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NASA NTRS1989

The simulation of 2D compressible viscous high speed flow by the finite element method

Am implicit/explicit procedure for the solution of problems of two-dimensional steady compressible viscous high-speed flows is presented. In the vicinity of solid walls, a grid which need only exhibit structure in the normal direction is employed while, away from this region, the grid is totally unstructured. The implicit form of the algorithm is used near solid walls, with the grid structure being utilized in an equation solution approach, based upon line relaxation. The explicit form of the algorithm is used elsewhere. Grid adaptation is achieved by means of adaptive remeshing. To illustrate the performance of the proposed method, problems of shock-boundary layer interaction and flow over a simulated forebody at high Mach number are included.

Hassan, O.↗

NASA NTRS1982

Solution of axisymmetric fluid structure interaction problems with NASTRAN

The solution of axisymmetric acoustic fluid structure interaction problems, employing the NASTRAN computer program is presented. A previously developed 3-D Cartesian Coordinates pressure element formulation is adapted especially for axisymmetric elements. Analogous to the 3-D Cartesian Coordinate predecessor, the fluid portion of the problem is modeled with finite elements wherein one of the displacement components serves as a dummy variable for the pressure unknowns. Two alternatives for implementation of the analogy are presented: (1) an approximate method by which dummy values of G, and nu are used to approximately invoke the analogy wherein the accuracy of the approximation is made as close as desired to the proper analogy within an arbitrary small parameter epsiton; (2) an exact method whereby the NASTRAN FORTRAN coding is slightly changed to invoke the analogy exactly. Comparison of the finite element solution to the exact solution to the same problem is given.

Kalinowski, A. J.↗

DOE OSTI2014

TH-A-BRF-08: Deformable Registration of MRI and CT Images for MRI-Guided Radiation Therapy

Purpose: To evaluate the quality of a commercially available MRI-CT image registration algorithm and then develop a method to improve the performance of this algorithm for MRI-guided prostate radiotherapy. Methods: Prostate contours were delineated on ten pairs of MRI and CT images using Eclipse. Each pair of MRI and CT images was registered with an intensity-based B-spline algorithm implemented in Velocity. A rectangular prism that contains the prostate volume was partitioned into a tetrahedral mesh which was aligned to the CT image. A finite element method (FEM) was developed on the mesh with the boundary constraints assigned from the Velocity generated displacement vector field (DVF). The resultant FEM displacements were used to adjust the Velocity DVF within the prism. Point correspondences between the CT and MR images identified within the prism could be used as additional boundary constraints to enforce the model deformation. The FEM deformation field is smooth in the interior of the prism, and equal to the Velocity displacements at the boundary of the prism. To evaluate the Velocity and FEM registration results, three criteria were used: prostate volume conservation and center consistence under contour mapping, and unbalanced energy of their deformation maps. Results: With the DVFs generated by the Velocity and FEM simulations, the prostate contours were warped from MRI to CT images. With the Velocity DVFs, the prostate volumes changed 10.2% on average, in contrast to 1.8% induced by the FEM DVFs. The average of the center deviations was 0.36 and 0.27 cm, and the unbalance energy was 2.65 and 0.38 mJ/cc3 for the Velocity and FEM registrations, respectively. Conclusion: The adaptive FEM method developed can be used to reduce the error of the MIbased registration algorithm implemented in Velocity in the prostate region, and consequently may help improve the quality of MRI-guided radiation therapy.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2024

Advanced multimaterial shape optimization methods as applied to advanced manufacturing of wind turbine generators

Abstract Currently, many utility‐scale wind turbine generator original equipment manufacturers are dependent on imported rare earth permanent magnets, which are susceptible to market risks from cost instability. To lower the production costs of these generators and stay competitive in the market, several small wind manufacturers are pursuing continuous improvements to both generator design and manufacturing. However, traditional design and manufacturing methods have yielded marginal improvements in wind power performance. This work presents novel methods to redesign a baseline 15‐kW wind turbine generator with reduced rare‐earth permanent magnets by leveraging cutting‐edge three‐dimensional (3D) printed polymer‐bonded permanent magnets and steel. Symmetric, asymmetric, and multimaterial‐magnet parametrization methods are introduced for shape optimization. We extend the symmetric and asymmetric methods to the back iron in the stator to further investigate the impact and opportunities for performance improvements with lesser active materials. We employ a design‐of‐experiments approach with parametric computer‐aided design for shape generation and evaluate different designs by magneto‐thermal modeling and finite‐element analysis. We use adaptive sampling technique to identify better performing designs with lesser magnet mass, higher efficiency, and lower cogging torque when compared with the baseline generator. Asymmetric pole designs resulted in a magnet mass in the range of 4.77–5.37 kg, which was 27%–35% lighter than the baseline generator, suggesting that a new design freedom exists that can be enabled by advanced manufacturing, such as 3D printing. Shaping the back iron in the stator resulted in material savings in electrical steel of up to 14.62 kg, which was 20% lighter than the baseline stator. We conducted a structural analysis to evaluate an optimized asymmetric rotor design from the point of view of mechanical integrity and air‐gap stiffness. The magnetically optimal shape profile was shown as having a positive impact on the radial stiffness, and an optimal solution was discovered to reduce the structural mass by nearly 30 kg, which was 29% lighter than the baseline.

17 WIND ENERGY↗

NASA NTRS1996

Active Control of Fan Noise: Feasibility Study: Numerical Computation of Acoustic Mode Reflection Coefficients for an Unflanged Cylindrical Duct - Volume 5

A computational method to predict modal reflection coefficients in cylindrical ducts has been developed based on the work of Homicz, Lordi, and Rehm, which uses the Wiener-Hopf method to account for the boundary conditions at the termination of a thin cylindrical pipe. The purpose of this study is to develop a computational routine to predict the reflection coefficients of higher order acoustic modes impinging on the unflanged termination of a cylindrical duct. This effort was conducted wider Task Order 5 of the NASA Lewis LET Program, Active Noise Control of aircraft Engines: Feasibility Study, and will be used as part of the development of an integrated source noise, acoustic propagation, ANC actuator coupling, and control system algorithm simulation. The reflection coefficient prediction will be incorporated into an existing cylindrical duct modal analysis to account for the reflection of modes from the duct termination. This will provide a more accurate, rapid computation design tool for evaluating the effect of reflected waves on active noise control systems mounted in the duct, as well as providing a tool for the design of acoustic treatment in inlet ducts. As an active noise control system design tool, the method can be used preliminary to more accurate but more numerically intensive acoustic propagation models such as finite element methods. The resulting computer program has been shown to give reasonable results, some examples of which are presented. Reliable data to use for comparison is scarce, so complete checkout is difficult, and further checkout is needed over a wider range of system parameters. In future efforts the method will be adapted as a subroutine to the GEAE segmented cylindrical duct modal analysis program.

Kraft, R. E.↗

NASA NTRS1993

Analytical and experimental investigation of flutter suppression by piezoelectric actuation

The objective of this research was to analytically and experimentally study the capabilities of piezoelectric plate actuators for suppressing flutter. Piezoelectric materials are characterized by their ability to produce voltage when subjected to a mechanical strain. The converse piezoelectric effect can be utilized to actuate a structure by applying a voltage. For this investigation, a two-degree-of-freedom wind tunnel model was designed, analyzed, and tested. The model consisted of a rigid wing and a flexible mount system that permitted a translational and a rotational degree of freedom. The model was designed such that flutter was encountered within the testing envelope of the wind tunnel. Actuators made of piezoelectric material were affixed to leaf springs of the mount system. Command signals, applied to the piezoelectric actuators, exerted control over the damping and stiffness properties. A mathematical aeroservoelastic model was constructed by using finite element methods, laminated plate theory, and aeroelastic analysis tools. Plant characteristics were determined from this model and verified by open loop experimental tests. A flutter suppression control law was designed and implemented on a digital control computer. Closed loop flutter testing was conducted. The experimental results represent the first time that adaptive materials have been used to actively suppress flutter. They demonstrate that small, carefully placed actuating plates can be used effectively to control aeroelastic response.

Heeg, Jennifer↗

DOE OSTI2014

SU-D-BRF-06: A Brachytherapy Simulator with Realistic Haptic Force Feedback and Real-Time Ultrasounds Image Simulation for Training and Teaching

Purpose: Surgical procedures require dexterity, expertise and repetition to reach optimal patient outcomes. However, efficient training opportunities are usually limited. This work presents a simulator system with realistic haptic force-feedback and full, real-time ultrasounds image simulation. Methods: The simulator is composed of a custom-made Linear-DELTA force-feedback robotic platform. The needle tip is mounted on a force gauge at the end effector of the robot, which responds to needle insertion by providing reaction forces. 3D geometry of the tissue is using a tetrahedral finite element mesh (FEM) mimicking tissue properties. As the needle is inserted/retracted, tissue deformation is computed using a mass-tensor nonlinear visco-elastic FEM. The real-time deformation is fed to the L-DELTA to take into account the force imparted to the needle, providing feedback to the end-user when crossing tissue boundaries or needle bending. Real-time 2D US image is also generated synchronously showing anatomy, needle insertion and tissue deformation. The simulator is running on an Intel I7 6- core CPU at 3.26 MHz. 3D tissue rendering and ultrasound display are performed on a Windows 7 computer; the FEM computation and L-DELTA control are executed on a similar PC using the Neutrino real-time OS. Both machines communicate through an Ethernet link. Results: The system runs at 500 Hz for a 8333-tetrahedron tissue mesh and a 100-node angular spring needle model. This frame rate ensures a relatively smooth displacement of the needle when pushed or retracted (±20 N in all directions at speeds of up to 2 m/s). Unlike commercially-available haptic platforms, the oblong workspace of the L-DELTA robot complies with that required for brachytherapy needle displacements of 0.1m by 0.1m by 0.25m. Conclusion: We have demonstrated a real-life, realistic brachytherapy simulator developed for prostate implants (LDR/HDR). The platform could be adapted to other sites or training for other types of needle-based procedures.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

NASA NTRS1991

Single-strain-gage force/stiffness buckling prediction techniques on a hat-stiffened panel

Predicting the buckling characteristics of a test panel is necessary to ensure panel integrity during a test program. A single-strain-gage buckling prediction method was developed on a hat-stiffened, monolithic titanium buckling panel. The method is an adaptation of the original force/stiffness method which requires back-to-back gages. The single-gage method was developed because the test panel did not have back-to-back gages. The method was used to predict buckling loads and temperatures under various heating and loading conditions. The results correlated well with a finite element buckling analysis. The single-gage force/stiffness method was a valid real-time and post-test buckling prediction technique.

Hudson, Larry D.↗

DOE OSTI2023

Linearization errors in discrete goal-oriented error estimation

This paper is concerned with goal-oriented a posteriori error estimation for nonlinear functionals in the context of nonlinear variational problems solved with continuous Galerkin finite element discretizations. A two-level, or discrete, adjoint-based approach for error estimation is considered. The traditional method to derive an error estimate in this context requires linearizing both the nonlinear variational form and the nonlinear functional of interest which introduces linearization errors into the error estimate. In this paper, we investigate these linearization errors. In particular, we develop a novel discrete goal-oriented error estimate that accounts for traditionally neglected nonlinear terms at the expense of greater computational cost. We demonstrate how this error estimate can be used to drive mesh adaptivity. Here, we show that accounting for linearization errors in the error estimate can improve its effectivity for several nonlinear model problems and quantities of interest. We also demonstrate that an adaptive strategy based on the newly proposed estimate can lead to more accurate approximations of the nonlinear functional with fewer degrees of freedom when compared to uniform refinement and traditional adjoint-based approaches.

42 ENGINEERING↗

DOE OSTI2016

Partition of unity finite element method for quantum mechanical materials calculations

The current state of the art for large-scale quantum-mechanical simulations is the planewave (PW) pseudopotential method, as implemented in codes such as VASP, ABINIT, and many others. However, since the PW method uses a global Fourier basis, with strictly uniform resolution at all points in space, it suffers from substantial inefficiencies in calculations involving atoms with localized states, such as first-row and transition-metal atoms, and requires significant nonlocal communications, which limit parallel efficiency. Real-space methods such as finite-differences (FD) and finite-elements (FE) have partially addressed both resolution and parallel-communications issues but have been plagued by one key disadvantage relative to PW: excessive number of degrees of freedom (basis functions) needed to achieve the required accuracies. In this paper, we present a real-space partition of unity finite element (PUFE) method to solve the Kohn–Sham equations of density functional theory. In the PUFE method, we build the known atomic physics into the solution process using partition-of-unity enrichment techniques in finite element analysis. The method developed herein is completely general, applicable to metals and insulators alike, and particularly efficient for deep, localized potentials, as occur in calculations at extreme conditions of pressure and temperature. Full self-consistent Kohn–Sham calculations are presented for LiH, involving light atoms, and CeAl, involving heavy atoms with large numbers of atomic-orbital enrichments. We find that the new PUFE approach attains the required accuracies with substantially fewer degrees of freedom, typically by an order of magnitude or more, than the PW method. As a result, we compute the equation of state of LiH and show that the computed lattice constant and bulk modulus are in excellent agreement with reference PW results, while requiring an order of magnitude fewer degrees of freedom to obtain.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

NASA NTRS1988

Vibration and Control of Flexible Rotor Supported by Magnetic Bearings

Active vibration control of flexible rotors supported by magnetic bearings is discussed. Using a finite-element method for a mathematical model of the flexible rotor, the eigenvalue problem is formulated taking into account the interaction between a mechanical system of the flexible rotor and an electrical system of the magnetic bearings and the controller. However, for the sake of simplicity, gyroscopic effects are disregarded. It is possible to adapt this formulation to a general flexible rotor-magnetic bearing system. Controllability with and without collocation sensors and actuators located at the same distance along the rotor axis is discussed for the higher order flexible modes of the test rig. In conclusion, it is proposed that it is necessary to add new active control loops for the higher flexible modes even in the case of collocation. Then it is possible to stabilize for the case of uncollocation by means of this method.

Nonami, Kenzou↗

NASA NTRS1993

NASA Langley developments in response calculations needed for failure and life prediction

NASA Langley developments in response calculations needed for failure and life predictions are discussed. Topics covered include: structural failure analysis in concurrent engineering; accuracy of independent regional modeling demonstrated on classical example; functional interface method accurately joins incompatible finite element models; interface method for insertion of local detail modeling extended to curve pressurized fuselage window panel; interface concept for joining structural regions; motivation for coupled 2D-3D analysis; compression panel with discontinuous stiffener coupled 2D-3D model and axial surface strains at the middle of the hat stiffener; use of adaptive refinement with multiple methods; adaptive mesh refinement; and studies on quantity effect of bow-type initial imperfections on reliability of stiffened panels.

Housner, Jerrold M.↗

NASA NTRS2021

Efficiency of Mixed-Element USM3D for Benchmark Three-Dimensional Flows

The unstructured, mixed-element, cell-centered, finite-volume flow solver USM3D is enhanced with new capabilities such as line generation for general unstructured grids and optimization of the iterative solver. The efficiency of the new developments is assessed in a massively parallel environment. The assessments are conducted using a baseline method and the recent hierarchical adaptive nonlinear iteration method framework. Three benchmark turbulent flows, namely, a subsonic separated flow around a three-dimensional hemisphere cylinder configuration, a transonic flow around the ONERA M6 wing, and a supersonic flow through a square duct are considered.

Mohagna J Pandya↗

DOE OSTI2013

Adaptive scapula bone remodeling computational simulation: Relevance to regenerative medicine

Shoulder arthroplasty success has been attributed to many factors including, bone quality, soft tissue balancing, surgeon experience, and implant design. Improved long-term success is primarily limited by glenoid implant loosening. Prosthesis design examines materials and shape and determines whether the design should withstand a lifetime of use. Finite element (FE) analyses have been extensively used to study stresses and strains produced in implants and bone. However, these static analyses only measure a moment in time and not the adaptive response to the altered environment produced by the therapeutic intervention. Computational analyses that integrate remodeling rules predict how bone will respond over time. Recent work has shown that subject-specific two- and three dimensional adaptive bone remodeling models are feasible and valid. Feasibility and validation were achieved computationally, simulating bone remodeling using an intact human scapula, initially resetting the scapular bone material properties to be uniform, numerically simulating sequential loading, and comparing the bone remodeling simulation results to the actual scapula’s material properties. Three-dimensional scapula FE bone model was created using volumetric computed tomography images. Muscle and joint load and boundary conditions were applied based on values reported in the literature. Internal bone remodeling was based on element strain-energy density. Initially, all bone elements were assigned a homogeneous density. All loads were applied for 10 iterations. After every iteration, each bone element’s remodeling stimulus was compared to its corresponding reference stimulus and its material properties modified. The simulation achieved convergence. At the end of the simulation the predicted and actual specimen bone apparent density were plotted and compared. Location of high and low predicted bone density was comparable to the actual specimen. High predicted bone density was greater than actual specimen. Low predicted bone density was lower than actual specimen. Differences were probably due to applied muscle and joint reaction loads, boundary conditions, and values of constants used. Work is underway to study this. Nonetheless, the results demonstrate three dimensional bone remodeling simulation validity and potential. Such adaptive predictions take physiological bone remodeling simulations one step closer to reality. Computational analyses are needed that integrate biological remodeling rules and predict how bone will respond over time. We expect the combination of computational static stress analyses together with adaptive bone remodeling simulations to become effective tools for regenerative medicine research.

60 APPLIED LIFE SCIENCES↗

NASA NTRS2015

Aeroelastic Airworthiness Assesment of the Adaptive Compliant Trailing Edge Flaps

The Adaptive Compliant Trailing Edge (ACTE) demonstrator is a joint task under the National Aeronautics and Space Administration Environmentally Responsible Aviation Project in partnership with the Air Force Research Laboratory and FlexSys, Inc. (Ann Arbor, Michigan). The project goal is to develop advanced technologies that enable environmentally friendly aircraft, such as adaptive compliant technologies. The ACTE demonstrator flight-test program encompassed replacing the Fowler flaps on the SubsoniC Aircraft Testbed, a modified Gulfstream III (Gulfstream Aerospace, Savannah, Georgia) aircraft, with control surfaces developed by FlexSys. The control surfaces developed by FlexSys are a pair of uniquely-designed unconventional flaps to be used as lifting surfaces during flight-testing to validate their structural effectiveness. The unconventional flaps required a multidisciplinary airworthiness assessment to prove they could withstand the prescribed flight envelope. Several challenges were posed due to the large deflections experienced by the structure, requiring non-linear analysis methods. The aeroelastic assessment necessitated both conventional and extensive testing and analysis methods. A series of ground vibration tests (GVTs) were conducted to provide modal characteristics to validate and update finite element models (FEMs) used for the flutter analyses for a subset of the various flight configurations. Numerous FEMs were developed using data from FlexSys and the ground tests. The flap FEMs were then attached to the aircraft model to generate a combined FEM that could be analyzed for aeroelastic instabilities. The aeroelastic analysis results showed the combined system of aircraft and flaps were predicted to have the required flutter margin to successfully demonstrate the adaptive compliant technology. This paper documents the details of the aeroelastic airworthiness assessment described, including the ground testing and analyses, and subsequent flight-testing performed on the unconventional ACTE flaps.

aeroelasticity↗

NASA NTRS1988

Finite element Euler computations in three dimensions

A two-step explicit FEM solution algorithm for the three-dimensional compressible Euler and Navier-Stokes equations based on unstructured triangular and tetrahedral grids is described and demonstrated. The method represents an extension and refinement of the algorithms presented by Loehner et al. (1984 and 1985), Peraire et al. (1987), and Morgan et al. (1987). The formulation and numerical implementation are outlined; the mesh generation, data structures, and adaptive remeshing are explained; and results for a two-dimensional airfoil, a three-dimensional engine air intake, a B747 in landing configuration, and a generic fighter aircraft are presented in extensive graphics and discussed in detail.

Peraire, Jaime↗

NASA NTRS2006

Adapting Analysis Tools to Engine Externals Analysis

Market forces are driving industry to reproduce product cycle time (the time required to conceive, design, build, test, validate and deliver a product). Application of existing tools in new areas can reduce the time required to design a new product and increase the confidence of acceptable test results later in the expensive testing and validation phase. Finite element methods, computational fluid dynamics codes and sharing of CAD datasets when applied to the design of engine externals can provide methods for product improvement and expedited delivery to the customer.

Dunkelberg, Ken↗

NASA NTRS1994

FRANC2D: A two-dimensional crack propagation simulator. Version 2.7: User's guide

FRANC 2D (FRacture ANalysis Code, 2 Dimensions) is a menu driven, interactive finite element computer code that performs fracture mechanics analyses of 2-D structures. The code has an automatic mesh generator for triangular and quadrilateral elements. FRANC2D calculates the stress intensity factor using linear elastic fracture mechanics and evaluates crack extension using several methods that may be selected by the user. The code features a mesh refinement and adaptive mesh generation capability that is automatically developed according to the predicted crack extension direction and length. The code also has unique features that permit the analysis of layered structure with load transfer through simulated mechanical fasteners or bonded joints. The code was written for UNIX workstations with X-windows graphics and may be executed on the following computers: DEC DecStation 3000 and 5000 series, IBM RS/6000 series, Hewlitt-Packard 9000/700 series, SUN Sparc stations, and most Silicon Graphics models.

Wawrzynek, Paul↗