Results for “VARIABLE GEOMETRY STRUCTURE” — Page 21

DOE OSTI2020

Tunable mechanical behavior of graphene nanoribbon-metal composites fabricated through an electrocharge-assisted process

This work investigates the role of a carbon nanophase on the local mechanical behavior of nanocarbon metal matrix composites (NCMCs) produced through an electrocharge-assisted process. Nanoindentation experiments on single crystal Al, Al 1350 parent alloys, and Al 1350 NCMCs revealed variable mechanical properties, caused by an interplay between microstructure and graphitic reinforcements. TEM and AFM studies also reveal nanoscale structural changes based on the incorporation of a carbon nanophase. In order to decouple the effects of the aforementioned mechanical behaviors, molecular dynamics nanoindentation simulations were performed on the (111) surface of Al and Al NCMC samples containing semi-infinite graphene nanoribbons to examine the evolution of plasticity over time. Findings indicate that the arrangement of a finite graphene nanophase within a host matrix can alter plasticity mechanisms and therefore yield strength in near-surface mechanical behavior with little effect on elastic properties. Here, this understanding enables further study into tunable bulk properties of Al-based NCMCs while isolating microstructural effects and reinforcement effects of the carbon phase. Such an understanding will lead to application-specific material geometries ranging from highperforming vehicle structures to next-generation electrical devices.

36 MATERIALS SCIENCE↗

NASA NTRS1986

Definition and empirical structure of the range of stellar chromospheres-coronae across the H-R diagram: Cool stars

Major advances in our understanding of non-radiative heating and other activity in stars cooler than T sub eff = 10,000K has occured in the last few years. This observational evidence is reviewed and the trends that are now becoming apparent are discussed. The evidence for non-radiatively heated outer atmospheric layers (chromospheres, transition regions, and coronae) in dwarf stars cooler than spectral type A7, in F and G giants, pre-main sequence stars, and close bindary systems is unambiguous, as is the evidence for chromospheres in the K and M giants and supergiants. The existence of non-radiative heating in the outer layers of the A stars remains undetermined despite repeated searches at all wavelengths. Two important trends in the data are the decrease in plasma emission measure with age on the main sequence and decreasing rotational velocity. Variability and atmospheric inhomogeneity are commonly seen, and there is considerable evidence that magnetic fields define the geometry and control the energy balance in the outer atmospheric layers. In addition, the microwave observations imply that non-thermal electrons are confined in coronal magnetic flux tubes in at least the cool dwarfs and RS CVn systems. The chromospheres in the K and M giants and supergiants are geometrically extended, as are the coronae in the RS CVn systems and probably also in other stars.

Linsky, J. L.↗

NASA NTRS2013

Next Generation Lightweight Mirror Modeling Software

The advances in manufacturing techniques for lightweight mirrors, such as EXELSIS deep core low temperature fusion, Corning's continued improvements in the Frit bonding process and the ability to cast large complex designs, combined with water-jet and conventional diamond machining of glasses and ceramics has created the need for more efficient means of generating finite element models of these structures. Traditional methods of assembling 400,000 + element models can take weeks of effort, severely limiting the range of possible optimization variables. This paper will introduce model generation software developed under NASA sponsorship for the design of both terrestrial and space based mirrors. The software deals with any current mirror manufacturing technique, single substrates, multiple arrays of substrates, as well as the ability to merge submodels into a single large model. The modeler generates both mirror and suspension system elements, suspensions can be created either for each individual petal or the whole mirror. A typical model generation of 250,000 nodes and 450,000 elements only takes 5-10 minutes, much of that time being variable input time. The program can create input decks for ANSYS, ABAQUS and NASTRAN. An archive/retrieval system permits creation of complete trade studies, varying cell size, depth, and petal size, suspension geometry with the ability to recall a particular set of parameters and make small or large changes with ease. The input decks created by the modeler are text files which can be modified by any editor, all the key shell thickness parameters are accessible and comments in deck identify which groups of elements are associated with these parameters. This again makes optimization easier. With ANSYS decks, the nodes representing support attachments are grouped into components; in ABAQUS these are SETS and in NASTRAN as GRIDPOINT SETS, this make integration of these models into large telescope or satellite models possible.

Arnold, William↗

NASA NTRS2013

Next-Generation Lightweight Mirror Modeling Software

The advances in manufacturing techniques for lightweight mirrors, such as EXELSIS deep core low temperature fusion, Corning's continued improvements in the Frit bonding process and the ability to cast large complex designs, combined with water-jet and conventional diamond machining of glasses and ceramics has created the need for more efficient means of generating finite element models of these structures. Traditional methods of assembling 400,000 + element models can take weeks of effort, severely limiting the range of possible optimization variables. This paper will introduce model generation software developed under NASA sponsorship for the design of both terrestrial and space based mirrors. The software deals with any current mirror manufacturing technique, single substrates, multiple arrays of substrates, as well as the ability to merge submodels into a single large model. The modeler generates both mirror and suspension system elements, suspensions can be created either for each individual petal or the whole mirror. A typical model generation of 250,000 nodes and 450,000 elements only takes 5-10 minutes, much of that time being variable input time. The program can create input decks for ANSYS, ABAQUS and NASTRAN. An archive/retrieval system permits creation of complete trade studies, varying cell size, depth, and petal size, suspension geometry with the ability to recall a particular set of parameters and make small or large changes with ease. The input decks created by the modeler are text files which can be modified by any editor, all the key shell thickness parameters are accessible and comments in deck identify which groups of elements are associated with these parameters. This again makes optimization easier. With ANSYS decks, the nodes representing support attachments are grouped into components; in ABAQUS these are SETS and in NASTRAN as GRIDPOINT SETS, this make integration of these models into large telescope or satellite models possible

Arnold, William R., Sr.↗

NASA NTRS2013

Next Generation Lightweight Mirror Modeling Software

The advances in manufacturing techniques for lightweight mirrors, such as EXELSIS deep core low temperature fusion, Corning's continued improvements in the Frit bonding process and the ability to cast large complex designs, combined with water-jet and conventional diamond machining of glasses and ceramics has created the need for more efficient means of generating finite element models of these structures. Traditional methods of assembling 400,000 + element models can take weeks of effort, severely limiting the range of possible optimization variables. This paper will introduce model generation software developed under NASA sponsorship for the design of both terrestrial and space based mirrors. The software deals with any current mirror manufacturing technique, single substrates, multiple arrays of substrates, as well as the ability to merge submodels into a single large model. The modeler generates both mirror and suspension system elements, suspensions can be created either for each individual petal or the whole mirror. A typical model generation of 250,000 nodes and 450,000 elements only takes 5-10 minutes, much of that time being variable input time. The program can create input decks for ANSYS, ABAQUS and NASTRAN. An archive/retrieval system permits creation of complete trade studies, varying cell size, depth, and petal size, suspension geometry with the ability to recall a particular set of parameters and make small or large changes with ease. The input decks created by the modeler are text files which can be modified by any editor, all the key shell thickness parameters are accessible and comments in deck identify which groups of elements are associated with these parameters. This again makes optimization easier. With ANSYS decks, the nodes representing support attachments are grouped into components; in ABAQUS these are SETS and in NASTRAN as GRIDPOINT SETS, this make integration of these models into large telescope or satellite models easier.

Arnold, William R., Sr.↗

NASA NTRS1987

Raman spectroscopic investigations of Hg-Cd-Te melts

Raman scattering measurements are reported for a series of Hg sub1-xCd subxTe (with x less than or =0.2) materials from 295 K (room temperature) to 1126K (up to and above their liquidus temperatures), and for Hg sub1-xCd subxTe (x=0.3) at 285K. The samples were contained in high-temperature optically-flat fused silica cell. Variable temperature measurements were effected in a three-zone, high-temperature furnace equipped with optical windows, and monitored externally by three independently programmable temperature controllers. All studies were made in the backscattering geometry using the 5145 A line of an Ar+ ion laser, with incident power less than 250 mW, as the excitiation source. An intensity enhancement is observed for a mode in each of the compositions studied. The frequency of this mode varies with composition, 142/cm for HgTe, and 128/cm for both the Hg sub1-xCd subxTe (x=0.053 and 0.204) samples. In addition, a shift to lower frequency as a function of temperature is observed in all samples. This shift is most prominent for the x=0.053 sample. The temperature dependence of these modes as the liquidus temperatures are achieved and surpassed for these samples is presented as being associated with a structural transition in the Hg-rich compositions of the Hg sub1-xCd subxTe series. To our knowledge, this is the first reported study of Raman scattering by phonons in the melts of these materials.

Morrobel-Sosa, Anny↗

NASA NTRS2021

Continuum, cyclotron line, and absorption variability in the high-mass X-ray binary Vela X-1

Because of its complex clumpy wind, prominent cyclotron resonant scattering features, intrinsic variability, and convenient physical parameters (close distance, high inclination, and small orbital separation), which facilitate the observation and analysis of the system, Vela X-1 is one of the key systems for understanding accretion processes in high-mass X-ray binaries on all scales. We revisit Vela X-1 with two new observations taken with NuSTAR at orbital phases ∼0.68–0.78 and ∼0.36–0.52, which show a plethora of variability and allow us to study the accretion geometry and stellar wind properties of the system. We follow the evolution of spectral parameters down to the pulse period timescale using a partially covered power law continuum with a Fermi-Dirac cutoff to model the continuum and local absorption. We are able to confirm anti-correlations between the photon index and the luminosity and, for low fluxes, between the folding energy and the luminosity, implying a change of properties in the Comptonising plasma. We were not able to confirm a previously seen correlation between the cyclotron line energy and the luminosity of the source in the overall observation, but we observed a drop in the cyclotron line energy following a strong flare. We see strong variability in absorption between the two observations and within one observation (for the ∼0.36–0.52 orbital phases) that can be explained by the presence of a large-scale structure, such as accretion and photoionisation wakes in the system, and our variable line of sight through this structure.

C. M. Diez↗

NASA NTRS1994

Spectral study of GX 339-4 in the low-intensity state observed with Ginga

The energy spectra of the black-hole candidate GX 339-4 in the low-intensity state were observed on four occasions through 1989 to 1991 with the Large Area Counter on board the Ginga satellite. The spectra showed significant deviations from a power-law, with an iron K(sub alpha) emission line at approximetaly 6.4 keV and a broad iron K-edge structure above approximately 7 keV. The enrgy spectra above approximately 4 keV were successfully explained with a reflection model, in which part of the incident X-rays with a power-law spectrum is Compton reflected by optically thick matter, resulting in a harder continuum component with iron K-edge absorption and an iron flourescent line. The line equivalent width with respect to the reflection component decreases as the source flux increases. This is consistent with an increase in the ionization state of the material, so that resonant absorption followed by Auger ionization depletes the line. The photon-index of the power-law component was clearly variable, and it correlated with the relative amount of the reflection component. Such a correlation may be explained in the context of the anisotropic Comptonization models of Haardt et al. (1993), or by a variation of the relative geometry of the source and disk.

Ueda, Yoshihiro↗

NASA NTRS1998

Studying Turbulence Using Numerical Simulation Databases: Proceedings of the Summer Program - No. 7

The Seventh Summer Program of the Center for Turbulence Research took place in the four-week period, July 5 to July 31, 1998. This was the largest CTR Summer Program to date, involving thirty-six participants from the U. S. and nine other countries. Thirty-one Stanford and NASA-Ames staff members facilitated and contributed to most of the Summer projects. A new feature, and perhaps a preview of the future programs, was that many of the projects were executed on non-NASA computers. These included supercomputers located in Europe as well as those operated by the Departments of Defense and Energy in the United States. In addition, several simulation programs developed by the visiting participants at their home institutions were used. Another new feature was the prevalence of lap-top personal computers which were used by several participants to carry out some of the work that in the past were performed on desk-top workstations. We expect these trends to continue as computing power is enhanced and as more researchers (many of whom CTR alumni) use numerical simulations to study turbulent flows. CTR's main role continues to be in providing a forum for the study of turbulence for engineering analysis and in facilitating intellectual exchange among the leading researchers in the field. Once again the combustion group was the largest. Turbulent combustion has enjoyed remarkable progress in using simulations to address increasingly complex and practically more relevant questions. The combustion group's studies included such challenging topics as fuel evaporation, soot chemistry, and thermonuclear reactions. The latter study was one of three projects related to the Department of Energy's ASCI Program (www.llnl.gov/asci); the other two (rocket propulsion and fire safety) were carried out in the turbulence modeling group. The flow control and acoustics group demonstrated a successful application of the so-called evolution algorithms which actually led to a previously unknown forcing strategy for jets yielding increased spreading rate. A very efficient algorithm for flow in complex geometries with moving boundaries based on the immersed boundary forcing technique was tested with very encouraging results. Also a new strategy for the destruction of aircraft trailing vortices was introduced and tested. The Reynolds Averaged Modeling (RANS) group demonstrated that the elliptic relaxation concept for RANS calculations is also applicable to transonic flows with shocks; however, prediction of laminar/turbulent transition remains an important pacing item. A large fraction of the LES effort was devoted to the development and testing of a new algorithmic procedure (as opposed to phenomenological model) for subgrid scale modeling based on regularized de-filtering of the flow variables. This appears to be a very promising approach, and a significant effort is currently underway to assess its robustness in high Reynolds number flows and in conjunction with numerical methods for complex flows. As part of the Summer Program two review tutorials were given on Turbulent structures in hydrocarbon pool fires (Sheldon Tieszen), and Turbulent combustion modeling: from RANS to LES via DNS (Luc Vervisch); and two seminars entitled Assessment of turbulence models for engineering applications (Paul Durbin) and Subgrid-scale modeling for non-premixed, turbulent reacting flows (James Riley) were presented. A number of colleagues from universities, government agencies, and industry attended the final presentations of the participants on July 31 and participated in the discussions. There are twenty-six papers in this volume grouped in five areas. Each group is preceded with an overview by its coordinator.

Source record↗

DOE OSTI2025

Remote sensing images, DEM, and point clouds associated with “Accuracy evaluation of cost-effective 3D reconstruction approaches for hydrobiogeochemical processes in non-perennial stream riverbeds”

This data package is associated with the publication “Accuracy evaluation of cost-effective 3D reconstruction approaches for hydrobiogeochemical processes in non-perennial stream riverbeds” published in Frontiers in Environmental Science, Environmental Informatics and Remote Sensing (Bao et al., 2026; doi: 10.3389/fenvs.2026.1725258). This data package includes the drone photos for a section of Umtanum Creek in Washington, Unted States. The photos were used to reconstruct the 3-dimensional (3D) digital elevation model (DEM) of the riverbed for the investigated stream section. The reconstruction results from four approaches are provided: (1) unoccupied aerial vehicle (UAV, colloquially known as drone) imagery-based Structure-from-Motion (SfM), (2) a machine learning-based 3D reconstruction model, Visual Geometry Grounded Deep Structure from Motion (VGGSfM), (3) Visual Geometry Grounded Transformer for long sequence of images (VGGT-Long), and (4) handheld smartphone LiDAR scanning. The ground truth measurements by tripod-mounted optical level kit and ground control points GPS locations for evaluating the accuracy of the four reconstruction approaches are also provided in this data package. A preliminary version of this data package was published in October 2025 at the time of manuscript submission. It was updated in March 2026, at the time of manuscript acceptance, to include additional metadata (this readme, data dictionary, and file level metadata). The data did not change. For details on how to navigate data packages generated by this project, see https://data.ess-dive.lbl.gov/portals/PNNLRiverCorridorSFA/About. In addition to a readme, this data package also includes a file-level metadata (FLMD) file that describes each file and a data dictionary (DD) that describes all column/row headers and variable definitions. This dataset is comprised of (1) 8 folders; (2) the detailed flight configuration html files; (3) field metadata; (4) a readme; (5) a data dictionary; and (6) file-level metadata. The folders “2024_10_18_d01” and “2024_10_18_d02” contain the original drone photos for the two drone flights (d01 and d02) on October 18, 2024. The reconstruction results from each of the approaches are in the folders called “ODM_SfM”, “VGGSfM”, “VGGTLong”, and “LiDAR”. The ground truth measurements are in the folder called “optical_level_kit”. Lastly, results comparing the different approaches are in the folder called “comparisons”. All files are .csv, .html, .jpg, .obj, .txt, and .npy. For information on using the .obj and .npy files, see the readme files within the same folder as the files.

54 ENVIRONMENTAL SCIENCES↗

NASA NTRS2006

Metallurgical Mechanisms Controlling Mechanical Properties of Aluminum Alloy 2219 Produced By Electron Beam Freeform Fabrication

The electron beam freeform fabrication (EBF3) layer-additive manufacturing process has been developed to directly fabricate complex geometry components. EBF3 introduces metal wire into a molten pool created on the surface of a substrate by a focused electron beam. Part geometry is achieved by translating the substrate with respect to the beam to build the part one layer at a time. Tensile properties have been demonstrated for electron beam deposited aluminum and titanium alloys that are comparable to wrought products, although the microstructures of the deposits exhibit features more typical of cast material. Understanding the metallurgical mechanisms controlling mechanical properties is essential to maximizing application of the EBF3 process. In the current study, mechanical properties and resulting microstructures were examined for aluminum alloy 2219 fabricated over a range of EBF3 process variables. Material performance was evaluated based on tensile properties and results were compared with properties of Al 2219 wrought products. Unique microstructures were observed within the deposited layers and at interlayer boundaries, which varied within the deposit height due to microstructural evolution associated with the complex thermal history experienced during subsequent layer deposition. Microstructures exhibited irregularly shaped grains, typically with interior dendritic structures, which were described based on overall grain size, morphology, distribution, and dendrite spacing, and were correlated with deposition parameters. Fracture features were compared with microstructural elements to define fracture paths and aid in definition of basic processing-microstructure-property correlations.

Domack, Marcia S.↗

DOE OSTI2022

Computational Study of Variable Fuel-Air Ratio and Hydrogen Doping in a Rotating Detonation Engine

Rotating detonation engines (RDEs) hold great promise as a technology for powering aviation engines. The pressure gain that results from continuously traversing detonation waves enables high theoretical performance compared to deflagration-based combustion. However, the harsh operating conditions inside an RDE restrict the availability of suitable experimental diagnostics to study these systems in detail and the range of spatial and temporal scales render numerical simulations of these systems difficult. In this study, we have combined adaptive mesh refinement and a robust shock-capturing approach to study RDE systems computationally using the compressible, reactive solver PeleC. Multi-species transport along with compressible Navier-Stokes equations are solved in the model along with finite-rate chemistry. Complex geometries are represented using an embedded boundary method with second-order spatial accuracy and the system is evolved in time using a second-order Runge-Kutta method. We present studies of a methane-air RDE system that is doped with varying levels of hydrogen. Our analysis focusses on how fuel mixture and doping levels effect the detonation flame structure and the generation of multiple wave modes.

ADVANCED PROPULSION SYSTEMS↗

NASA NTRS2001

The Plasma Wave Environment of Europa

The Galileo spacecraft has executed nine close flybys of Jupiter's moon Europa for which plasma wave observations were obtained. This paper presents an analysis of the observations from these flybys taking into consideration the variable geometry of the trajectories in an attempt to characterize the general plasma-wave environment associated with the interaction of the Jovian magnetosphere with the moon. A wide variety of plasma-wave phenomena are found to be associated with this interaction. While there are apparently temporal variations which complicate the analysis, a crude model of the distribution of these phenomena around Europa is derived. Primarily on the upstream side of Europa, and working inward to the moon, electron-cyclotron harmonics are first observed, followed by a region within about two Europa radii of the moon with whistler-mode hiss or chorus, and culminating in a region closest to the moon where a band at the upper hybrid resonance frequency is sometimes enhanced over its ambient intensity. The wake region is approximately two Europa radii across and comprises a broadband, highly variable, and bursty electrostatic phenomenon. Upon closer inspection, these bursty emissions appear as solitary structures similar to those in Earth's auroral zone and plasma sheet boundary layer. In addition to the survey of wave phenomena in the vicinity of Europa, we provide density profiles derived primarily from the upper hybrid resonance frequency which is readily apparent throughout most of each of the flybys. Finally, we suggest that the whistler mode, electron cyclotron harmonic, and upper hybrid resonance emissions are driven by some combination of factors including variations in the magnetic field near Europa and the loss and production of plasma at Europa as a result of the interaction of the Jovian magnetosphere with the moon. By analogy with studies of the ion and electron holes and broadband electrostatic noise at Earth and Jupiter, we argue that the electrostatic solitary structures in the wake are associated with currents and beams coupling Europa to Jupiter's ionosphere.

Kurth, W. S.↗

NASA NTRS2021

Experimental Flight Validation of the Prandtl 1933 Bell Spanload

This report describes the validation of the 1933 Prandtl bell spanload. This spanload is the minimum induced drag of a wing for a given structural weight with properties that eliminate adverse yaw. Aircraft using the Prandtl bell spanload were flown and investigated. The results of this research show that many previously held assumptions should be rethought, and the creation of aircraft using the Prandtl bell spanload will require considerable new techniques. Part of this work centered on the use of inverse methods. The usual first-step approach to a computational fluids problem is to create a geometry of the aircraft. Once this geometry exists, the computational fluids solution has been solved; however, the problem of creating the geometry still exists. A very small segment of the computational fluids world has concentrated on inverse solutions. This design approach begins with an end result - the computational fluids solution; from this end result, the geometry is sought. A more generic inverse tool was desired that would allow for the design of wings - specifically Prandtl bell spanload wings. Such a tool has been developed and allows for variable taper, aspect ratio, sweep, airfoils, and design-lift coefficients; output from the tool results in twist distribution of wings.

Albion H. Bowers↗

NASA NTRS1992

Tension fracture of laminates for transport fuselage. Part 1: Material screening

Transport fuselage structures are designed to contain pressure following a large penetrating damage event. Applications of composites to fuselage structures require a database and supporting analysis on tension damage tolerance. Tests with 430 fracture specimens were used to accomplish the following: (1) identify critical material and laminate variables affecting notch sensitivity; (2) evaluate composite failure criteria; and (3) recommend a screening test method. Variables studied included fiber type, matrix toughness, lamination manufacturing process, and intraply hybridization. The laminates found to have the lowest notch sensitivity were manufactured using automated tow placement. This suggests a possible relationship between the stress distribution and repeatable levels of material inhomogeneity that are larger than found in traditional tape laminates. Laminates with the highest notch sensitivity consisted of toughened matrix materials that were resistant to a splitting phenomena that reduces stress concentrations in major load bearing plies. Parameters for conventional fracture criteria were found to increase with crack length for the smallest notch sizes studied. Most material and laminate combinations followed less than a square root singularity for the largest crack sizes studied. Specimen geometry, notch type, and notch size were evaluated in developing a screening test procedure. Traitional methods of correcting for specimen finite width were found to be lacking. Results indicate that a range of notch sizes must be tested to determine notch sensitivity. Data for a single small notch size (0.25 in. diameter) was found to give no indication of the sensitivity of a particular material and laminate layup to larger notch sizes.

Walker, T. H.↗

NASA NTRS1992

Tension fracture of laminates for transport fuselage. Part 1: Material screening

Transport fuselage structures are designed to contain pressure following a large penetrating damage event. Application of composites to fuselage structures requires a data base and supporting analysis on tension damage tolerance. Tests with 430 fracture specimens were used to accomplish the following: (1) identify critical material and laminate variables affecting notch sensitivity, (2) evaluate composite failure criteria, and (3) recommend a screening test method. Variables studied included fiber type, matrix toughness, lamination manufacturing process, and intraply hybridization. The laminates found to have the lowest notch sensitivity were manufactured using automated tow placement. This suggests a possible relationship between the stress distribution and repeatable levels of material inhomogeneity that are larger than found in traditional tape laminates. Laminates with the highest notch sensitivity consisted of toughened matrix materials that were resistant to a splitting phenomena that reduces stress concentrations in load bearing plies. Parameters for conventional fracture criteria were found to increase with the crack length of the smallest notch sizes studied. Most materials and laminate combinations followed less than a square root singularity for the largest crack sizes studied. Specimen geometry, notch type, and notch size were evaluated in developing a screening test procedure. Results indicate that a range of notch sizes must be tested to determine notch sensitivity.

Walker, T. H.↗

NASA NTRS1994

Discrete-Layer Piezoelectric Plate and Shell Models for Active Tip-Clearance Control

The objectives of this work were to develop computational tools for the analysis of active-sensory composite structures with added or embedded piezoelectric layers. The targeted application for this class of smart composite laminates and the analytical development is the accomplishment of active tip-clearance control in turbomachinery components. Two distinct theories and analytical models were developed and explored under this contract: (1) a discrete-layer plate theory and corresponding computational models, and (2) a three dimensional general discrete-layer element generated in curvilinear coordinates for modeling laminated composite piezoelectric shells. Both models were developed from the complete electromechanical constitutive relations of piezoelectric materials, and incorporate both displacements and potentials as state variables. This report describes the development and results of these models. The discrete-layer theories imply that the displacement field and electrostatic potential through-the-thickness of the laminate are described over an individual layer rather than as a smeared function over the thickness of the entire plate or shell thickness. This is especially crucial for composites with embedded piezoelectric layers, as the actuating and sensing elements within these layers are poorly represented by effective or smeared properties. Linear Lagrange interpolation polynomials were used to describe the through-thickness laminate behavior. Both analytic and finite element approximations were used in the plane or surface of the structure. In this context, theoretical developments are presented for the discrete-layer plate theory, the discrete-layer shell theory, and the formulation of an exact solution for simply-supported piezoelectric plates. Finally, evaluations and results from a number of separate examples are presented for the static and dynamic analysis of the plate geometry. Comparisons between the different approaches are provided when possible, and initial conclusions regarding the accuracy and limitations of these models are given.

Heyliger, P. R.↗

NASA NTRS2003

Using Plate Finite Elements for Modeling Fillets in Design, Optimization, and Dynamic Analysis

A methodology has been developed that allows the use of plate elements instead of numerically inefficient solid elements for modeling structures with 90 degree fillets. The technique uses plate bridges with pseudo Young's modulus (Eb) and thickness (tb) values placed between the tangent points of the fillets. These parameters are obtained by solving two nonlinear simultaneous equations in terms of the independent variables rlt and twallt. These equations are generated by equating the rotation at the tangent point of a bridge system with that of a fillet, where both rotations are derived using beam theory. Accurate surface fits of the solutions are also presented to provide the user with closed-form equations for the parameters. The methodology was verified on the subcomponent level and with a representative filleted structure, where the technique yielded a plate model exhibiting a level of accuracy better than or equal to a high-fidelity solid model and with a 90-percent reduction in the number of DOFs. The application of this method for parametric design studies, optimization, and dynamic analysis should prove extremely beneficial for the finite element practitioner. Although the method does not attempt to produce accurate stresses in the filleted region, it can also be used to obtain stresses elsewhere in the structure for preliminary analysis. A future avenue of study is to extend the theory developed here to other fillet geometries, including fillet angles other than 90 and multifaceted intersections.

Brown, A. M.↗