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NASA NTRS1995

Simulation of patch and slot antennas using FEM with prismatic elements and investigations of artificial absorber mesh termination schemes

Year 1 progress can be characterized with four major achievements which are crucial toward the development of robust, easy to use antenna analysis code on doubly conformal platforms. (1) A new FEM code was developed using prismatic meshes. This code is based on a new edge based distorted prism and is particularly attractive for growing meshes associated with printed slot and patch antennas on doubly conformal platforms. It is anticipated that this technology will lead to interactive, simple to use codes for a large class of antenna geometries. Moreover, the codes can be expanded to include modeling of the circuit characteristics. An attached report describes the theory and validation of the new prismatic code using reference calculations and measured data collected at the NASA Langley facilities. The agreement between the measured and calculated data is impressive even for the coated patch configuration. (2) A scheme was developed for improved feed modeling in the context of FEM. A new approach based on the voltage continuity condition was devised and successfully tested in modeling coax cables and aperture fed antennas. An important aspect of this new feed modeling approach is the ability to completely separate the feed and antenna mesh regions. In this manner, different elements can be used in each of the regions leading to substantially improved accuracy and meshing simplicity. (3) A most important development this year has been the introduction of the perfectly matched interface (PMI) layer for truncating finite element meshes. So far the robust boundary integral method has been used for truncating the finite element meshes. However, this approach is not suitable for antennas on nonplanar platforms. The PMI layer is a lossy anisotropic absorber with zero reflection at its interface. (4) We were able to interface our antenna code FEMA_CYL (for antennas on cylindrical platforms) with a standard high frequency code. This interface was achieved by first generating equivalent magnetic currents across the antenna aperture using the FEM code. These currents were employed as the sources in the high frequency code.

Gong, J.↗

NASA NTRS2008

A Novel Multiscale Physics Based Progressive Failure Methodology for Laminated Composite Structures

A variable fidelity, multiscale, physics based finite element procedure for predicting progressive damage and failure of laminated continuous fiber reinforced composites is introduced. At every integration point in a finite element model, progressive damage is accounted for at the lamina-level using thermodynamically based Schapery Theory. Separate failure criteria are applied at either the global-scale or the microscale in two different FEM models. A micromechanics model, the Generalized Method of Cells, is used to evaluate failure criteria at the micro-level. The stress-strain behavior and observed failure mechanisms are compared with experimental results for both models.

Pineda, Evan J.↗

NASA NTRS2007

Build-Up Approach to Updating the Mock Quiet Spike Beam Model

When a new aircraft is designed or a modification is done to an existing aircraft, the aeroelastic properties of the aircraft should be examined to ensure the aircraft is flight worthy. Evaluating the aeroelastic properties of a new or modified aircraft can include performing a variety of analyses, such as modal and flutter analyses. In order to produce accurate results from these analyses, it is imperative to work with finite element models (FEM) that have been validated by or correlated to ground vibration test (GVT) data, Updating an analytical model using measured data is a challenge in the area of structural dynamics. The analytical model update process encompasses a series of optimizations that match analytical frequencies and mode shapes to the measured modal characteristics of structure. In the past, the method used to update a model to test data was "trial and error." This is an inefficient method - running a modal analysis, comparing the analytical results to the GVT data, manually modifying one or more structural parameters (mass, CG, inertia, area, etc.), rerunning the analysis, and comparing the new analytical modal characteristics to the GVT modal data. If the match is close enough (close enough defined by analyst's updating requirements), then the updating process is completed. If the match does not meet updating-requirements, then the parameters are changed again and the process is repeated. Clearly, this manual optimization process is highly inefficient for large FEM's and/or a large number of structural parameters. NASA Dryden Flight Research Center (DFRC) has developed, in-house, a Mode Matching Code that automates the above-mentioned optimization process, DFRC's in-house Mode Matching Code reads mode shapes and frequencies acquired from GVT to create the target model. It also reads the current analytical model, as we11 as the design variables and their upper and lower limits. It performs a modal analysis on this model and modifies it to create an updated model that has similar mode shapes and frequencies as those of the target model. The Mode Matching Code output frequencies and modal assurance criteria (MAC) values that allow for the quantified comparison of the updated model versus the target model. A recent application of this code is the F453 supersonic flight testing platform, NASA DFRC possesses a modified F-15B that is used as a test bed aircraft for supersonic flight experiments. Traditionally, the finite element model of the test article is generated. A GVT is done on the test article ta validate and update its FEM. This FEM is then mated to the F-15B model, which was correlated to GVT data in fall of 2004, A GVT is conducted with the test article mated to the aircraft, and this mated F-15B/ test article FEM is correlated to this final GVT.

Herrera, Claudia Y.↗

NASA NTRS1992

DAMVIBS looks at rotorcraft vibration

A review is presented of the NASA program of design analysis methods for vibrations (DAMVIBS) whose objective was to establish the technology base needed for developing an advanced FEM-based dynamics design capability for vibrations. New experimental/analytical studies have been performed to identify an airframe's components that require better representation in the finite element model for improved correlation with test results.

Kvaternik, Raymond G.↗

NASA NTRS2001

Response of the Alliance 1 Proof-of-Concept Airplane Under Gust Loads

This report presents the work performed by Lockheed Martin's Langley Program Office in support of NASA's Environmental Research Aircraft and Sensor Technology (ERAST) program. The primary purpose of this work was to develop and demonstrate a gust analysis method which accounts for the span-wise variation of gust velocity. This is important because these unmanned aircraft having high aspect ratios and low wing loading are very flexible, and fly at low speeds. The main focus of the work was therefore to perform a two-dimensional Power Spectrum Density (PSD) analysis of the Alliance 1 Proof-of-Concept Unmanned Aircraft, As of this writing, none of the aircraft described in this report have been constructed. They are concepts represented by analytical models. The process first involved the development of suitable structural and aeroelastic Finite Element Models (FEM). This was followed by development of a one-dimensional PSD gust analysis, and then the two-dimensional (PSD) analysis of the Alliance 1. For further validation and comparison, two additional analyses were performed. A two-dimensional PSD gust analysis was performed on a simplet MSC/NASTRAN example problem. Finally a one-dimensional discrete gust analysis was performed on Alliance 1. This report describes this process, shows the relevant comparisons between analytical methods, and discusses the physical meanings of the results.

Naser, A. S.↗

NASA NTRS1993

Mutual Inductance Problem for a System Consisting of a Current Sheet and a Thin Metal Plate

Rapid inspection of aircraft structures for flaws is of vital importance to the commercial and defense aircraft industry. In particular, inspecting thin aluminum structures for flaws is the focus of a large scale R&D effort in the nondestructive evaluation (NDE) community. Traditional eddy current methods used today are effective, but require long inspection times. New electromagnetic techniques which monitor the normal component of the magnetic field above a sample due to a sheet of current as the excitation, seem to be promising. This paper is an attempt to understand and analyze the magnetic field distribution due to a current sheet above an aluminum test sample. A simple theoretical model, coupled with a two dimensional finite element model (FEM) and experimental data will be presented in the next few sections. A current sheet above a conducting sample generates eddy currents in the material, while a sensor above the current sheet or in between the two plates monitors the normal component of the magnetic field. A rivet or a surface flaw near a rivet in an aircraft aluminum skin will disturb the magnetic field, which is imaged by the sensor. Initial results showed a strong dependence of the flaw induced normal magnetic field strength on the thickness and conductivity of the current-sheet that could not be accounted for by skin depth attenuation alone. It was believed that the eddy current imaging method explained the dependence of the thickness and conductivity of the flaw induced normal magnetic field. Further investigation, suggested the complexity associated with the mutual inductance of the system needed to be studied. The next section gives an analytical model to better understand the phenomenon.

Fulton, J. P.↗

NASA NTRS1986

Application of physical parameter identification to finite element models

A time domain technique for matching response predictions of a structural dynamic model to test measurements is developed. Significance is attached to prior estimates of physical model parameters and to experimental data. The Bayesian estimation procedure allows confidence levels in predicted physical and modal parameters to be obtained. Structural optimization procedures are employed to minimize an error functional with physical model parameters describing the finite element model as design variables. The number of complete FEM analyses are reduced using approximation concepts, including the recently developed convoluted Taylor series approach. The error function is represented in closed form by converting free decay test data to a time series model using Prony' method. The technique is demonstrated on simulated response of a simple truss structure.

Bronowicki, Allen J.↗

NASA NTRS2019

Improving Accuracy of Structural Dynamic Modification with Augmented Residual Vectors

It is often important to perform sensitivity analysis to determine how a structural model will be impacted by design changes. Often, the structural analysts will manually make changes to the finite element model (FEM) to determine the effects. But when dealing with a large FEM with millions of degrees of freedom these manual changes can be cumbersome and calculation of the effects can computationally expensive. Therefore, it is desirable to determine the effects of model changes through approximation methods. One common technique is to determine the analytical sensitivity of the FEM model with respect to the given change. These analytical sensitivities are valid when small changes are made to the structural model, but invalid if large changes need to be assessed. Another approach is to use Structural Dynamic Modification (SDM) to create a surrogate model to analyze model changes. SDM is a widely-used sensitivity method and is used in applications of model updating, uncertainty quantification, and model design studies. SMD is valid for moderate (10-20 percent) changes in the structural model, but model approximations are often needed for large parameter changes (greater than 20 percent). Structural Dynamic Modification can be improved by using residual vectors to augment the surrogate model formulation from SDM. Adding the residual modes increases the fidelity of the surrogate model while keeping the computational cost low. This paper discusses the application and limitations of the augmented residual modes method to two structures: the Integrated Spacecraft and Payload Element (ISPE) of the Space Launch System (SLS) and the full SLS as it is configured during its Integrated Modal Test (IMT).

Stewart, Eric C.↗

NASA NTRS1989

Coupled rotor/fuselage dynamic analysis of the AH-1G helicopter and correlation with flight vibrations data

Under a research program designated Design Analysis Methods for VIBrationS (DAMVIBS), existing analytical methods are used for calculating coupled rotor-fuselage vibrations of the AH-1G helicopter for correlation with flight test data from an AH-1G Operational Load Survey (OLS) test program. The analytical representation of the fuselage structure is based on a NASTRAN finite element model (FEM), which has been developed, extensively documented, and correlated with ground vibration test. One procedure that was used for predicting coupled rotor-fuselage vibrations using the advanced Rotorcraft Flight Simulation Program C81 and NASTRAN is summarized. Detailed descriptions of the analytical formulation of rotor dynamics equations, fuselage dynamic equations, coupling between the rotor and fuselage, and solutions to the total system of equations in C81 are included. Analytical predictions of hub shears for main rotor harmonics 2p, 4p, and 6p generated by C81 are used in conjunction with 2p OLS measured control loads and a 2p lateral tail rotor gearbox force, representing downwash impingement on the vertical fin, to excite the NASTRAN model. NASTRAN is then used to correlate with measured OLS flight test vibrations. Blade load comparisons predicted by C81 showed good agreement. In general, the fuselage vibration correlations show good agreement between anslysis and test in vibration response through 15 to 20 Hz.

Corrigan, J. C.↗

NASA NTRS1999

Practical Aspects of Stabilized FEM Discretizations of Nonlinear Conservation Law Systems with Convex Extension

This talk considers simplified finite element discretization techniques for first-order systems of conservation laws equipped with a convex (entropy) extension. Using newly developed techniques in entropy symmetrization theory, simplified forms of the Galerkin least-squares (GLS) and the discontinuous Galerkin (DG) finite element method have been developed and analyzed. The use of symmetrization variables yields numerical schemes which inherit global entropy stability properties of the POE system. Central to the development of the simplified GLS and DG methods is the Degenerative Scaling Theorem which characterizes right symmetrizes of an arbitrary first-order hyperbolic system in terms of scaled eigenvectors of the corresponding flux Jacobean matrices. A constructive proof is provided for the Eigenvalue Scaling Theorem with detailed consideration given to the Euler, Navier-Stokes, and magnetohydrodynamic (MHD) equations. Linear and nonlinear energy stability is proven for the simplified GLS and DG methods. Spatial convergence properties of the simplified GLS and DO methods are numerical evaluated via the computation of Ringleb flow on a sequence of successively refined triangulations. Finally, we consider a posteriori error estimates for the GLS and DG demoralization assuming error functionals related to the integrated lift and drag of a body. Sample calculations in 20 are shown to validate the theory and implementation.

Barth, Timothy↗

NASA NTRS1986

Summary of AH-1G flight vibration data for validation of coupled rotor-fuselage analyses

Under a NASA research program designated DAMVIBS (Design Analysis Methods for VIBrationS), four U. S. helicopter industry participants (Bell Helicopter, Boeing Vertol, McDonnell Douglas Helicopter, and Sikorsky Aircraft) are to apply existing analytical methods for calculating coupled rotor-fuselage vibrations of the AH-1G helicopter for correlation with flight test data from an AH-1G Operational Load Survey (OLS) test program. Bell Helicopter, as the manufacturer of the AH-1G, was asked to provide pertinent rotor data and to collect the OLS flight vibration data needed to perform the correlations. The analytical representation of the fuselage structure is based on a NASTRAN finite element model (FEM) developed by Bell which has been extensively documented and correlated with ground vibration tests.The AH-1G FEM was provided to each of the participants for use in their coupled rotor-fuselage analyses. This report describes the AH-1G OLS flight test program and provides the flight conditions and measured vibration data to be used by each participant in their correlation effort. In addition, the mechanical, structural, inertial and aerodynamic data for the AH-1G two-bladed teetering main rotor system are presented. Furthermore, modifications to the NASTRAN FEM of the fuselage structure that are necessary to make it compatible with the OLS test article are described. The AH-1G OLS flight test data was found to be well documented and provide a sound basis for evaluating currently existing analysis methods used for calculation of coupled rotor-fuselage vibrations.

Dompka, R. V.↗

NASA NTRSDate not supplied

Structural Sizing of a Transonic Truss-Braced Wing

Accurate finite element modeling (FEM) is a vital part of the modern aircraft design process. As aircraft become increasingly complex, the time-consuming nature of detailed FEM approaches comes at a significant cost to program timeline and budget. In an effort produce modeling efforts that are sufficiently accurate and minimally costly, a proposed FEM approach and optimization scheme for a composite aircraft is explored, including a discussion of the manufacturing constraints of a highly tailored composite panel design. A high-fidelity structural model of a transonic truss-braced wing (TTBW) is generated, and the components are sized by structural optimization to satisfy buckling and strength constraints while subjected to critical maneuver loads. The structural modeling approaches and sizing of a TTBW are discussed, including details for FEM approaches, verification of an approximated FEM approach, a sizing optimization using the optimization software LS-OPT, and a manufacturing trial of integrally stiffened composite panels conducted to explore the validity of highly tailored composites as a design consideration. The results of study discussed herein indicate that the proposed FEM approach is suitable for modeling composite-construction aircraft and for use in sizing optimization. Further efforts regarding integrally stiffened composite panels will indicate the suitability of this method for the integration of highly tailored composite panels into the design and optimization process, given the manufacturability of such panels as shown here.

Finite Element↗

NASA NTRSDate not supplied

Structural Sizing of a Composite Transonic Truss-Braced Wing

Finite Element↗

NASA NTRS2003

Methods Developed by the Tools for Engine Diagnostics Task to Monitor and Predict Rotor Damage in Real Time

Tools for Engine Diagnostics is a major task in the Propulsion System Health Management area of the Single Aircraft Accident Prevention project under NASA s Aviation Safety Program. The major goal of the Aviation Safety Program is to reduce fatal aircraft accidents by 80 percent within 10 years and by 90 percent within 25 years. The goal of the Propulsion System Health Management area is to eliminate propulsion system malfunctions as a primary or contributing factor to the cause of aircraft accidents. The purpose of Tools for Engine Diagnostics, a 2-yr-old task, is to establish and improve tools for engine diagnostics and prognostics that measure the deformation and damage of rotating engine components at the ground level and that perform intermittent or continuous monitoring on the engine wing. In this work, nondestructive-evaluation- (NDE-) based technology is combined with model-dependent disk spin experimental simulation systems, like finite element modeling (FEM) and modal norms, to monitor and predict rotor damage in real time. Fracture mechanics time-dependent fatigue crack growth and damage-mechanics-based life estimation are being developed, and their potential use investigated. In addition, wireless eddy current and advanced acoustics are being developed for on-wing and just-in-time NDE engine inspection to provide deeper access and higher sensitivity to extend on-wing capabilities and improve inspection readiness. In the long run, these methods could establish a base for prognostic sensing while an engine is running, without any overt actions, like inspections. This damage-detection strategy includes experimentally acquired vibration-, eddy-current- and capacitance-based displacement measurements and analytically computed FEM-, modal norms-, and conventional rotordynamics-based models of well-defined damages and critical mass imbalances in rotating disks and rotors.

Baaklini, George Y.↗

NASA NTRS1992

Finite element computation of incompressible flows

Among the solution techniques presented for FEM computation of incompressible flows are stabilized formulations designed to prevent the numerical oscillations that may be generated by (1) the presence of dominant advection terms in the governing equations, or (2) the failure to use an acceptable combination of interpolation functions to represent velocity and pressure fields. It is shown that the space-time formulation, in conjunction with the Galerkin-least squares methods, can be used to compute steady incompressible flows involving moving boundaries and interfaces; it is recommended that iteration methods be used to reduce the associated computational costs.

Tezduyar, T. E.↗

NASA NTRS1995

A verification procedure for MSC/NASTRAN Finite Element Models

Finite Element Models (FEM's) are used in the design and analysis of aircraft to mathematically describe the airframe structure for such diverse tasks as flutter analysis and actively controlled landing gear design. FEM's are used to model the entire airplane as well as airframe components. The purpose of this document is to describe recommended methods for verifying the quality of the FEM's and to specify a step-by-step procedure for implementing the methods.

Stockwell, Alan E.↗

NASA NTRS2014

Elastic Model Transitions: a Hybrid Approach Utilizing Quadratic Inequality Constrained Least Squares (LSQI) and Direct Shape Mapping (DSM)

A method for transitioning linear time invariant (LTI) models in time varying simulation is proposed that utilizes both quadratically constrained least squares (LSQI) and Direct Shape Mapping (DSM) algorithms to determine physical displacements. This approach is applicable to the simulation of the elastic behavior of launch vehicles and other structures that utilize multiple LTI finite element model (FEM) derived mode sets that are propagated throughout time. The time invariant nature of the elastic data for discrete segments of the launch vehicle trajectory presents a problem of how to properly transition between models while preserving motion across the transition. In addition, energy may vary between flex models when using a truncated mode set. The LSQI-DSM algorithm can accommodate significant changes in energy between FEM models and carries elastic motion across FEM model transitions. Compared with previous approaches, the LSQI-DSM algorithm shows improvements ranging from a significant reduction to a complete removal of transients across FEM model transitions as well as maintaining elastic motion from the prior state.

Jurenko, Robert J.↗

NASA NTRS2014

Elastic Model Transitions: A Hybrid Approach Utilizing Quadratic Inequality Constrained Least Squares (LSQI) and Direct Shape Mapping (DSM)

A method for transitioning linear time invariant (LTI) models in time varying simulation is proposed that utilizes a hybrid approach for determining physical displacements by augmenting the original quadratically constrained least squares (LSQI) algorithm with Direct Shape Mapping (DSM) and modifying the energy constraints. The approach presented is applicable to simulation of the elastic behavior of launch vehicles and other structures that utilize discrete LTI finite element model (FEM) derived mode sets (eigenvalues and eigenvectors) that are propagated throughout time. The time invariant nature of the elastic data presents a problem of how to properly transition elastic states from the prior to the new model while preserving motion across the transition and ensuring there is no truncation or excitation of the system. A previous approach utilizes a LSQI algorithm with an energy constraint to effect smooth transitions between eigenvector sets with no requirement that the models be of similar dimension or have any correlation. This approach assumes energy is conserved across the transition, which results in significant non-physical transients due to changing quasi-steady state energy between mode sets, a phenomenon seen when utilizing a truncated mode set. The computational burden of simulating a full mode set is significant so a subset of modes is often selected to reduce run time. As a result of this truncation, energy between mode sets may not be constant and solutions across transitions could produce non-physical transients. In an effort to abate these transients an improved methodology was developed based on the aforementioned approach, but this new approach can handle significant changes in energy across mode set transitions. It is proposed that physical velocities due to elastic behavior be solved for using the LSQI algorithm, but solve for displacements using a two-step process that independently addresses the quasi-steady-state and non-steady-state contributions to the elastic displacement. For structures subject to large external forces, such as thrust or atmospheric drag, it is imperative to capture these forces when solving for elastic displacement. To simplify the mathematical formulation, assumptions are made regarding mass matrix normalization, constant external forcing, and constant viscous damping. These simplifications allow for direct solutions to the quasi-steady-state displacements through a process titled Direct Shape Mapping. DSM solves for the displacements using the eigenvalues of the elastic modes and the external forcing and returns a set of elastic displacements dictated by the eigenvectors of the post-transition mode set. For the non-steady-state contributions to displacement we formulate a LSQI problem that is constrained by energy of the non-steady state terms. The contributions from the quasi-steady-state and non-steady state solutions are then combined to obtain the physical displacements associated with the new set of eigenvectors. Results for the LSQI-DSM approach show significant reduction/complete removal of transients across mode set transitions while maintaining elastic motion from the prior state. For time propagation applications employing discrete elastic models that need to be transitioned in time and where running with full a full mode set is not feasible, the method developed offers a practical solution to simulating vehicle elasticity.

Hannan, Mike R.↗