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NASA NTRS2011

Seeding Cracks Using a Fatigue Tester for Accelerated Gear Tooth Breaking

This report describes fatigue-induced seeded cracks in spur gears and compares them to cracks created using a more traditional seeding method, notching. Finite element analysis (FEA) compares the effective compliance of a cracked tooth to the effective compliance of a notched tooth where the crack and the notch are of the same depth. In this analysis, cracks are propagated to the desired depth using FRANC2D and effective compliances are computed in ANSYS. A compliance-based feature for detecting cracks on the fatigue tester is described. The initiated cracks are examined using both nondestructive and destructive methods. The destructive examination reveals variability in the shape of crack surfaces.

Nenadic, Nenad G.↗

NASA NTRS1987

Re-analysis procedure based on the mixed formulation

An analysis procedure is presented for large-scale structural systems, with large numbers of degrees of freedom and design variables. The procedure uses a mixed formulation with the fundamental unknowns consisting of both stress and displacement parameters. Other elements of the procedure include: (1) lumping the design variables into a single tracing parameter; (2) operator splitting or additive decomposition of different arrays in the finite element equations into the corresponding arrays of the original structure plus correction terms; and (3) application of a reduction method through the use of the finite element method and the classical Bubnov-Galerkin technique. The re-analysis procedure is applied to the linear static and free vibration problems of plate and shell structures.

Noor, Ahmed K.↗

NASA NTRS2020

An Improved Plastically Dilatant Unified Viscoplastic Constitutive Formulation for Multiscale Analysis of Polymer Matrix Composites Under High Strain Rate Loading

Polymer matrix composites are commonly used to fabricate energy-absorbing structures expected to experience impact loading. As such, a detailed understanding of the dynamic response of the constituent materials is necessary. Since the rate, temperature, and pressure dependence of carbon fiber reinforced polymer matrix composites are primarily manifestations of the rate, temperature, and pressure dependence of the polymer matrix, it is crucial that the constitutive behavior of the matrix be accurately characterized. In this work, an existing unified viscoplastic constitutive formulation is extended to ensure thermodynamic consistency and to more accurately account for the tension-compression asymmetry observed in the response of polymeric materials. A new plastic potential function is proposed, and elementary loading conditions are utilized to determine relations between model constants to ensure nonnegative plastic dissipation, a necessary thermodynamic requirement. Expressions for plastic Poisson’s ratios are derived and are bounded by enforcing nonnegative plastic dissipation. The model is calibrated against available experimental data from tests conducted over a range of strain rates, temperatures, and loading cases on a representative thermoset epoxy; good correlation between simulations and experimental data is obtained. Temperature rises due to the conversion of plastic work to heat are computed via the adiabatic heat energy equation. The viscoplastic polymer model is then used as a constitutive model in the generalized method of cells micromechanics theory to investigate the effects of matrix adiabatic heating on the high strain rate response of a unidirectional composite. The thermodynamic consistency of the model ensures plastic dissipation can only cause an increase in temperature. Simulation results indicate that significant thermal softening due to the conversion of plastic work to heat is observed in the composite for matrix dominated deformation modes.

Impact loading↗

NASA NTRS2013

Applications of Automation Methods for Nonlinear Fracture Test Analysis

Using automated and standardized computer tools to calculate the pertinent test result values has several advantages such as: 1. allowing high-fidelity solutions to complex nonlinear phenomena that would be impractical to express in written equation form, 2. eliminating errors associated with the interpretation and programing of analysis procedures from the text of test standards, 3. lessening the need for expertise in the areas of solid mechanics, fracture mechanics, numerical methods, and/or finite element modeling, to achieve sound results, 4. and providing one computer tool and/or one set of solutions for all users for a more "standardized" answer. In summary, this approach allows a non-expert with rudimentary training to get the best practical solution based on the latest understanding with minimum difficulty.Other existing ASTM standards that cover complicated phenomena use standard computer programs: 1. ASTM C1340/C1340M-10- Standard Practice for Estimation of Heat Gain or Loss Through Ceilings Under Attics Containing Radiant Barriers by Use of a Computer Program 2. ASTM F 2815 - Standard Practice for Chemical Permeation through Protective Clothing Materials: Testing Data Analysis by Use of a Computer Program 3. ASTM E2807 - Standard Specification for 3D Imaging Data Exchange, Version 1.0 The verification, validation, and round-robin processes required of a computer tool closely parallel the methods that are used to ensure the solution validity for equations included in test standard. The use of automated analysis tools allows the creation and practical implementation of advanced fracture mechanics test standards that capture the physics of a nonlinear fracture mechanics problem without adding undue burden or expense to the user. The presented approach forms a bridge between the equation-based fracture testing standards of today and the next generation of standards solving complex problems through analysis automation.

Allen, Phillip A.↗

NASA NTRSDate not supplied

Parallelized Quadrupole Simulations of Thermographic Responses of Composites

Thermography has been shown to be a viable technique for inspection of composites. Model inversion of the thermography data requires a fast method for performing the forward problem. Viable numerical methods for the thermal response forward problem are finite element, finite difference and the quadrupole method. Normally both the finite element and finite difference methods solve for the thermal response in the time domain which limits one’s ability to increase the speed of the simulation by parallelization. In contrast, the quadrupole method solves for the Laplace transform of the thermal response. One of the features of the Laplace transform methodology is the solution at any discrete time is independent of the solution at all other times. Therefore, it is easy to separate into a set of independent calculations with each of the times of interest being performed in parallel. Additionally, the numeric inversion of the Laplace transform typically involves numerically solving for the Laplace transform at multiple Laplace frequencies. Each of those solutions are also independent of solutions at other frequencies and can be calculated in parallel. By parallelization of this method, it is possible to perform the simulations of three-dimensional configurations in seconds. When the input stimulus for thermal response is a delta function heat flux (a reasonable approximation for flash heating), the thermal response is smooth. For this case, it is possible to accurately estimate the thermal response at any time within a given time interval from a set of simulations separated by exponentially increasing time steps. From these simulations, it is possible to accurately interpolate to find the response at intermediate times by a spline interpolation of the logarithm of time versus logarithm of temperature. The thermal response with exponential time stepping is shown to produce values for the thermal response which are within 1% of values within the time interval. The simulations are compared to finite element simulations of the same inspection configurations. The simulations are also compared to the thermographic measurements on composites where shape and depth of the delaminations are obtained from other inspection methods.

Thermography↗

NASA NTRSDate not supplied

Parallelized Quadrupole Simulations of Thermographic Responses of Composites

Thermography↗

NASA NTRS1996

The Prediction of Ducted Fan Engine Noise Via a Boundary Integral Equation Method

A computationally efficient Boundary Integral Equation Method (BIEM) for the prediction of ducted fan engine noise is presented. The key features of the BIEM are its versatility and the ability to compute rapidly any portion of the sound field without the need to compute the entire field. Governing equations for the BIEM are based on the assumptions that all acoustic processes are linear, generate spinning modes, and occur in a uniform flow field. An exterior boundary value problem (BVP) is defined that describes the scattering of incident sound by an engine duct with arbitrary profile. Boundary conditions on the duct walls are derived that allow for passive noise control treatment. The BVP is recast as a system of hypersingular boundary integral equations for the unknown duct surface quantities. BIEM solution methodology is demonstrated for the scattering of incident sound by a thin cylindrical duct with hard walls. Numerical studies are conducted for various engine parameters and continuous portions of the total pressure field are computed. Radiation and duct propagation results obtained are in agreement with the classical results of spinning mode theory for infinite ducts.

Boundary integral equation↗

NASA NTRS1971

ELAS8 - Computer program for linear structure equilibrium problems

Program generates and solves governing equations for unknown deflection of mesh points as if problem were to locate stationary point of total potential function associated with given loading and unknown deflections. Solution is obtained by means of displacement method and finite element technique.

Utku, S.↗

NASA NTRS1971

NASTRAN computer system level 12.1

Program uses finite element displacement method for solving linear response of large, three-dimensional structures subject to static, dynamic, thermal, and random loadings. Program adapts to computers of different manufacture, permits up-dating and extention, allows interchange of output and input information between users, and is extensively documented.

Butler, T. G.↗

NASA NTRS1972

Study of effects of design details on structural response to acoustic excitation

The normal mode vibration characteristics of one-dimensional and two-dimensional panel arrays were investigated analytically and experimentally. The finite element displacement method was used to formulate the structural models. The structural models include a stiffness and consistent mass matrix for thin-walled open-section beams not previously reported, and a modification of a rectangular plate bending element to include a fundamental interior mode for the element as a generalized coordinate. Provision for adding lumped masses to represent accelerometers is also included. For the one-dimensional panel, the normal mode stress resultants are obtained by integrating the equilibrium equations directly. For the two-dimensional panel arrays, the solution for the stress resultants in the cover sheet was attempted by introducing stress functions dependent upon the displacement field of the plate element. This approach, although incomplete, is a natural extension of the one-dimensional analysis for plate elements. The exerimental program which was used to verify the analysis is described and experimental results are compared with the analysis.

Rudder, F. F., Jr.↗

NASA NTRS1975

Feasibility study for the implementation of NASTRAN on the ILLIAC 4 parallel processor

The ILLIAC IV, a fourth generation multiprocessor using parallel processing hardware concepts, is operational at Moffett Field, California. Its capability to excel at matrix manipulation, makes the ILLIAC well suited for performing structural analyses using the finite element displacement method. The feasibility of modifying the NASTRAN (NASA structural analysis) computer program to make effective use of the ILLIAC IV was investigated. The characteristics are summarized of the ILLIAC and the ARPANET, a telecommunications network which spans the continent making the ILLIAC accessible to nearly all major industrial centers in the United States. Two distinct approaches are studied: retaining NASTRAN as it now operates on many of the host computers of the ARPANET to process the input and output while using the ILLIAC only for the major computational tasks, and installing NASTRAN to operate entirely in the ILLIAC environment. Though both alternatives offer similar and significant increases in computational speed over modern third generation processors, the full installation of NASTRAN on the ILLIAC is recommended. Specifications are presented for performing that task with manpower estimates and schedules to correspond.

Field, E. I.↗

NASA NTRS1976

Considerations for the application of finite element beam modeling to vibration analysis of flight vehicle structures

The manner of representing a flight vehicle structure as an assembly of beam, spring, and rigid-body components for vibration analysis is described. The development is couched in terms of a substructures methodology which is based on the finite-element stiffness method. The particular manner of employing beam, spring, and rigid-body components to model such items as wing structures, external stores, pylons supporting engines or external stores, and sprung masses associated with launch vehicle fuel slosh is described by means of several simple qualitative examples. A detailed numerical example consisting of a tilt-rotor VTOL aircraft is included to provide a unified illustration of the procedure for representing a structure as an equivalent system of beams, springs, and rigid bodies, the manner of forming the substructure mass and stiffness matrices, and the mechanics of writing the equations of constraint which enforce deflection compatibility at the junctions of the substructures. Since many structures, or selected components of structures, can be represented in this manner for vibration analysis, the modeling concepts described and their application in the numerical example shown should prove generally useful to the dynamicist.

Kvaternik, R. G.↗

NASA NTRS1977

A finite element technique for non-deterministic thermal deformation analyses including temperature dependent material properties

A technique utilizing the finite element displacement method is developed for the static analysis of structures subjected to non-deterministic thermal loading in which the material properties, assumed isotropic, are temperature dependent. Matrix equations are developed for the first two statistical moments of the displacements using a third order series expansion for the displacements in terms of the random temperatures. Sample problems are included to demonstrate the range of applicability of the third order series solutions. These solutions are compared with results from Monte Carlo analyses and also, for some problems, with solutions obtained by numerically integrating equations for the statistical properties of the displacements. In general, it is shown that the effect of temperature dependent material properties can have a significant effect on the covariances of the displacements.

Case, W. R., Jr.↗

NASA NTRS1979

Accuracy of an approximate static structural analysis technique based on stiffness matrix eigenmodes

Use of the stiffness matrix eigenmodes, instead of the vibration eigenmodes, as generalized coordinates is proposed for condensation of static load deflection equations in finite element stiffness method. The modes are selected by strain energy criteria and the resulting fast, approximate analysis technique is evaluated by applications to idealized built-up wings and a fuselage segment. The best results obtained are a two-order of magnitude reduction of the number of degrees of freedom in a high aspect ratio wing associated with less than one percent error in prediction of the largest displacement.

Sobieszczanski-Sobieski, J.↗

NASA NTRS1979

NASTRAN processing at Johnson Space Center

The processing behavior of NASTRAN, a general purpose system of computer software used for solving engineering analysis problems by means of the finite element displacement method, is discussed. The host system for the NASTRAN is the Univac 1110, and the primary function is performing static and dynamic structural analyses of the Space Shuttle. The processing implications of the NASTRAN structural analysis are addressed and the current NASTRAN situation on the Univac 1110 is examined. The current NASTRAN workload is described and the effect of workload growth due to increased structure size is estimated. A cost and performance analysis is presented.

Richards, F. M., Jr.↗

NASA NTRS1979

Solution of a few nonlinear problems in aerodynamics by the finite elements and functional least squares methods

The numerical simulation of the transonic flows of idealized fluids and of incompressible viscous fluids, by the nonlinear least squares methods is presented. The nonlinear equations, the boundary conditions, and the various constraints controlling the two types of flow are described. The standard iterative methods for solving a quasi elliptical nonlinear equation with partial derivatives are reviewed with emphasis placed on two examples: the fixed point method applied to the Gelder functional in the case of compressible subsonic flows and the Newton method used in the technique of decomposition of the lifting potential. The new abstract least squares method is discussed. It consists of substituting the nonlinear equation by a problem of minimization in a H to the minus 1 type Sobolev functional space.

Periaux, J.↗

NASA NTRS1981

Noise suppression characteristics of peripherally segmented duct liners

The acoustic fields and transmission losses produced in semi-infinite circular ducts with peripherally segmented liners are analyzed using a series expansion of hard-wall duct modes. The coefficients of the series are computed using Galerkin's method. Unlike finite element approaches, this analysis includes the effects of realistic sources and the number of peripheral strips need not be small. It is shown that peripherally segmented liners redistribute the acoustic energy in waves composed of only a single circumferential mode at the source into other waves which contain a multitude of circumferential modes in the lined section. The accuracy of eigenfunctions computed from the analysis was observed to increase as either the frequency or radial mode order increased. The transmission losses were found to be accurate at frequencies above the cut-on value of the first-order radial mode in a hard-wall duct. The results show that for plane wave sources, peripherally segmented liners may attenuate as much sound as an optimized uniform liner at the optimal point while giving more noise suppression at most other frequencies.

Watson, W. R.↗

NASA NTRS1983

Moving finite elements in 2-D

The mathematical background regarding the moving finite element (MFE) method of Miller and Miller (1981) is discussed, taking into account a general system of partial differential equations (PDE) and the amenability of the MFE method in two dimensions to code modularization and to semiautomatic user-construction of numerous PDE systems for both Dirichlet and zero-Neumann boundary conditions. A description of test problem results is presented, giving attention to aspects of single square wave propagation, and a solution of the heat equation.

Gelinas, R. J.↗