Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “stiff problem”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 541 records · Page 30
All sourcesNASA NTRSDOE OSTI
NASA NTRS2016

Multifunctional Hybrid Carbon Nanotube/Carbon Fiber Polymer Composites

For aircraft primary structures, carbon fiber reinforced polymer (CFRP) composites possess many advantages over conventional aluminum alloys due to their light weight, higher strengthand stiffness-to-weight ratio, and low life-cycle maintenance costs. However, the relatively low electrical and thermal conductivities of CFRP composites fail to provide structural safety in certain operational conditions such as lightning strikes. Despite several attempts to solve these issues with the addition of carbon nanotubes (CNT) into polymer matrices, and/or by interleaving CNT sheets between conventional carbon fiber (CF) composite layers, there are still interfacial problems that exist between CNTs (or CF) and the resin. In this study, hybrid CNT/CF polymer composites were fabricated by interleaving layers of CNT sheets with Hexcel® IM7/8852 prepreg. Resin concentrations from 1 wt% to 50 wt% were used to infuse the CNT sheets prior to composite fabrication. The interlaminar properties of the resulting hybrid composites were characterized by mode I and II fracture toughness testing (double cantilever beam and end-notched flexure test). Fractographical analysis was performed to study the effect of resin concentration. In addition, multi-directional physical properties like thermal conductivity of the orthotropic hybrid polymer composite were evaluated. Interleaving CNT sheets significantly improved the in-plane (axial and perpendicular direction of CF alignment) thermal conductivity of the hybrid composite laminates by 50 - 400%.

Kang, Jin Ho↗
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.↗
NASA NTRS1983

The effect of matrix properties and fiber properties on impact failure mechanics

The low-velocity impact problem in graphite/epoxy composite sheets must be solved before large amounts of that material can be used in commercial aircraft. Many of the low-velocity impacts that affect aircraft parts occur during normal ground operations and maintenance. Service equipment and tools have masses above 1 kg, and at velocities of less than 3 m/s can impact structural parts with energies higher than composites can endure without degradation of stiffness or strength. Simple solutions were developed for large-mass, low-velocity impacts which can be modeled as quasi-static events. Static test data and impact data show that the fiber properties control the impact energy which can be absorbed before penetration. Matrix shear strength and peel resistance control the extent of delamination. Comparison of results from tough matrix and brittle matrix composites show that although tough matrices reduce the extent of delamination, they lead to more fiber damage in the contact area.

Elber, W.↗
NASA NTRS1985

An analysis of cross-coupling of a multicomponent jet engine test stand using finite element modeling techniques

A two axis thrust measuring system was analyzed by using a finite a element computer program to determine the sensitivities of the thrust vectoring nozzle system to misalignment of the load cells and applied loads, and the stiffness of the structural members. Three models were evaluated: (1) the basic measuring element and its internal calibration load cells; (2) the basic measuring element and its external load calibration equipment; and (3) the basic measuring element, external calibration load frame and the altitude facility support structure. Alignment of calibration loads was the greatest source of error for multiaxis thrust measuring systems. Uniform increases or decreases in stiffness of the members, which might be caused by the selection of the materials, have little effect on the accuracy of the measurements. It is found that the POLO-FINITE program is a viable tool for designing and analyzing multiaxis thrust measurement systems. The response of the test stand to step inputs that might be encountered with thrust vectoring tests was determined. The dynamic analysis show a potential problem for measuring the dynamic response characteristics of thrust vectoring systems because of the inherently light damping of the test stand.

Schweikhard, W. G.↗
NASA NTRS1989

Exploiting symmetries in the modeling and analysis of tires

A computational procedure is presented for reducing the size of the analysis models of tires having unsymmetric material, geometry and/or loading. The two key elements of the procedure when applied to anisotropic tires are: (1) decomposition of the stiffness matrix into the sum of an orthotropic and nonorthotropic parts; and (2) successive application of the finite-element method and the classical Rayleigh-Ritz technique. The finite-element method is first used to generate few global approximation vectors (or modes). Then the amplitudes of these modes are computed by using the Rayleigh-Ritz technique. The proposed technique has high potential for handling practical tire problems with anisotropic materials, unsymmetric imperfections and asymmetric loading. It is also particularly useful for use with three-dimensional finite-element models of tires.

Noor, Ahmed K.↗
NASA NTRS1989

Integrated aerodynamic-structural design of a transport wing

The integrated aerodynamic-structural design of a subsonic transport wing for minimum weight subject to required range is formulated and solved. The problem requires large computational resources, and two methods are used to alleviate the computational burden. First, a modular sensitivity method that permits the usage of black-box disciplinary software packages, is used to reduce the cost of sensitivity derivatives. In particular, it is shown that derivatives of the aeroelastic response and divergence speed can be calculated without the costly computation of derivatives of aerodynamic influence coefficient and structural stiffness matrices. A sequential approximate optimization is used to further reduce computational cost. The optimization procedure is shown to require a relatively small number of analysis and sensitivity calculations.

Grossman, B.↗
DOE OSTI2023

Mathematical solutions in internal dose assessment: A comparison of Python-based differential equation solvers in biokinetic modeling

Abstract In biokinetic modeling systems employed for radiation protection, biological retention and excretion have been modeled as a series of discretized compartments representing the organs and tissues of the human body. Fractional retention and excretion in these organ and tissue systems have been mathematically governed by a series of coupled first-order ordinary differential equations (ODEs). The coupled ODE systems comprising the biokinetic models are usually stiff due to the severe difference between rapid and slow transfers between compartments. In this study, the capabilities of solving a complex coupled system of ODEs for biokinetic modeling were evaluated by comparing different Python programming language solvers and solving methods with the motivation of establishing a framework that enables multi-level analysis. The stability of the solvers was analyzed to select the best performers for solving the biokinetic problems. A Python-based linear algebraic method was also explored to examine how the numerical methods deviated from an analytical or semi-analytical method. Results demonstrated that customized implicit methods resulted in an enhanced stable solution for the inhaled 60 Co (Type M) and 131 I (Type F) exposure scenarios for the inhalation pathway of the International Commission on Radiological Protection (ICRP) Publication 130 Human Respiratory Tract Model (HRTM). The customized implementation of the Python-based implicit solvers resulted in approximately consistent solutions with the Python-based matrix exponential method ( expm ). The differences generally observed between the implicit solvers and expm are attributable to numerical precision and the order of numerical approximation of the numerical solvers. This study provides the first analysis of a list of Python ODE solvers and methods by comparing their usage for solving biokinetic models using the ICRP Publication 130 HRTM and provides a framework for the selection of the most appropriate ODE solvers and methods in Python language to implement for modeling the distribution of internal radioactivity.

61 RADIATION PROTECTION AND DOSIMETRY↗
NASA NTRS1974

Dynamics of tilting proprotor aircraft in cruise flight

A nine degree-of-freedom theoretical model is developed for investigations of the dynamics of a proprotor operating in high inflow axial flight on a cantilever wing. The basic characteristics of the rotor high inflow aerodynamics and the resulting rotor aeroelastic behavior are discussed. The problems of classical whirl flutter, the two-bladed rotor, and the influence of the proprotor on the stability derivatives of the aircraft are treated briefly. The influence of various elements of the theoretical model is discussed, including the modeling used for the blade and wing aerodynamics, and the influence of the rotor lag degree of freedom. The results from tests of two full-scale proprotors - a gimballed, stiff-inplane rotor and a hingeless, soft-inplane rotor - are presented; comparisons with the theoretical results show good correlation.

Johnson, W.↗
NASA NTRS1983

A pressurized cylindrical shell with a fixed end which contains an axial part-through or through crack

A cylindrical shell having a very stiff and plate or a flange is considered. It is assumed that near the end the cylinder contains an axial flaw which may be modeled as a part through surface crack or a through crack. The effect of the end constraining on the stress intensity factor which is the main fracture mechanics parameter is studied. The applied loads acting on the cylinder are assumed to be axisymmetric. Thus the crack problem under consideration is symmetric with respect to the plane of the crack and consequently only the Mode 1 stress intensity factors are nonzero. With this limitation, the general perturbation problem for a cylinder with a built in end containing an axial crack is considered. Reissner's shell theory is used to formulate the problem. The part through crack problem is treated by using a line spring model. In the case of a crack tip terminating at the fixed end it is shown that the integral equations of the shell problem has the same generalized Cauchy kernel as the corresponding plane stress elasticity problem.

Yahsi, O. S.↗
NASA NTRS1985

The response of Helmholtz resonators to external excitation. I - Single resonators

The response of single two- and three-dimensional Helmholtz resonators subject to external excitation by a plane acoustic wave is studied. The inviscid linearized problem is solved by the matched-asymptotic-expansion technique in the low-frequency limit, i.e. when the characteristic neck dimension is small compared with the acoustic wavelength. The scale of the cavity is chosen such as to tune the system to the lowest Helmholtz mode. The results are compared with the classical lumped-element model, and refined expressions are derived for the effective mass (added length) and stiffness (effective cavity volume) of the resonator.

Monkewitz, P. A.↗
NASA NTRS1989

Model reduction in the physical coordinate system

In the dynamics modeling of a flexible structure, finite element analysis employs reduction techniques, such as Guyan's reduction, to remove some of the insignificant physical coordinates, thus producing a dynamics model that has smaller mass and stiffness matrices. But this reduction is limited in the sense that it removes certain degrees of freedom at a node points themselves in the model. From the standpoint of linear control design, the resultant model is still too large despite the reduction. Thus, some form of the model reduction is frequently used in control design by approximating a large dynamical system with a fewer number of state variables. However, a problem arises from the placement of sensors and actuators in the reduced model, because a model usually undergoes, before being reduced, some form of coordinate transformations that do not preserve the physical meanings of the states. To correct such a problem, a method is developed that expresses a reduced model in terms of a subset of the original states. The proposed method starts with a dynamic model that is originated and reduced in finite element analysis. Then the model is converted to the state space form, and reduced again by the internal balancing method. At this point, being in the balanced coordinate system, the states in the reduced model have no apparent resemblance to those of the original model. Through another coordinate transformation that is developed, however, this reduced model is expressed by a subset of the original states.

Yae, K. Harold↗
NASA NTRS1994

Superconducting axisymmetric finite elements based on a gauged potential variational principle. Part 2: Solutions and numerical results

This paper discusses an incremental-iterative nonlinear solution technique for solving the nonlinear finite element equations of the superconducting state of a superconductor. The untreated equations are highly ill-conditioned and are impossible to solve within the typical 16-place double precision supplied by most computers. A combination of matrix scaling and mesh grading techniques is used to reduce the condition number of the tangent stiffness matrix and increase the accuracy of the current carrying boundary layer representation. Numerical results for a one-dimensional model of a time-independent superconductor treated by the Ginzburg-Landau model are presented and discussed. The computed solutions clearly display the Meissner effect of magnetic field expulsion from the central region of the superconductor. These results are compared to the physics of a low-viscosity fluid problem. From this analogy, a physical argument is advanced about the macroscopic behavior of superconductors.

Schuler, James J.↗
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 NTRS2008

Development of the Aquarius Antenna Deployment Mechanisms and Spring/Damper Actuator

The Aquarius Instrument s large radar reflector dish needed to be stowed for launch, and then deployed on-orbit. The Deployment Subsystem consisted of a cantilevered boom structure and two single-axis hinge mechanisms to accurately deploy and position the reflector dish relative to the radar feed horns. The cantilevered design demanded high stiffness and accuracy from the deployment mechanism at the root of the boom. A preload-generating end-of-travel latch was also required. To largely eliminate the need for control systems, each deployment mechanism was actuated by a passive spring motor with viscous-fluid damping. Tough requirements and adaptation of a heritage actuator to the new application resulted in numerous challenges. Fabrication, assembly, and testing encountered additional problems, though ultimately the system was demonstrated very successfully. This paper revisits the development to highlight which design concepts worked and the many important lessons learned.

Johnson, Joel A.↗
DOE OSTI2020

Slow manifold reduction for plasma science

The classical Chapman–Enskog procedure admits a substantial geometrical generalization known as slow manifold reduction. This generalization provides a paradigm for deriving and understanding most reduced models in plasma physics that are based on controlled approximations applied to problems with multiple timescales. In this Review we develop the theory of slow manifold reduction with a plasma physics audience in mind. In particular we illustrate (a) how the slow manifold concept may be used to understand breakdown of a reduced model over sufficiently-long time intervals, and (b) how a discrete-time analogue of slow manifold theory provides a useful framework for developing implicit integrators for temporally-stiff plasma models. For readers with more advanced mathematical training we also use slow manifold reduction to explain the phenomenon of inheritance of Hamiltonian structure in dissipation-free reduced plasma models. Various facets of the theory are illustrated in the context of the Abraham–Lorentz model of a single charged particle experiencing its own radiation drag. As a culminating example we derive the slow manifold underlying kinetic quasineutral plasma dynamics up to first-order in perturbation theory. This first-order result incorporates several physical effects associated with small deviations from exact charge neutrality that lead to slow drift away from predictions based on the leading-order approximation n e = Z i n i .

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1993

A parameter identification method for the rotordynamic coefficients of a high Reynolds number hydrostatic bearing

In identifying the rotordynamic coefficients of a high-Reynolds-number hydrostatic bearing, fluid-flow induced forces present a unique problem, in that they provide an unmeasureable and uncontrollable excitation to the bearing. An analysis method is developed that effectively eliminates the effects of fluid-flow induced excitation on the estimation of the bearing rotordynamic coefficients, by using power spectral densities. In addition to the theoretical development, the method is verified experimentally by single-frequency testing, and repeatability tests. Results obtained for a bearing are the twelve rotordynamic coefficients (stiffness, damping, and inertia coefficients) as functions of eccentricity ratio, speed, and supply pressure.

Rouvas, C.↗
NASA NTRS1996

Spray Combustion Modeling with VOF and Finite-Rate Chemistry

A spray atomization and combustion model is developed based on the volume-of-fluid (VOF) transport equation with finite-rate chemistry model. The gas-liquid interface mass, momentum and energy conservation laws are modeled by continuum surface force mechanisms. A new solution method is developed such that the present VOF model can be applied for all-speed range flows. The objectives of the present study are: (1) to develop and verify the fractional volume-of-fluid (VOF) cell partitioning approach into a predictor-corrector algorithm to deal with multiphase (gas-liquid) free surface flow problems; (2) to implement the developed unified algorithm in a general purpose computational fluid dynamics (CFD) code, Finite Difference Navier-Stokes (FDNS), with droplet dynamics and finite-rate chemistry models; and (3) to demonstrate the effectiveness of the present approach by simulating benchmark problems of jet breakup/spray atomization and combustion. Modeling multiphase fluid flows poses a significant challenge because a required boundary must be applied to a transient, irregular surface that is discontinuous, and the flow regimes considered can range from incompressible to highspeed compressible flows. The flow-process modeling is further complicated by surface tension, interfacial heat and mass transfer, spray formation and turbulence, and their interactions. The major contribution of the present method is to combine the novel feature of the Volume of Fluid (VOF) method and the Eulerian/Lagrangian method into a unified algorithm for efficient noniterative, time-accurate calculations of multiphase free surface flows valid at all speeds. The proposed method reformulated the VOF equation to strongly couple two distinct phases (liquid and gas), and tracks droplets on a Lagrangian frame when spray model is required, using a unified predictor-corrector technique to account for the non-linear linkages through the convective contributions of VOF. The discontinuities within the sharp interface will be modeled as a volume force to avoid stiffness. Formations of droplets, tracking of droplet dynamics and modeling of the droplet breakup/evaporation, are handled through the same unified predictor-corrector procedure. Thus the new algorithm is non-iterative and is flexible for general geometries with arbitrarily complex topology in free surfaces. The FDNS finite-difference Navier-Stokes code is employed as the baseline of the current development. Benchmark test cases of shear coaxial LOX/H2 liquid jet with atomization/combustion and impinging jet test cases are investigated in the present work. Preliminary data comparisons show good qualitative agreement between data and the present analysis. It is indicative from these results that the present method has great potential to become a general engineering design analysis and diagnostics tool for problems involving spray combustion.

Chen, Yen-Sen↗
DOE OSTI2021

Implicit Multirate GARK Methods

This article considers multirate generalized-structure additively partitioned Runge–Kutta methods for solving stiff systems of ordinary differential equations with multiple time scales. These methods treat different partitions of the system with different timesteps for a more targeted and efficient solution compared to monolithic single rate approaches. With implicit methods used across all partitions, methods must find a balance between stability and the cost of solving nonlinear equations for the stages. In order to characterize this important trade-off, we explore multirate coupling strategies, problems for assessing linear stability, and techniques to efficiently implement Newton iterations for stage equations. Unlike much of the existing multirate stability analysis which is limited in scope to particular methods, we present general statements on stability and describe fundamental limitations for certain types of multirate schemes. New implicit multirate methods up to fourth order are derived, and their accuracy and efficiency properties are verified with numerical tests.

97 MATHEMATICS AND COMPUTING↗