily used kernels in large-scale numerical simulations.

Oliker, Leonid↗

NASA NTRS1981

Substructure program for analysis of helicopter vibrations

A substructure vibration analysis which was developed as a design tool for predicting helicopter vibrations is described. The substructure assembly method and the composition of the transformation matrix are analyzed. The procedure for obtaining solutions to the equations of motion is illustrated for the steady-state forced response solution mode, and rotor hub load excitation and impedance are analyzed. Calculation of the mass, damping, and stiffness matrices, as well as the forcing function vectors of physical components resident in the base program code, are discussed in detail. Refinement of the model is achieved by exercising modules which interface with the external program to represent rotor induced variable inflow and fuselage induced variable inflow at the rotor. The calculation of various flow fields is discussed, and base program applications are detailed.

Sopher, R.↗

NASA NTRS1986

Thermal stability of lightweight graphite glass sandwich reflectors for far infrared astronomy

Graphite fiber-reinforced glass matrix composites are being developed for a variety of structural applications requiring excellent thermomechanical stability. These materials are ideally suited for lightweight, high strength, thermally stable infrared mirrors because of their low density, low thermal expansion, high strength and stiffness, and their ability to be machined, replicated and figured using standard polishing techniques. These properties are particularly promising for applications such as a 3-meter balloon-borne far-infrared and submillimeter telescope mirror which must be both very lightweight and able to retain its figure accuracy when cycled between room temperature and its operating temperature of -50 C. This paper presents the results of a set of low temperature optical tests conducted to determine the figure stability of a 30-cm diameter, frit-bonded graphite/glass mirror in the +20 to -60 C temperature range using a 10.6 micron laser interferometer. The results indicate that the residual change in figure was less than 0.3 microns, rms.

Bluege, J. H.↗

NASA NTRS1999

Thermomechanical Fatigue Durability of T650-35/PMR-15 Sheet-Molding Compound Evaluated

High-performance polymer matrix composites (PMC's) continue to be the focus of a number of research efforts aimed at developing cost-effective, lightweight material alternatives for advanced aerospace and aeropropulsion applications. These materials not only offer significant advantages in specific stiffness and strength over their current metal counterparts, but they can be designed and manufactured to eliminate joints and fasteners by combining individual components into integral subassemblies, thus making them extremely attractive for commercial applications. With much emphasis on the low-cost manufacturing aspects of advanced composite structures, there is heightened interest in high-performance sheet-molding compounds (SMC's). Researchers at the NASA Lewis Research Center, in cooperation with the Allison Advanced Development Company, completed an investigation examining the use of T650-35/PMR-15 SMC for a midstage inner-vane endwall application within a gas turbine engine compressor. This component resides in the engine flow path and is subjected not only to high airflow rates, but also to elevated temperatures and pressures. This application is unique in that it represents a very aggressive use of high-performance SMC's, raising obvious concerns related to durability and property retention in the presence of microstructural damage. Therefore, it was necessary to evaluate the fatigue behavior and damage tolerance of this material subjected to a representative thermomechanical fatigue (TMF) mission-cycle loading spectrum.

Castelli, Michael G.↗

NASA NTRS2014

A Numerical and Experimental Study of Damage Growth in a Composite Laminate

The present study has three goals: (1) perform an experiment where a simple laminate damage process can be characterized in high detail; (2) evaluate the performance of existing commercially available laminate damage simulation tools by modeling the experiment; (3) observe and understand the underlying physics of damage in a composite honeycomb sandwich structure subjected to low-velocity impact. A quasi-static indentation experiment has been devised to provide detailed information about a simple mixed-mode damage growth process. The test specimens consist of an aluminum honeycomb core with a cross-ply laminate facesheet supported on a stiff uniform surface. When the sample is subjected to an indentation load, the honeycomb core provides support to the facesheet resulting in a gradual and stable damage growth process in the skin. This enables real time observation as a matrix crack forms, propagates through a ply, and then causes a delamination. Finite element analyses were conducted in ABAQUS/Explicit(TradeMark) 6.13 that used continuum and cohesive modeling techniques to simulate facesheet damage and a geometric and material nonlinear model to simulate core crushing. The high fidelity of the experimental data allows a detailed investigation and discussion of the accuracy of each numerical modeling approach.

McElroy, Mark↗

NASA NTRS2015

FEAMAC-CARES Software Coupling Development Effort for CMC Stochastic-Strength-Based Damage Simulation

Reported here is a coupling of two NASA developed codes: CARES (Ceramics Analysis and Reliability Evaluation of Structures) with the MACGMC composite material analysis code. The resulting code is called FEAMACCARES and is constructed as an Abaqus finite element analysis UMAT (user defined material). Here we describe the FEAMACCARES code and an example problem (taken from the open literature) of a laminated CMC in off-axis loading is shown. FEAMACCARES performs stochastic-strength-based damage simulation response of a CMC under multiaxial loading using elastic stiffness reduction of the failed elements.

Reliability↗

NASA NTRS2014

TPSAS-NF1676L-19616-DND

Mark McElroy↗

NASA NTRS1971

Statistical analysis of the modal properties of large structural systems.

A theory is developed to predict eigenvalue and eigenvector uncertainty in large dynamic models. The uncertainty is based on physical property uncertainty and should not be confused with numerical roundoff, although the method can be extended to include the latter. The theory, when implemented on a computer, is used to analyze the uncertainties in frequencies and mode shapes based on uncertainties in mass, stiffness, modulus of elasticity, etc. The method incorporates a linear statistical model which is quite adequate for handling property uncertainties of 10% or more. The model is not limited to small systems but uses certain statistical assumptions as well as selective matrix manipulations to keep the size of all matrix operations to within the number of degrees of freedom of the system. Examples are given for two longitudinal vibration problems, and the results are supported by a Monte Carlo analysis.

Collins, J. D.↗