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NASA NTRS1995

Parallelized modelling and solution scheme for hierarchically scaled simulations

This two-part paper presents the results of a benchmarked analytical-numerical investigation into the operational characteristics of a unified parallel processing strategy for implicit fluid mechanics formulations. This hierarchical poly tree (HPT) strategy is based on multilevel substructural decomposition. The Tree morphology is chosen to minimize memory, communications and computational effort. The methodology is general enough to apply to existing finite difference (FD), finite element (FEM), finite volume (FV) or spectral element (SE) based computer programs without an extensive rewrite of code. In addition to finding large reductions in memory, communications, and computational effort associated with a parallel computing environment, substantial reductions are generated in the sequential mode of application. Such improvements grow with increasing problem size. Along with a theoretical development of general 2-D and 3-D HPT, several techniques for expanding the problem size that the current generation of computers are capable of solving, are presented and discussed. Among these techniques are several interpolative reduction methods. It was found that by combining several of these techniques that a relatively small interpolative reduction resulted in substantial performance gains. Several other unique features/benefits are discussed in this paper. Along with Part 1's theoretical development, Part 2 presents a numerical approach to the HPT along with four prototype CFD applications. These demonstrate the potential of the HPT strategy.

Padovan, Joe↗

NASA NTRS2010

Ares I-X Flight Test Vehicle Modal Test

The first test flight of NASA's Ares I crew launch vehicle, called Ares I-X, was launched on October 28, 2009. Ares I-X used a 4-segment reusable solid rocket booster from the Space Shuttle heritage with mass simulators for the 5th segment, upper stage, crew module and launch abort system. Flight test data will provide important information on ascent loads, vehicle control, separation, and first stage reentry dynamics. As part of hardware verification, a series of modal tests were designed to verify the dynamic finite element model (FEM) used in loads assessments and flight control evaluations. Based on flight control system studies, the critical modes were the first three free-free bending mode pairs. Since a test of the free-free vehicle was not practical within project constraints, modal tests for several configurations during vehicle stacking were defined to calibrate the FEM. Test configurations included two partial stacks and the full Ares I-X flight test vehicle on the Mobile Launcher Platform. This report describes the test requirements, constraints, pre-test analysis, test execution and results for the Ares I-X flight test vehicle modal test on the Mobile Launcher Platform. Initial comparisons between pre-test predictions and test data are also presented.

Buehrle, Ralph D.↗

NASA NTRS2010

Ares I-X Launch Vehicle Modal Test Overview

The first test flight of NASA's Ares I crew launch vehicle, called Ares I-X, is scheduled for launch in 2009. Ares IX will use a 4-segment reusable solid rocket booster from the Space Shuttle heritage with mass simulators for the 5th segment, upper stage, crew module and launch abort system. Flight test data will provide important information on ascent loads, vehicle control, separation, and first stage reentry dynamics. As part of hardware verification, a series of modal tests were designed to verify the dynamic finite element model (FEM) used in loads assessments and flight control evaluations. Based on flight control system studies, the critical modes were the first three free-free bending mode pairs. Since a test of the free-free vehicle is not practical within project constraints, modal tests for several configurations in the nominal integration flow were defined to calibrate the FEM. A traceability study by Aerospace Corporation was used to identify the critical modes for the tested configurations. Test configurations included two partial stacks and the full Ares I-X launch vehicle on the Mobile Launcher Platform. This paper provides an overview for companion papers in the Ares I-X Modal Test Session. The requirements flow down, pre-test analysis, constraints and overall test planning are described.

Buehrle, Ralph D.↗

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 NTRS1993

An explicit solution to the optimal LQG problem for flexible structures with collocated rate sensors

We present a class of compensators in explicit form (not requiring numerical computer calculations) for stabilizing flexible structures with collocated rate sensors. They are based on the explicit solution, valid for both Continuum and FEM Models, of the LQG problem for minimizing mean square rate. They are robust with respect to system stability (will not destabilize modes even with mismatch of parameters), can be instrumented in state space form suitable for digital controllers, and can be specified directly from the structure modes and mode 'signature' (displacement vectors at sensor locations). Some simulation results are presented for the NASA LaRC Phase-Zero Evolutionary Model - a modal Trust model with 86 modes - showing damping ratios attainable as a function of compensator design parameters and complexity.

Balakrishnan, A. V.↗

NASA NTRSDate not supplied

Solar Cruiser TRAC Boom Development

The TRAC boom studied is a 30 meter, high-aspect ratio and highly nonlinear structural element planned for the NASA Solar Cruiser spacecraft where it would serve as the solar sail’s skeletal system designed to deploy the packaged reflective sail membrane as well as support operational sail tension loads for flight. Key design drivers for this boom are understanding and characterizing load-deformation behavior and quantifying buckling performance–under flight conditions (zero gravity). Knowing that the full-scale solar sail system cannot be feasibly tested for flight conditions under Earth’s gravity, a building block approach is methodically followed to verify finite element analysis (FEA) predictions and to evolve the finite element model (FEM) accordingly, beginning with the lowest level complexity to match global elastic behavior to the highest level complexity to bound theoretical responses under conservative expected flight conditions. Although the testing campaign for the TRAC boom has not developed yet to produce a full-scale test data point that loads the boom to failure, the fidelity of simulations have evolved with success and warrant further interest and work on this high-aspect ratio, but highly stable, deployable structural boom.

Lee Nguyen↗

NASA NTRS1995

Simulation of thin slot spirals and dual circular patch antennas using the finite element method with mixed elements

This semi-annual report describes progress up to mid-January 1995. The report contains five sections all dealing with the modeling of spiral and patch antennas recessed in metallic platforms. Of significance is the development of decomposition schemes which separate the different regions of the antenna volume. Substantial effort was devoted to improving the feed model in the context of the finite element method (FEM). Finally, an innovative scheme for truncating finite element meshes is presented.

Gong, Jian↗

NASA NTRS2018

Advanced Mirror Technology Development (AMTD) II Modal Test of A 1.5 m Glass Slumped Mirror

The Advanced Mirror Technology Development (AMTD) project is in Phase 2 of a multiyear effort initiated in Fiscal Year 2012 to mature toward the next technology readiness level critical technologies required to enable 4-m-or-larger monolithic or segmented ultraviolet, optical, and infrared (UVOIR) space telescope primary-mirror assemblies for general astrophysics and ultra-high-contrast observations of exoplanets. As part of AMTD II, a free-free modal test was performed of a light weighted slumped 1.5 m mirror made of Corning Ultra Low Expansion (ULE®) material. The test article and support structure were suspended via bungee to simulate a free-free environment. Modes were excited by roaming an instrumented modal test hammer and responses were measured. Predicted and measured frequencies are presented as well as Modal Assurance Criteria (MAC) results to compare the mode shapes. The finite element mirror model used for pre-test predictions and posttest comparisons was provided by the mirror vendor, Harris Corporation. The mirror FEM included deformations of the ribs that were a result of the slumping process. Modal test frequencies matched predictions within the 5% target with the exception of one mode and that pair differed by 5.2%. Of the seven modes measured and predicted, four had MAC values meeting the target of ≥ 0.90, one was just under and two were notably below the target.

Knight, J. Brent↗

NASA NTRS2012

Elastic Model Transitions Using Quadratic Inequality Constrained Least Squares

A technique is presented for initializing multiple discrete finite element model (FEM) mode sets for certain types of flight dynamics formulations that rely on superposition of orthogonal modes for modeling the elastic response. Such approaches are commonly used for modeling launch vehicle dynamics, and challenges arise due to the rapidly time-varying nature of the rigid-body and elastic characteristics. By way of an energy argument, a quadratic inequality constrained least squares (LSQI) algorithm is employed to e ect a smooth transition from one set of FEM eigenvectors to another with no requirement that the models be of similar dimension or that the eigenvectors be correlated in any particular way. The physically unrealistic and controversial method of eigenvector interpolation is completely avoided, and the discrete solution approximates that of the continuously varying system. The real-time computational burden is shown to be negligible due to convenient features of the solution method. Simulation results are presented, and applications to staging and other discontinuous mass changes are discussed

Orr, Jeb S.↗

NASA NTRS1992

ROM/RMF control of the flexible, articulated-truss space crane

The large size and extreme flexibility of an articulated space crane entail great difficulties in precision positioning. Control strategies for the flexible multibody system are here developed using a Timoshenko-beam finite-element model (FEM) which captures the system's low frequency characteristics. From the FEM, a reduced-order model (ROM) controller is designed which rotates the fixed shape crane about the base alpha joint to actuate positioning control. Eigenvalue analysis of the closed-loop system shows the destabilizing effect of controller-structure interaction (CSI). Making use of a parallel bank of residual mode filters (RMFs) compensated for CSI, restoring system stability and performance. The linear control law is simulated in closed-loop with the beam model. The ROM-based control law with RMF compensation is an effective, low-order controller.

Reisenauer, Brian T.↗

NASA NTRSDate not supplied

Error Localization Examples: Looking for a Needle in a Haystack

Finite element models (FEM) are routinely developed and used during fabrication of high dollar-value hardware. NASA, as part of the pre-flight certification of launch vehicles, routinely conducts vibration and static tests to calibrate models used for flight-risk assessments. During model calibration, certain areas of the model are modified, using engineering judgment and sensitivity analysis, to match the test results. Unfortunately, tools to identify problem areas in the FEM using test data directly are scarce and infrequently applied. Over the years, error localization algorithms have been proposed with very limited success. Recently, the Analytical Dynamics Model Improvement (ADMI) algorithm, which computes closed-form mass and stiffness corrections to match the test data exactly, have been shown to be an effective Error Localization Algorithm (ELA). The paper discusses three examples where ELA is used with simulated test data to locate problem areas. To gain confidence in the approach, the exact answer is shown along with ELA results. Results show that ELA is able to identify general problem areas consistent with known problem areas. In all examples, the ELA identified area is larger than the exact problem area. Nonetheless, with proper optimization tools, calibration results using the ELA identified areas provide excellent results.

model calibration↗

NASA NTRS1992

Finite-element solution scheme for compressible viscous flow

Adaptivity offers the possibility of using FEM for problems that are otherwise intractable. The solution algorithm is combined with an adaptive approach in which the unstructured portion of the grid is adaptively regenerated as the solution proceeds; the structured portion of the mesh is modified accordingly, to ensure both compatibility along the interface between the implicit and explicit element groups and increased resolution of the viscous layer. The approach offers significant computational savings in 3D simulations.

Hassan, O.↗

NASA NTRS2010

Resistance Curves in the Tensile and Compressive Longitudinal Failure of Composites

This paper presents a new methodology to measure the crack resistance curves associated with fiber-dominated failure modes in polymer-matrix composites. These crack resistance curves not only characterize the fracture toughness of the material, but are also the basis for the identification of the parameters of the softening laws used in the analytical and numerical simulation of fracture in composite materials. The method proposed is based on the identification of the crack tip location by the use of Digital Image Correlation and the calculation of the J-integral directly from the test data using a simple expression derived for cross-ply composite laminates. It is shown that the results obtained using the proposed methodology yield crack resistance curves similar to those obtained using FEM-based methods in compact tension carbon-epoxy specimens. However, it is also shown that the Digital Image Correlation based technique can be used to extract crack resistance curves in compact compression tests for which FEM-based techniques are inadequate.

Camanho, Pedro P.↗

NASA NTRSDate not supplied

Simulation of Lift plus Cruise Vehicle Models to Define a Full-Scale Crash Test Campaign

A series of dynamic simulations were completed on the National Aeronautics and Space Administration(NASA) Lift plus Cruise (LPC) concept electric Vertical Take-off and Landing (eVTOL) vehicle in preparation for an anticipated future full-scale crash-test campaign. The crash test campaign is envisioned as a data gathering exercise with an intent generating full-scale test data to inform eVTOL crashworthiness regulations, evaluate the use of energy absorbing concepts within vehicle design, and validate finite element modeling techniques used in crashworthiness predictions. This report discusses the two main objectives for the simulation efforts: the development of a structural cabin section, and a series of analyses utilized to determine the sensitivities of impact variables. A structural cabin section was created based from previous research efforts involving the LPC vehicle utilized for occupant response. To refine for the structural modifications, the wing and tail sections of the vehicle were removed. The tail was replaced with a representative mass at the aft of the fuselage. The overhead wing was replaced with a beam structure sized to approximate the bending response of the wing under crash loading conditions. The beam structure was fixed to the fuselage similar to the original Wingbox design in order to properly capture effects of this overhead mass on survivable volume within the vehicle. The fidelity of the fuselage frame structure within the FEM was increased to quantify the effect of frame sizing on structural response. From this an eVTOL test article design was developed, which satisfied basic crashworthiness requirements, was reconfigurable to assess the effect of various design avenues on structural response and optimized to improve manufacturability. The impact variable sensitivity results primarily show the orientation of the impact vector played a major role in types of injuries sustained, along with their severity. The vehicle was largely insensitive to small variations in pitch attitude but highly sensitive to both impact surface at certain angles and landing gear location.

eVTOL↗

NASA NTRS1977

A numerical investigation of the finite element method in compressible primitive variable Navier-Stokes flow

The results of a comprehensive numerical investigation of the basic capabilities of the finite element method (FEM) for numerical solution of compressible flow problems governed by the two-dimensional and axis-symmetric Navier-Stokes equations in primitive variables are presented. The strong and weak points of the method as a tool for computational fluid dynamics are considered. The relation of the linear element finite element method to finite difference methods (FDM) is explored. The calculation of free shear layer and separated flows over aircraft boattail afterbodies with plume simulators indicate the strongest assets of the method are its capabilities for reliable and accurate calculation employing variable grids which readily approximate complex geometry and capably adapt to the presence of diverse regions of large solution gradients without the necessity of domain transformation.

Cook, C. H.↗

NASA NTRS1988

An application of MSC/NASTRAN in the interdisciplinary analysis of large space-based structures

The Integrated Multidisciplinary Analysis Tool (IMAT), a computer software system developed at NASA Langley to analyze and simulate the dynamics of space-structure/control-system interactions, is described, and its application to the MAST problem (a 60-m truss with fundamental frequency less than 200 mHz and equipped with linear proof-mass actuators, to be deployed from the Space Shuttle as part of COFS-I flight experiment) is demonstrated. Particular attention is given to the IMAT procedures which facilitate the use of the MCS/NASTRAN code to recover physical results from time-domain state-space solutions obtained with an FEM control-design code. Diagrams, drawings, and graphs are provided.

Stockwell, Alan E.↗

NASA NTRS2017

Sensitivity Analysis of the Bone Fracture Risk Model

Introduction: The probability of bone fracture during and after spaceflight is quantified to aid in mission planning, to determine required astronaut fitness standards and training requirements and to inform countermeasure research and design. Probability is quantified with a probabilistic modeling approach where distributions of model parameter values, instead of single deterministic values, capture the parameter variability within the astronaut population and fracture predictions are probability distributions with a mean value and an associated uncertainty. Because of this uncertainty, the model in its current state cannot discern an effect of countermeasures on fracture probability, for example between use and non-use of bisphosphonates or between spaceflight exercise performed with the Advanced Resistive Exercise Device (ARED) or on devices prior to installation of ARED on the International Space Station. This is thought to be due to the inability to measure key contributors to bone strength, for example, geometry and volumetric distributions of bone mass, with areal bone mineral density (BMD) measurement techniques. To further the applicability of model, we performed a parameter sensitivity study aimed at identifying those parameter uncertainties that most effect the model forecasts in order to determine what areas of the model needed enhancements for reducing uncertainty. Methods: The bone fracture risk model (BFxRM), originally published in (Nelson et al) is a probabilistic model that can assess the risk of astronaut bone fracture. This is accomplished by utilizing biomechanical models to assess the applied loads; utilizing models of spaceflight BMD loss in at-risk skeletal locations; quantifying bone strength through a relationship between areal BMD and bone failure load; and relating fracture risk index (FRI), the ratio of applied load to bone strength, to fracture probability. There are many factors associated with these calculations including environmental factors, factors associated with the fall event, mass and anthropometric values of the astronaut, BMD characteristics, characteristics of the relationship between BMD and bone strength and bone fracture characteristics. The uncertainty in these factors is captured through the use of parameter distributions and the fracture predictions are probability distributions with a mean value and an associated uncertainty. To determine parameter sensitivity, a correlation coefficient is found between the sample set of each model parameter and the calculated fracture probabilities. Each parameters contribution to the variance is found by squaring the correlation coefficients, dividing by the sum of the squared correlation coefficients, and multiplying by 100. Results: Sensitivity analyses of BFxRM simulations of preflight, 0 days post-flight and 365 days post-flight falls onto the hip revealed a subset of the twelve factors within the model which cause the most variation in the fracture predictions. These factors include the spring constant used in the hip biomechanical model, the midpoint FRI parameter within the equation used to convert FRI to fracture probability and preflight BMD values. Future work: Plans are underway to update the BFxRM by incorporating bone strength information from finite element models (FEM) into the bone strength portion of the BFxRM. Also, FEM bone strength information along with fracture outcome data will be incorporated into the FRI to fracture probability.

mathematical models↗

NASA NTRS2003

Mechanical Testing of PMCs under Simulated Rapid Heat-Up Propulsion Environments: In-Plane Compressive Behavior - II

Carbon fiber thermoset polymer matrix composites (PMC) with high temperature polyimide based in-situ polymerized monomer reactant (PMR) resin has been used for some time in applications which can see temperatures up to 550 F. Currently, graphite fiber PMR based composites are used in several aircraft engine components including the outer bypass duct for the GE F-404, exit flaps for the P&W F-100-229, and the core cowl for the GE/Snecma CF6-80A3. Newer formulations, including PMR-II-50 are being investigated as potential weight reduction replacements of various metallic components in next generation high performance propulsion rocket engines that can see temperatures which exceed 550 F. Extensive FEM thermal modeling indicates that these components are exposed to rapid heat-up rates (up to -200 F/sec) and to a maximum temperature of around 600 F. Even though the predicted maximum part temperatures were within the capability of PW-II-50, the rapid heat-up causes significant through-thickness thermal gradients in the composite part and even more unstable states when combined with moisture. Designing composite parts for such extreme service environments will require accurate measurement of intrinsic and transient mechanical properties and the hygrothermal performance of these materials under more realistic use conditions. The mechanical properties of polymers degrade when exposed to elevated temperatures even in the absence of gaseous oxygen. Accurate mechanical characterization of the material is necessary in order to reduce system weight while providing sufficient factors of safety. Historically, the testing of PMCs at elevated temperatures has been plagued by the antagonism between two factors. First, moisture has been shown to profoundly affect the mechanical response of these materials at temperatures above their glass transition temperature while concurrently lowering the material's Tg. Moisture phenomena is due to one or a combination of three effects, i.e., plastization of polymeric material by water, the internal pressure generated by the volatilization of water at elevated temperatures, and hydrolytic chemical decomposition. However, moisture is lost from the material at increasing rates as temperature increases. Second, because PMCs are good thermal insulators, when they are externally heated at even mild rates large thermal gradients can develop within the material. At temperatures where a material property changes rapidly with temperature the presence of a large thermal gradient is unacceptable for intrinsic property characterization purposes. Therefore, long hold times are required to establish isothermal conditions. However, in the service environments high-heating-rates, high temperatures, high-loading rates are simultaneous present along with residual moisture. In order to capture the effects of moisture on the material, holding at- temperature until isothermal conditions are reached is unacceptable particularly in materials with small physical dimensions. Thus, the effects due to moisture on the composite's mechanical characteristics, ie., their so-called analog response, may be instructive. One approach employed in this program was rapid heat-up (approx. 200 F/sec.) and loading of both dry and wet in-plane compressive specimens to examine the effects of moisture on this resin dominated mechanical property of the material.

Stokes, Eric H.↗