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At least 685 records · Page 38

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NASA NTRS1993

Contact stress analysis of spiral bevel gears using nonlinear finite element static analysis

A procedure is presented for performing three-dimensional stress analysis of spiral bevel gears in mesh using the finite element method. The procedure involves generating a finite element model by solving equations that identify tooth surface coordinates. Coordinate transformations are used to orientate the gear and pinion for gear meshing. Contact boundary conditions are simulated with gap elements. A solution technique for correct orientation of the gap elements is given. Example models and results are presented.

Bibel, G. D.↗

NASA NTRS1993

Hybrid equations of motion for flexible multibody systems using quasi-coordinates

A variety of engineering systems, such as automobiles, aircraft, rotorcraft, robots, spacecraft, etc., can be modeled as flexible multibody systems. The individual flexible bodies are in general characterized by distributed parameters. In most earlier investigations they were approximated by some spatial discretization procedure, such as the classical Rayleigh-Ritz method or the finite element method. This paper presents a mathematical formulation for distributed-parameter multibody systems consisting of a set of hybrid (ordinary and partial) differential equations of motion in terms of quasi-coordinates. Moreover, the equations for the elastic motions include rotatory inertia and shear deformation effects. The hybrid set is cast in state form, thus making it suitable for control design.

Meirovitch, L.↗

NASA NTRS1994

Theoretical and Experimental Study of Microstrip-to-Slot Line Uniplanar Transition

Recent advances in MMCI technology make it possible to construct transitions from CPW-to-microstrip with via hole, microstrip-to-slot line and microshield line-to-CPW all of which have potential applications in the feed network of antennas. In this study we investigate the characteristics of the microstrip-to-slot line uniplanar transition using the finite element methods (FEM) and finite difference time domain (FDTD) techniques, and compared the theoretical results with the measurements. In both cases, the results agree with the measurements within a few percent.

Yook, Jong-Gwan↗

NASA NTRS1999

Unified CFD Methods Via Flowfield-Dependent Variation Theory

This paper addresses the flowfield-dependent variation (FDV) methods in which complex physical phenomena are taken into account in the final form of partial differential equations to be solved so that finite difference methods (FDM) or finite element methods (FEM) themselves will not dictate the physics, but rather are no more than simply the options how to discretize between adjacent nodal points or within an element. The variation parameters introduced in the formulation are calculated from the current flowfield based on changes of Mach numbers, Reynolds numbers, Peclet numbers, and Damkohler numbers between adjacent nodal points, which play many significant roles such as adjusting the governing equations (hyperbolic, parabolic, and/or e!liptic), resolving various physical phenomena, and controlling the accuracy and stability of the numerical solution. The theory is verified by a number of example problems addressing the physical implications of the variation parameters which resemble the flowfield itself, shock capturing mechanism, transitions and interactions between inviscid/viscous, compressibility/incompressibility, and laminar/turbulent flows.

Chung, T. J.↗

NASA NTRS1995

Contact Stress Analysis of Spiral Bevel Gears Using Finite Element Analysis

Bibel, G. D.↗

NASA NTRS2019

How Certain Physical Considerations Impact Aerostructural Wing Optimization

Wing design optimization has been studied extensively and is of continued interest as optimization tools are developed and become more accessible. In each of these studies, certain assumptions and simplifications are made to make the design problem tractable. However, it is difficult to find systematic studies in which several considerations are added or removed one at a time to study how much impact they have. In this work, we examine how certain physical considerations (viscous drag, wave drag, thrust loads, and inertial relief from structural, fuel, and engine masses), impact the aerostructural optimization results for three distinct aircraft wings. The goal is to help develop a rough idea of how important these physical considerations are. We do this using gradient-based optimization and a multidisciplinary design optimization framework, OpenMDAO. We use the open-source tool OpenAeroStruct that couples a vortex lattice method to a finite element method. We establish a baseline aerostructural design optimization problem then perform a series of optimizations, each with one physical consideration removed from the baseline case. We find that depending on the size of the aircraft and flight conditions, the importance of some of these physical considerations varies considerably whereas the importance of others do not. Specifically, the optimal designs change radically without proper viscous and wave drag considerations and smaller aircraft with more distributed propulsion are more affected by the inclusion of engine loads.

Aeropropulsion↗

DOE OSTI2022

Pronghorn Porous Media Model Validation with Pressure Drop Measurements

The verification and validation (V&V) of Pronghorn is imperative to assert its accuracy when predicting the fluid velocity, temperature, and pressure in high temperature gas-cooled reactors. Pronghorn is a coarse-mesh, intermediate-fidelity, and multidimensional thermal-hydraulics (TH) code developed by the Idaho National Laboratory (INL). New pebble bed experiments are used to observe the details of the fluid motion and pressure drop in the porous bed under the reactor normal operation. This paper focuses on the validation of the Pronghorn compressible and incompressible Navier-Stokes equations using the pressure drop measurements performed at the engineering-scale pebble bed facility at the Texas A&M university (TAMU). Various pressure drop correlations and porosity functions are implemented in both Pronghorn and STAR-CCM+ to compare the pressure drop due to the combined viscous and inertial resistances in the porous bed. The correlations accounting for the near-wall effect are also utilized to observe if the pressure drop estimates can be improved. Pronghorn porous media models predict the pressure drop well relative to the STAR-CCM+ simulation results and 1D correlations, and both the finite element method (FEM) and finite volume method (FVM) perform accurately. Pronghorn models are also validated with the experimental measurements given the different Reynolds number ranges and specific aspect ratios. The likelihood of the statistical significance between the pressure drop measurements and specific correlations or simulations is low provided that the overlap of their confidence intervals is more than the half of a single arm. Several validation metrics are reasonable in regard to the similar studies from other literature. The precise average pebble bed porosity estimation has much impact on the pressure drop, and the Foumeny and Montillet (dense packing) models carry out the accurate pressure drop prediction by considering the near-wall effect.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2020

Simulation of coupled multiphase flow and geomechanics in porous media with embedded discrete fractures

In fractured natural formations, the equations governing fluid flow and geomechanics are strongly coupled. Hydrodynamical properties depend on the mechanical configuration, and they are therefore difficult to accurately resolve using uncoupled methods. In recent years, significant research has focused on discretization strategies for these coupled systems, particularly in the presence of complicated fracture network geometries. In this work, we explore a finite-volume discretization for the multiphase flow equations coupled with a finite-element scheme for the mechanical equations. Fractures are treated as lower dimensional surfaces embedded in a background grid. Interactions are captured using the embedded discrete fracture model (EDFM) and the embedded finite element method (EFEM) for the flow and the mechanics, respectively. This nonconforming approach significantly alleviates meshing challenges. EDFM considers fractures as lower dimension finite volumes that exchange fluxes with the rock matrix cells. The EFEM method provides, instead, a local enrichment of the finite-element space inside each matrix cell cut by a fracture element. Both the use of piecewise constant and piecewise linear enrichments are investigated. They are also compared to an extended finite element approach. One key advantage of EFEM is the element-based nature of the enrichment, which reduces the geometric complexity of the implementation and leads to linear systems with advantageous properties. Synthetic numerical tests are presented to study the convergence and accuracy of the proposed method. It is also applied to a realistic scenario, involving a heterogeneous reservoir with a complex fracture distribution, to demonstrate its relevance for field applications.

58 GEOSCIENCES↗

NASA NTRS1990

Practical model reduction for flexible structures

The most accepted methods for developing models of flexible structures for the analysis, design and simulation of control systems are finite element methods and extraction from experimental data. Using either of these methods, models are often produced with modes that do not significantly add to the fidelity of the model. This paper presents techniques for eliminating these modes. Particular attention is paid to multiple-input, multiple-output systems. First, control system models developed for flexible structures, using finite element methods and experimental data, are briefly discussed. the shortcomings of using models with unnecessary and/or residual modes are delineated. Then, two techniques for reducing the order of models are presented; the first is applicable to single-input, single-output systems and the second for multiple-input, multiple-output systems. Finally, both are illustrated using model data from the proposed NASA Shuttle-C.

Mitchell, Jerrel R.↗

DOE OSTI2017

A posteriori error estimation for multi-stage Runge–Kutta IMEX schemes

Implicit–Explicit (IMEX) schemes are widely used for time integration methods for approximating solutions to a large class of problems. In this work, we develop accurate a posteriori error estimates of a quantity-of-interest for approximations obtained from multi-stage IMEX schemes. This is done by first defining a finite element method that is nodally equivalent to an IMEX scheme, then using typical methods for adjoint-based error estimation. Furthermore, the use of a nodally equivalent finite element method allows a decomposition of the error into multiple components, each describing the effect of a different portion of the method on the total error in a quantity-of-interest.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Using porous random fields to predict the elastic modulus of unoxidized and oxidized superfine graphite

Nuclear graphite is a candidate material for Generation IV nuclear power plants. Porous materials such as graphite can contain complex networks of pores that influence the material's mechanical and irradiation response. A methodology known as the random finite element method (RFEM) was adapted to create synthetic microstructures and predict the influence of porosity on the elastic properties of graphite during oxidation. RFEM combines random field theory and the finite element method in a Monte Carlo framework to estimate the mechanical response of a given grade of graphite. In this research, the random fields were verified through experimental characterization to predict the elastic response of three nuclear graphite grades, ETU-10, IG-110, and 2114. Finite element models (FEM) were generated using segmentations of x-ray computed tomography (XCT) data known as image-based models (IBMs) to validate and compare with the RFEM results and better understand the effects of uniform oxidation in these graphite grades. The RFEM predictions appear to correlate well with the experimental values of the measured Young’s modulus of the three graphite grades and display the same trends as IBMs.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

NASA NTRS1972

Finite elements of nonlinear continua.

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.

Oden, J. T.↗

DOE OSTI2019

High Order Discontinuous Galerkin Method and Applications (Final Technical Report)

This project aims at the developments and improvements of high order accurate discontinuous Galerkin finite element methods for solving partial differential equations arising from DOE applications. Algorithm development, improvement, analysis, implementation and applications aspects are addressed. The partial differential equations under study involve solutions with shocks or other discontinuities, rapidly changing regions, or multiscale solutions. These include the so-called convection dominated cases, such as the hyperbolic equations (e.g. Euler equations of gas dynamics), parabolic equations with small viscosities (e.g. high Reynolds number Navier-Stokes equations), KdV type equations with small dispersion describing water waves (small third derivative terms), time-dependent bi-harmonic equations and equations with hyper-viscosity (small fourth or higher even derivative terms), problems with highly oscillatory coefficients, or problems for which the macro-scale PDE models may not be correct in localized regions and a micro-scale model must be used instead. Furthermore, we are interested in the long time solutions of such equations with waves traveling a long distance, such as the electromagnetic waves. The requirement on numerical methods is thus high order accuracy, low dissipation/dispersion errors over long time, and a clean and sharp discontinuity resolution. It would also be highly desirable to have the numerical methods to be flexible for complicated geometry and boundary conditions, and to be easy in an adaptive and massively parallel environment. The discontinuous Galerkin finite element method has this potential, however the design and analysis of the discontinuous Galerkin method for each specific class of partial differential equations would require detailed research.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1988

Impact induced stresses, strains, and delaminations in composite plates

A method is presented for calculating the locations and sizes of delaminations which occur in a rectangular, fiber reinforced composite plate subjected to nonpenetrating (low velocity) impact of a solid object. The plate may be simply supported or clamped along its edges. In-plane loads or in-plane strains may be imposed on the plate during the impact. The method includes two steps. First, the stresses and strains in the plate are calculated by a three-dimensional, transient finite element method using 8-node brick elements with incompatible modes. Second, the locations, lengths, and widths of delaminations inside the plate are predicted by means of a proposed failure criterion, which is based on the concept of dimensional analysis. The finite element method and the failure criterion were implemented by a computer code which can be used to calculate the impactor position and velocity, the displacements of the plate, the stresses and strains inside the plate during the impact, and the locations and dimensions of the delaminations after the impact. Parametric studies were performed to illustrate the information which can be generated by the computer code.

Wu, Hsi-Yung T.↗

NASA NTRS1994

An HP Adaptive Discontinuous Galerkin Method for Hyperbolic Conservation Laws

This dissertation addresses various issues for model classes of hyperbolic conservation laws. The basic approach developed in this work employs a new family of adaptive, hp-version, finite element methods based on a special discontinuous Galerkin formulation for hyperbolic problems. The discontinuous Galerkin formulation admits high-order local approximations on domains of quite general geometry, while providing a natural framework for finite element approximations and for theoretical developments. The use of hp-versions of the finite element method makes possible exponentially convergent schemes with very high accuracies in certain cases; the use of adaptive hp-schemes allows h-refinement in regions of low regularity and p-enrichment to deliver high accuracy, while keeping problem sizes manageable and dramatically smaller than many conventional approaches. The use of discontinuous Galerkin methods is uncommon in applications, but the methods rest on a reasonable mathematical basis for low-order cases and has local approximation features that can be exploited to produce very efficient schemes, especially in a parallel, multiprocessor environment. The place of this work is to first and primarily focus on a model class of linear hyperbolic conservation laws for which concrete mathematical results, methodologies, error estimates, convergence criteria, and parallel adaptive strategies can be developed, and to then briefly explore some extensions to more general cases. Next, we provide preliminaries to the study and a review of some aspects of the theory of hyperbolic conservation laws. We also provide a review of relevant literature on this subject and on the numerical analysis of these types of problems.

Bey, Kim S.↗

NASA NTRS1980

A new look at numerical analyses of free-edge stresses in composite laminates

The edge stress problem for a + or - 45 deg graphite/epoxy laminate was examined. The reliability of the displacement formulated finite element method in analyzing the edge stress problem was investigated. Analyses of two well known elasticity problems, one involving a stress discontinuity and one a singularity, showed that the finite element analysis yields accurate stress distributions everywhere except in two elements closest to the stress discontinuity of singularity. Stress distributions for a + or - 45 deg laminate showed the same behavior near the singularity found in the well known problems with exact solutions. The displacement formulated finite element method appears to be a highly accurate technique for calculating interlaminar stress in composite laminates. The disagreement among the numerical methods was attributed to the unsymmetric stress tensor at the singularity.

Raju, I. S.↗

DOE OSTI2016

Pn-FEM Method for Solving the First-Order Neutron Transport Equation

A deterministic method was investigated and developed for the photon-neutron transport calculation for fusion reactor blanket. Firstly, considering the fact that the second order transport equation cannot describe void region accurately due to the appearance of zero total cross section in the denominator, the first order equation was selected as the starting point of the solution. The angular discretization uses the spherical harmonics (Pn) method. Although discrete ordinates (Sn) method has been most commonly applied due to its efficiency, it suffers from the ray effect. To describe unstructured geometry, the finite element method was used to discrete spatial variable. It is well known that Bubnov-Galerkin discretization of the first-order equation is inappropriate which will create oscillations. To obtain robust solutions, Petrov- Galerkin methods have been developed such as the Streamline-Upwind Petrov-Galerkin (SUPG) method and the Generalized Least-Squares (GLS) method. These methods require a stabilization term added to its test functions, which will incur additional computational cost. Another finite element formulation that usually used for first order equation is the Discontinuous-Galerkin (DG) method. In this method, each element has a unique and separate set of basis function. Then the adjacent elements can be connected by using the in-coming flux. Its main drawback is the number of unknowns, much larger than Continuous-Galerkin (CG) method. The Sub-Grid Scale (SGS) finite element method combines the advantages of CG and DG methods together. It inserts the DG method in each element to correct the CG solution, and provides numerically stable solution of first-order equation without increasing the number of unknowns. The boundary conditions and interface conditions for Pn method is a hard nut to crack. We use Riemann method to deal with this problem. It decomposes the neutron angular flux into in-coming and out-going information through an interface, and applies boundary condition to the in-coming one. (authors)

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

NASA NTRS1981

Pull-out fibers from composite materials at high rate of loading

Numerical and experimental results are presented on the pullout phenomenon in composite materials at a high rate of loading. The finite element method was used, taking into account the existence of a virtual shear deformation layer as the interface between fiber and matrix. Experimental results agree well with those obtained by the finite element method. Numerical results show that the interlaminar shear stress is time dependent, in addition, it is shown to depend on the applied load time history. Under step pulse loading, the interlaminar shear stress fluctuates, finally decaying to its value under static loading.

Amijima, S.↗